Rasoul Shabani - Academia.edu (original) (raw)
Papers by Rasoul Shabani
Journal of ocean engineering and marine energy, Feb 2, 2024
International journal of engineering. Transactions A: basics, 2010
With the aim of extending the use of integrated variational principles on fluid and deck plate to... more With the aim of extending the use of integrated variational principles on fluid and deck plate to the large deflection analysis of floating roofs, this paper investigates the significance of the flexural and membrane components in the formulations of the deck plate. Applying integrated variational principles on deck plate and fluid facilitate the treatment of the compatibility of deformation between floating roof and supporting liquid. Analysis results showed that different assumptions about deck plate formulation were commonly used in the literature which resulted in considerably different deflection and stress patterns on the floating roof. The results showed that modeling of the deck plate as a flexural element rather than membrane, by eliminating the need for nonlinear analysis, gave reasonable results for deflections and stresses in the deck plate. Finally, a simple and efficient procedure using linear finite element code analyzes of the floating roofs, considering only the flexural stiffness was developed.
International Journal of Engineering, Jul 1, 2016
In this paper, the dynamic response of a micro-beam immersed in a fluid with regard to the free b... more In this paper, the dynamic response of a micro-beam immersed in a fluid with regard to the free boundary of the operating fluid is investigated. In the other words, in addition to the kinematic compatibility on the boundary between micro-beam and its surrounding fluid, equations of the potential functions are modeled considering the free boundaries. It is also assumed that the micro-beam is a movable electrode, and the electrostatic force is used for the actuation of the system. Galerkin's method is utilized to solve the governing equations of the fluid-structure system. By imposing a fixed voltage to the system, in addition to investigating the geometrical effects, fluid type and the dimensions of the cavity, the effect of the free boundaries on the transient response of the system is studied. It is shown that the coefficient of relative permittivity of operating fluid, the length of the micro-beam, and the relative position of it to the lower side of the cavity have significant impact on the instability of system voltage. It is further shown that assuming the free boundaries in the modeling of the system, which is closer to the physical reality of the issue, increases the pull-in voltage.
Applied Mathematical Modelling, 2016
Abstract Vibration of a beam has extensive applications in engineering and industry. The objectiv... more Abstract Vibration of a beam has extensive applications in engineering and industry. The objective of this article is to provide a novel analytical model by free boundary approach to derive a more exact model for the small oscillations of a cantilever microbeam in contact with an incompressible bounded fluid in a cavity. First, a system of integral equations is proposed to solve and interpret the problem. Then, the existence of the solution is proved by the use of the Banach fixed point theorem. At the end, an example is presented for verifying the proposed method and comparing the results with the fixed boundary approach.
Journal of Solid Mechanics, Dec 30, 2012
In this paper, the quality factor of thermo-elastic damping in an electro-statically deflected mi... more In this paper, the quality factor of thermo-elastic damping in an electro-statically deflected micro-beam resonator has been investigated. The thermo-elastic coupled equations for the deflected micro-beam have been derived using variational and Hamilton principles based on modified couple stress theory and hyperbolic heat conduction model. The thermo-elastic damping has been obtained discretizing the governing equations over spatial domain and applying complex frequency approach. The effects of the applied bias DC voltage, playing simultaneously role of an external force and softening parameter, on the quality factor have been studied. The obtained results of the modified couple stress and classic theories are compared and the effects of the material internal length-scale parameter on the differences between results of two theories have been discussed. In addition, the effects of different parameters such as beam length and ambient temperature on the quality factor have been studied.
Meccanica, Sep 12, 2012
Abstract In this article stability and parametrically excited oscillations of a two stage micro-s... more Abstract In this article stability and parametrically excited oscillations of a two stage micro-shaft located in a Newtonian fluid with arrayed electrostatic actuation system is investigated. The static stability of the system is studied and the fixed points of the micro-shaft are ...
