Nonlinear vibrations Research Papers - Academia.edu (original) (raw)

2025, Procedia Materials Science

2025, Известия Саратовского университета. Новая серия. Серия: Математика. Механика. Информатика

В настоящей работе авторы представляют результаты вычислений поля напряжений цилиндрической оболочки, ослабленной круговым отверстием и находящейся под воздействием различных нагрузок: одноосного растяжения, внутреннего давления и... more

2025, Journal of Vibration and Control

Employing variable horizontal and vertical shifts for the unperturbed solution, a new perturbation method is proposed. The new method is named as the shift perturbation method. The existing perturbation methods are interpreted with respect to the horizontal and vertical shifts for the unperturbed solution. The new method is applied to some well-known vibrational problems. The method is capable of producing admissible approximate solutions for a wide range of problems such as the free and forced vibrations of the Duffing equation, equations with quadratic and cubic nonlinearities, variable amplitude nonlinear problems, and boundary layer problems. A variant of the method also produced