International journal of engineering. Transactions C: Aspects, Dec 1, 2017
This paper investigates the parametric excitation of a micro-pipe conveying fluid suspended betwe... more This paper investigates the parametric excitation of a micro-pipe conveying fluid suspended between two symmetric electrodes. Electrostatically actuated micro-pipes may become unstable when the exciting voltage is greater than the pull-in value. It is demonstrated that the parametric excitation of a micro-pipe by periodic (ac) voltages may have a stabilizing effect and permit an increase of the steady (dc) component of the actuation voltage beyond the pull-in value. Mathieu type equation of the system is obtained by applying Taylor series expansion and Galerkin method to the nonlinear partial differential equation of motion. Floquet theory is used to extract the transition curves and stability margins in physical parameters space (Vdc-Vac). In addition, the stability margins are plotted in flow velocity and excitation amplitude space (u-Vac space). The results depict that the micro-pipe remains stable even if the flow velocity is more than the critical value for a certain dc voltage. For instance, in absence of the (ac) component, it is shown that pull-in voltages associated to critical velocities 3 and 6 are 14.06 and 5.4 volt, respectively. However, transition curves show that superimposing an (ac) component with forcing frequency Ω=10 increases the pull-in voltage beyond these values. Furthermore, for the present pull-in voltages the critical velocities 3 and 6 could be increases with imposing some (ac) component. These results are discussed in detail in simulation results section where the transion curves are ploted quantitatively.
International Journal of Engineering, 2015
In this paper, the experimental vibration analysis of a single cylinder air compressor based on a... more In this paper, the experimental vibration analysis of a single cylinder air compressor based on a hypocycloid straight line mechanism (HSM) is investigated. The HSM mechanism uses planetary gears to convert rotational motion to purely linear motion. In the conventional air compressor, the slidercrank mechanism is replaced by the HSM mechanism with appropriate counterweights. The constructed setup is fixed over a base plate supported by an elastic foundation and is driven by a speedcontrolled electric motor. During the experiments, the driving frequency is varied and the vibrations of the base plate due to unbalanced forces are recorded in three directions. The results are compared with the experimental results of a compressor based on the conventional slider-crank mechanism. Time and frequency domain analyses indicated that the mechanism can be balanced effectively, and the shaking force and induced vibrations can be significantly suppressed.
International Journal of Engineering, 2014
In the design of high Quality factor (Q) micro or nano beam resonators, different dissipation mec... more In the design of high Quality factor (Q) micro or nano beam resonators, different dissipation mechanisms may have damaging effects on the quality factor. One of the major dissipation mechanisms is the thermoelastic damping (TED) that needs an accurate consideration for prediction. In this paper, thermoelastic damping of the longitudinal vibration of a homogeneous micro beam with both ends clamped have been investigated. A Galerkin method has been used to analyze thermoelastic damping for the first mode of vibration of the micro beam. Then the quality factor and longitudinal vibrations frequency are obtained. Changing of Quality factor versus geometrical properties and ambient temperature for different materials are plotted.
Journal of Solid Mechanics, Mar 30, 2012
The paper deals with the mechanical behavior of a micro-beam bonded with two piezoelectric layers... more The paper deals with the mechanical behavior of a micro-beam bonded with two piezoelectric layers. The micro-beam is suspended over a fixed substrate and undergoes the both piezoelectric and electrostatic actuation. The piezoelectric layers are poled through the thickness and equipped with surface electrodes. The equation governing the micro-beam deflection under electrostatic pressure is derived according to Euler-Bernoulli beam theory and considering the voltage applied to the piezoelectric layers and Maxwell's equations for the two dimensional electric potential distribution. The obtained nonlinear equation solved by step by step linearization method and Galerkin weighted residual method. The effects of the electric potential distribution and the ratio of the piezoelectric layer thickness respect to the elastic layer thickness on the mechanical behavior of the micro-beam are investigated. The obtained results are compared with the results of a model in which electric potential distribution is not considered.
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, May 26, 2021
Recently, hydraulic engine mounts have been used widely as an effective vibration isolator in aut... more Recently, hydraulic engine mounts have been used widely as an effective vibration isolator in automotive engines. They consist of two fluid chambers connected by an inertia track path and a decoupler mechanism with a floating plate. An ideal hydraulic mount should have high stiffness and damping at low frequencies and at high frequencies should act as a good isolator. Despite their acceptable performance, there are some drawbacks including switching, nonlinear behavior of the decoupler plate at low frequencies, and occurrence of the resonance due to the passage of the fluid through the decoupler in the high-frequency range. This paper proposes a new decoupler mechanism where the floating decoupler plate is replaced with a membrane where its tension could be controlled considering the operational frequency. Considering the discrete model of the operating fluid and the continuous model of the membrane, governing equations of the system are derived. By increasing the membrane tension at low frequencies, it is shown that the desired dynamic stiffness and damping can be achieved and the nonlinear switching behavior is eliminated. At the same time, by decreasing the membrane tension at high frequencies, it is shown that there is a significant increase in system compliance, resulting in better isolation. Results also show that the membrane replacement also eliminates the fluid resonances at high frequencies. Finally, the two-objective optimization method of the genetic algorithm is employed to find the optimal values of the membrane tension and the mount parameters. The results show that the proposed mechanism can be used as a suitable alternative to the conventional hydraulic mounts.
Microsystem Technologies-micro-and Nanosystems-information Storage and Processing Systems, Jan 2, 2019
In the present research, stability and static analyses of microelectromechanical systems microstr... more In the present research, stability and static analyses of microelectromechanical systems microstructure were investigated by presenting an out-of-plane structure for a lumped mass. The presented model consists of two stationary electrodes in the same plane along with a flexible electrode above and in the middle of the two electrodes. The nonlinear electrostatic force was valuated via numerical methods implemented in COMSOL software where three-dimensional simulations were performed for different gaps. The obtained numerical results were compared to those of previous research works, indicating a good agreement. Continuing with the research, curves of electrostatic and spring forces were demonstrated for different scenarios, with the intersection points (i.e., equilibrium points) further plotted. Also drawn were plots of deflection versus voltage for different cases and phase and time history curves for different values of applied voltage followed by introducing and explaining pull-in and pull-out snap-through voltages in the system for a specific design. It is worth noting that, at voltages between the pull-in and pull-out snap-through voltages, the system was in bi-stable state. Based on the obtained results, it was observed that the gap between the two electrodes and the applied voltage play significant roles in the number and type of the equilibrium points of the system.
International Journal of Engineering, Dec 1, 2012
This article deals with the mechanical analysis of a fixed-fixed nano-beam based on nonlocal theo... more This article deals with the mechanical analysis of a fixed-fixed nano-beam based on nonlocal theory of elasticity. The nano-beam is sandwiched with two piezoelectric layers through its upper and lower surfaces. The electromechanical coupled equations governing the problem are derived based on nonlocal theory of elasticity considering Euler-Bernoulli beam assumptions. Also, nonlocal piezoelectricity is according to Maxwell's electrostatic equations. The piezoelectric layers are subjected to a voltage to tune the stiffness of the nano-beam. The equations are solved through step by step linearization method and Galerkin's weighted residual method. The results are compared with those of the local model. The effect of piezoelectric voltages on the non-locality of the model is investigated as well.
International Journal of Applied Mechanics, Sep 1, 2018
This paper develops a theoretical model directed towards investigation of the static pull-in inst... more This paper develops a theoretical model directed towards investigation of the static pull-in instability of a functionally graded (FG) electrostatically actuated nano-bridge via nonlocal strain gradient theory (NLSGT) of elasticity and Euler–Bernoulli beam theory in thermal environment. The nano-beam is under the influence of electrostatic and van der Waals (vdW) forces. In addition to the nonlinear nature of the electrostatic force, the other type of nonlinearity namely geometric nonlinearity resulting from the mid-plane stretching is considered. Material properties of FG nano-beam are assumed to vary gradually along the thickness direction according to simple power-law form. With the purpose of eliminating the coupling between the stretching and bending due to the asymmetrical material variation along the thickness, a new surface reference is introduced. The nonlinear integro-differential governing equation is derived utilizing minimum total potential energy principle, linearized by means of the step-by-step linearization method (SSLM) and solved by Galerkin-based weighted residual method. The numerical investigations are performed while the emphasis is placed on studying the effect of various parameters including: nonlocal parameter, material characteristic length scale, material gradient index, thermal effect and intermolecular force on the static pull-in instability of FG nano-beam. To establish the validity of the present formulation, a comparison is conducted with experimental and numerical results reported in previous studies.
International Journal of Engineering, Mar 1, 2014
This paper addresses the static and dynamic stabilities of a parametrically excited torsional mic... more This paper addresses the static and dynamic stabilities of a parametrically excited torsional microactuator. The system is composed of a rectangular micro-mirror symmetrically suspended between two electrodes and acted upon by a steady (dc) while simultaneously superimposed to an (ac) voltage. First, the stability of the system subjected to a quasi-statically applied (dc) voltage is investigated, where the pull-in instability, equilibrium positions, and bifurcation points of the system are determined. Then by superimposing an (ac) voltage and extracting a Mathieu type governing equation the effects of (ac) component on the stability of the system is investigated. By varying excitation parameters (steady (dc) voltage and time-dependent amplitude of (ac) excitation), transition curves and the stability margins of the micro-mirror are demonstrated. Theoretically obtained margins are checked by means of numerical simulations. The results show that superimposing the harmonic (ac) component could have a stabilizing effect and allow an increase of the steady (dc) component beyond the pull-in value. These results could be used in design of micro-actuators.
Nonlinear Dynamics, Aug 23, 2018
Similar to elasticity and viscoelasticity, anelasticity is one of the rheological models of mater... more Similar to elasticity and viscoelasticity, anelasticity is one of the rheological models of materials. Like the viscoelastic materials, anelastic deformation is time dependent, while unlike viscoelasticity, it is full recoverable. Anelastic behavior is very sensitive to microstructure and is significant when things become small. In this paper, the nonlinear vibrations of an electrostatically actuated micro-beam made of anelastic material are studied based on the modified couple stress theory and considering compressible fluid media. The constitutive equation of micro-beams has been developed regarding the stress-strain behavior of classic anelastic materials. Considering the dependency of the effective viscosity on variable gap distance, an analytical model of an electrostatically actuated anelastic micro-beam has been developed through the variable Knudsen number. Then, multiple scales method has been applied to obtain an approximate analytical solution for nonlinear resonant curves. Additionally, the effects of different mechanical behaviors of materials including elasticity, viscoelasticity and anelasticity on the nonlinear dynamic response have been studied. Furthermore, influences of some effective parameters such as length scale, anelastic relaxation time, relaxation intensity, mid-plane stretching force, residual axial force, air-gap pressure and compressible fluid media on the nonlinear vibration analysis have been
International Journal of Engineering, Dec 1, 2012
In this article, thermo-elastic damping in nano-beam resonators is investigated based on nonlocal... more In this article, thermo-elastic damping in nano-beam resonators is investigated based on nonlocal theory of elasticity and the Euler-Bernoulli beam assumptions. To this end, governing equation of motion of the beam is obtained from stress-strain relationship of the nonlocal elasticity model and also governing equations of thermo-elastic damping are established using two dimensional non-Fourier heat conduction. Free vibration of the nano-beam resonators is analyzed using Galerkin reduced order model formulation for the first mode of vibration. In the present investigation a clamped-clamped nano-beam with isothermal boundary conditions at both ends is studied. This nonlocal model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect. The obtained results are compared with the numerical results of the classical thermo-elastic models. Thermo-elastic damping effects on the damping ratio are studied for the various nano-beam thicknesses and ambient temperatures. In addition, the study includes computations for different values of nonlocal theory parameter. The results show that with increasing the amount of nonlocal parameter and also with decreasing the length of the nano-beam, difference between the results of classical and nonlocal theory increases.
Nonlinear Dynamics, Nov 8, 2016
The present study investigates the nonlinear size-dependent behavior of micro-doubly curved shall... more The present study investigates the nonlinear size-dependent behavior of micro-doubly curved shallow shells based on the modified couple stress theory. Assuming von-Karman geometric nonlinearity and the first-order shear deformation theory, the governing equations of the system are derived using variational approach. The governing equations are reduced using the Galerkin method to a system of finite nonlinear ordinary differential equations. Multiple scales method is used to obtain an approximate analytical solution for nonlinear frequency response. Effect of the length scale parameter as well as the shell curvature on the frequency curves is addressed. It is shown that increasing the length scale parameter changes the softening behavior to a hardening one. On the shell curvature plane, it is depicted that for some values of the length scale parameter the system displays totally a hardening behavior. Influence of the length scale on the effective nonlinearity is discussed. It is found that in a flat shell the effective nonlinearity did not change significantly, while the variations are considerable for saddle shells. It is also shown that variation in the shell dimensions for spherical shells had significant effect on the frequency response, while this is not the case for hyperbolic paraboloidal shells. Finally, examining the effects of the damping on the nonlinear dynamics of the system shows wider response region for decreasing damping.
Measurement, Dec 1, 2013
ABSTRACT In the present article, a perceptive capacitive sensor for measuring angular speed of a ... more ABSTRACT In the present article, a perceptive capacitive sensor for measuring angular speed of a rotating shaft is proposed. The proposed sensor is capable of measuring rotating shaft angular speed, and its changes. The proposed model's sensing part is a suspended clamped-clamped micro-beam, which is parallel with two fixed substrates from the upper and lower sides through the micro-beam's width surface. An electric circuit is used to give out capacitance change as a result of angular speed change, in output voltage. The micro-beam undergoes non-linear electro-static pressure that is induced due to the applied bias DC voltage. The suggested sensor has high sensitivity for a large range of working machines rotating parts angular speed measurement. The governing nonlinear partial differential equation of the transversal motion of the beam is derived and solved by step by step linearization (SSLM) and Galerkin weighted residual methods and the stable region of the sensor is determined. The effects of the applied bias voltage and geometrical properties of the micro-beam on the sensitivity and the range of the measurable angular speed of the sensor are discussed.
Journal of ocean engineering and marine energy, Feb 2, 2024
International journal of engineering. Transactions A: basics, 2010
With the aim of extending the use of integrated variational principles on fluid and deck plate to... more With the aim of extending the use of integrated variational principles on fluid and deck plate to the large deflection analysis of floating roofs, this paper investigates the significance of the flexural and membrane components in the formulations of the deck plate. Applying integrated variational principles on deck plate and fluid facilitate the treatment of the compatibility of deformation between floating roof and supporting liquid. Analysis results showed that different assumptions about deck plate formulation were commonly used in the literature which resulted in considerably different deflection and stress patterns on the floating roof. The results showed that modeling of the deck plate as a flexural element rather than membrane, by eliminating the need for nonlinear analysis, gave reasonable results for deflections and stresses in the deck plate. Finally, a simple and efficient procedure using linear finite element code analyzes of the floating roofs, considering only the flexural stiffness was developed.
International Journal of Engineering, Jul 1, 2016
In this paper, the dynamic response of a micro-beam immersed in a fluid with regard to the free b... more In this paper, the dynamic response of a micro-beam immersed in a fluid with regard to the free boundary of the operating fluid is investigated. In the other words, in addition to the kinematic compatibility on the boundary between micro-beam and its surrounding fluid, equations of the potential functions are modeled considering the free boundaries. It is also assumed that the micro-beam is a movable electrode, and the electrostatic force is used for the actuation of the system. Galerkin's method is utilized to solve the governing equations of the fluid-structure system. By imposing a fixed voltage to the system, in addition to investigating the geometrical effects, fluid type and the dimensions of the cavity, the effect of the free boundaries on the transient response of the system is studied. It is shown that the coefficient of relative permittivity of operating fluid, the length of the micro-beam, and the relative position of it to the lower side of the cavity have significant impact on the instability of system voltage. It is further shown that assuming the free boundaries in the modeling of the system, which is closer to the physical reality of the issue, increases the pull-in voltage.
Applied Mathematical Modelling, 2016
Abstract Vibration of a beam has extensive applications in engineering and industry. The objectiv... more Abstract Vibration of a beam has extensive applications in engineering and industry. The objective of this article is to provide a novel analytical model by free boundary approach to derive a more exact model for the small oscillations of a cantilever microbeam in contact with an incompressible bounded fluid in a cavity. First, a system of integral equations is proposed to solve and interpret the problem. Then, the existence of the solution is proved by the use of the Banach fixed point theorem. At the end, an example is presented for verifying the proposed method and comparing the results with the fixed boundary approach.
Journal of Solid Mechanics, Dec 30, 2012
In this paper, the quality factor of thermo-elastic damping in an electro-statically deflected mi... more In this paper, the quality factor of thermo-elastic damping in an electro-statically deflected micro-beam resonator has been investigated. The thermo-elastic coupled equations for the deflected micro-beam have been derived using variational and Hamilton principles based on modified couple stress theory and hyperbolic heat conduction model. The thermo-elastic damping has been obtained discretizing the governing equations over spatial domain and applying complex frequency approach. The effects of the applied bias DC voltage, playing simultaneously role of an external force and softening parameter, on the quality factor have been studied. The obtained results of the modified couple stress and classic theories are compared and the effects of the material internal length-scale parameter on the differences between results of two theories have been discussed. In addition, the effects of different parameters such as beam length and ambient temperature on the quality factor have been studied.
Meccanica, Sep 12, 2012
Abstract In this article stability and parametrically excited oscillations of a two stage micro-s... more Abstract In this article stability and parametrically excited oscillations of a two stage micro-shaft located in a Newtonian fluid with arrayed electrostatic actuation system is investigated. The static stability of the system is studied and the fixed points of the micro-shaft are ...
International journal of engineering. Transactions C: Aspects, Dec 1, 2017
This paper investigates the parametric excitation of a micro-pipe conveying fluid suspended betwe... more This paper investigates the parametric excitation of a micro-pipe conveying fluid suspended between two symmetric electrodes. Electrostatically actuated micro-pipes may become unstable when the exciting voltage is greater than the pull-in value. It is demonstrated that the parametric excitation of a micro-pipe by periodic (ac) voltages may have a stabilizing effect and permit an increase of the steady (dc) component of the actuation voltage beyond the pull-in value. Mathieu type equation of the system is obtained by applying Taylor series expansion and Galerkin method to the nonlinear partial differential equation of motion. Floquet theory is used to extract the transition curves and stability margins in physical parameters space (Vdc-Vac). In addition, the stability margins are plotted in flow velocity and excitation amplitude space (u-Vac space). The results depict that the micro-pipe remains stable even if the flow velocity is more than the critical value for a certain dc voltage. For instance, in absence of the (ac) component, it is shown that pull-in voltages associated to critical velocities 3 and 6 are 14.06 and 5.4 volt, respectively. However, transition curves show that superimposing an (ac) component with forcing frequency Ω=10 increases the pull-in voltage beyond these values. Furthermore, for the present pull-in voltages the critical velocities 3 and 6 could be increases with imposing some (ac) component. These results are discussed in detail in simulation results section where the transion curves are ploted quantitatively.
International Journal of Engineering, 2015
In this paper, the experimental vibration analysis of a single cylinder air compressor based on a... more In this paper, the experimental vibration analysis of a single cylinder air compressor based on a hypocycloid straight line mechanism (HSM) is investigated. The HSM mechanism uses planetary gears to convert rotational motion to purely linear motion. In the conventional air compressor, the slidercrank mechanism is replaced by the HSM mechanism with appropriate counterweights. The constructed setup is fixed over a base plate supported by an elastic foundation and is driven by a speedcontrolled electric motor. During the experiments, the driving frequency is varied and the vibrations of the base plate due to unbalanced forces are recorded in three directions. The results are compared with the experimental results of a compressor based on the conventional slider-crank mechanism. Time and frequency domain analyses indicated that the mechanism can be balanced effectively, and the shaking force and induced vibrations can be significantly suppressed.
International Journal of Engineering, 2014
In the design of high Quality factor (Q) micro or nano beam resonators, different dissipation mec... more In the design of high Quality factor (Q) micro or nano beam resonators, different dissipation mechanisms may have damaging effects on the quality factor. One of the major dissipation mechanisms is the thermoelastic damping (TED) that needs an accurate consideration for prediction. In this paper, thermoelastic damping of the longitudinal vibration of a homogeneous micro beam with both ends clamped have been investigated. A Galerkin method has been used to analyze thermoelastic damping for the first mode of vibration of the micro beam. Then the quality factor and longitudinal vibrations frequency are obtained. Changing of Quality factor versus geometrical properties and ambient temperature for different materials are plotted.
Journal of Solid Mechanics, Mar 30, 2012
The paper deals with the mechanical behavior of a micro-beam bonded with two piezoelectric layers... more The paper deals with the mechanical behavior of a micro-beam bonded with two piezoelectric layers. The micro-beam is suspended over a fixed substrate and undergoes the both piezoelectric and electrostatic actuation. The piezoelectric layers are poled through the thickness and equipped with surface electrodes. The equation governing the micro-beam deflection under electrostatic pressure is derived according to Euler-Bernoulli beam theory and considering the voltage applied to the piezoelectric layers and Maxwell's equations for the two dimensional electric potential distribution. The obtained nonlinear equation solved by step by step linearization method and Galerkin weighted residual method. The effects of the electric potential distribution and the ratio of the piezoelectric layer thickness respect to the elastic layer thickness on the mechanical behavior of the micro-beam are investigated. The obtained results are compared with the results of a model in which electric potential distribution is not considered.
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, May 26, 2021
Recently, hydraulic engine mounts have been used widely as an effective vibration isolator in aut... more Recently, hydraulic engine mounts have been used widely as an effective vibration isolator in automotive engines. They consist of two fluid chambers connected by an inertia track path and a decoupler mechanism with a floating plate. An ideal hydraulic mount should have high stiffness and damping at low frequencies and at high frequencies should act as a good isolator. Despite their acceptable performance, there are some drawbacks including switching, nonlinear behavior of the decoupler plate at low frequencies, and occurrence of the resonance due to the passage of the fluid through the decoupler in the high-frequency range. This paper proposes a new decoupler mechanism where the floating decoupler plate is replaced with a membrane where its tension could be controlled considering the operational frequency. Considering the discrete model of the operating fluid and the continuous model of the membrane, governing equations of the system are derived. By increasing the membrane tension at low frequencies, it is shown that the desired dynamic stiffness and damping can be achieved and the nonlinear switching behavior is eliminated. At the same time, by decreasing the membrane tension at high frequencies, it is shown that there is a significant increase in system compliance, resulting in better isolation. Results also show that the membrane replacement also eliminates the fluid resonances at high frequencies. Finally, the two-objective optimization method of the genetic algorithm is employed to find the optimal values of the membrane tension and the mount parameters. The results show that the proposed mechanism can be used as a suitable alternative to the conventional hydraulic mounts.
Microsystem Technologies-micro-and Nanosystems-information Storage and Processing Systems, Jan 2, 2019
In the present research, stability and static analyses of microelectromechanical systems microstr... more In the present research, stability and static analyses of microelectromechanical systems microstructure were investigated by presenting an out-of-plane structure for a lumped mass. The presented model consists of two stationary electrodes in the same plane along with a flexible electrode above and in the middle of the two electrodes. The nonlinear electrostatic force was valuated via numerical methods implemented in COMSOL software where three-dimensional simulations were performed for different gaps. The obtained numerical results were compared to those of previous research works, indicating a good agreement. Continuing with the research, curves of electrostatic and spring forces were demonstrated for different scenarios, with the intersection points (i.e., equilibrium points) further plotted. Also drawn were plots of deflection versus voltage for different cases and phase and time history curves for different values of applied voltage followed by introducing and explaining pull-in and pull-out snap-through voltages in the system for a specific design. It is worth noting that, at voltages between the pull-in and pull-out snap-through voltages, the system was in bi-stable state. Based on the obtained results, it was observed that the gap between the two electrodes and the applied voltage play significant roles in the number and type of the equilibrium points of the system.
International Journal of Engineering, Dec 1, 2012
This article deals with the mechanical analysis of a fixed-fixed nano-beam based on nonlocal theo... more This article deals with the mechanical analysis of a fixed-fixed nano-beam based on nonlocal theory of elasticity. The nano-beam is sandwiched with two piezoelectric layers through its upper and lower surfaces. The electromechanical coupled equations governing the problem are derived based on nonlocal theory of elasticity considering Euler-Bernoulli beam assumptions. Also, nonlocal piezoelectricity is according to Maxwell's electrostatic equations. The piezoelectric layers are subjected to a voltage to tune the stiffness of the nano-beam. The equations are solved through step by step linearization method and Galerkin's weighted residual method. The results are compared with those of the local model. The effect of piezoelectric voltages on the non-locality of the model is investigated as well.
International Journal of Applied Mechanics, Sep 1, 2018
This paper develops a theoretical model directed towards investigation of the static pull-in inst... more This paper develops a theoretical model directed towards investigation of the static pull-in instability of a functionally graded (FG) electrostatically actuated nano-bridge via nonlocal strain gradient theory (NLSGT) of elasticity and Euler–Bernoulli beam theory in thermal environment. The nano-beam is under the influence of electrostatic and van der Waals (vdW) forces. In addition to the nonlinear nature of the electrostatic force, the other type of nonlinearity namely geometric nonlinearity resulting from the mid-plane stretching is considered. Material properties of FG nano-beam are assumed to vary gradually along the thickness direction according to simple power-law form. With the purpose of eliminating the coupling between the stretching and bending due to the asymmetrical material variation along the thickness, a new surface reference is introduced. The nonlinear integro-differential governing equation is derived utilizing minimum total potential energy principle, linearized by means of the step-by-step linearization method (SSLM) and solved by Galerkin-based weighted residual method. The numerical investigations are performed while the emphasis is placed on studying the effect of various parameters including: nonlocal parameter, material characteristic length scale, material gradient index, thermal effect and intermolecular force on the static pull-in instability of FG nano-beam. To establish the validity of the present formulation, a comparison is conducted with experimental and numerical results reported in previous studies.
International Journal of Engineering, Mar 1, 2014
This paper addresses the static and dynamic stabilities of a parametrically excited torsional mic... more This paper addresses the static and dynamic stabilities of a parametrically excited torsional microactuator. The system is composed of a rectangular micro-mirror symmetrically suspended between two electrodes and acted upon by a steady (dc) while simultaneously superimposed to an (ac) voltage. First, the stability of the system subjected to a quasi-statically applied (dc) voltage is investigated, where the pull-in instability, equilibrium positions, and bifurcation points of the system are determined. Then by superimposing an (ac) voltage and extracting a Mathieu type governing equation the effects of (ac) component on the stability of the system is investigated. By varying excitation parameters (steady (dc) voltage and time-dependent amplitude of (ac) excitation), transition curves and the stability margins of the micro-mirror are demonstrated. Theoretically obtained margins are checked by means of numerical simulations. The results show that superimposing the harmonic (ac) component could have a stabilizing effect and allow an increase of the steady (dc) component beyond the pull-in value. These results could be used in design of micro-actuators.
Nonlinear Dynamics, Aug 23, 2018
Similar to elasticity and viscoelasticity, anelasticity is one of the rheological models of mater... more Similar to elasticity and viscoelasticity, anelasticity is one of the rheological models of materials. Like the viscoelastic materials, anelastic deformation is time dependent, while unlike viscoelasticity, it is full recoverable. Anelastic behavior is very sensitive to microstructure and is significant when things become small. In this paper, the nonlinear vibrations of an electrostatically actuated micro-beam made of anelastic material are studied based on the modified couple stress theory and considering compressible fluid media. The constitutive equation of micro-beams has been developed regarding the stress-strain behavior of classic anelastic materials. Considering the dependency of the effective viscosity on variable gap distance, an analytical model of an electrostatically actuated anelastic micro-beam has been developed through the variable Knudsen number. Then, multiple scales method has been applied to obtain an approximate analytical solution for nonlinear resonant curves. Additionally, the effects of different mechanical behaviors of materials including elasticity, viscoelasticity and anelasticity on the nonlinear dynamic response have been studied. Furthermore, influences of some effective parameters such as length scale, anelastic relaxation time, relaxation intensity, mid-plane stretching force, residual axial force, air-gap pressure and compressible fluid media on the nonlinear vibration analysis have been
International Journal of Engineering, Dec 1, 2012
In this article, thermo-elastic damping in nano-beam resonators is investigated based on nonlocal... more In this article, thermo-elastic damping in nano-beam resonators is investigated based on nonlocal theory of elasticity and the Euler-Bernoulli beam assumptions. To this end, governing equation of motion of the beam is obtained from stress-strain relationship of the nonlocal elasticity model and also governing equations of thermo-elastic damping are established using two dimensional non-Fourier heat conduction. Free vibration of the nano-beam resonators is analyzed using Galerkin reduced order model formulation for the first mode of vibration. In the present investigation a clamped-clamped nano-beam with isothermal boundary conditions at both ends is studied. This nonlocal model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect. The obtained results are compared with the numerical results of the classical thermo-elastic models. Thermo-elastic damping effects on the damping ratio are studied for the various nano-beam thicknesses and ambient temperatures. In addition, the study includes computations for different values of nonlocal theory parameter. The results show that with increasing the amount of nonlocal parameter and also with decreasing the length of the nano-beam, difference between the results of classical and nonlocal theory increases.
Nonlinear Dynamics, Nov 8, 2016
The present study investigates the nonlinear size-dependent behavior of micro-doubly curved shall... more The present study investigates the nonlinear size-dependent behavior of micro-doubly curved shallow shells based on the modified couple stress theory. Assuming von-Karman geometric nonlinearity and the first-order shear deformation theory, the governing equations of the system are derived using variational approach. The governing equations are reduced using the Galerkin method to a system of finite nonlinear ordinary differential equations. Multiple scales method is used to obtain an approximate analytical solution for nonlinear frequency response. Effect of the length scale parameter as well as the shell curvature on the frequency curves is addressed. It is shown that increasing the length scale parameter changes the softening behavior to a hardening one. On the shell curvature plane, it is depicted that for some values of the length scale parameter the system displays totally a hardening behavior. Influence of the length scale on the effective nonlinearity is discussed. It is found that in a flat shell the effective nonlinearity did not change significantly, while the variations are considerable for saddle shells. It is also shown that variation in the shell dimensions for spherical shells had significant effect on the frequency response, while this is not the case for hyperbolic paraboloidal shells. Finally, examining the effects of the damping on the nonlinear dynamics of the system shows wider response region for decreasing damping.
Measurement, Dec 1, 2013
ABSTRACT In the present article, a perceptive capacitive sensor for measuring angular speed of a ... more ABSTRACT In the present article, a perceptive capacitive sensor for measuring angular speed of a rotating shaft is proposed. The proposed sensor is capable of measuring rotating shaft angular speed, and its changes. The proposed model's sensing part is a suspended clamped-clamped micro-beam, which is parallel with two fixed substrates from the upper and lower sides through the micro-beam's width surface. An electric circuit is used to give out capacitance change as a result of angular speed change, in output voltage. The micro-beam undergoes non-linear electro-static pressure that is induced due to the applied bias DC voltage. The suggested sensor has high sensitivity for a large range of working machines rotating parts angular speed measurement. The governing nonlinear partial differential equation of the transversal motion of the beam is derived and solved by step by step linearization (SSLM) and Galerkin weighted residual methods and the stable region of the sensor is determined. The effects of the applied bias voltage and geometrical properties of the micro-beam on the sensitivity and the range of the measurable angular speed of the sensor are discussed.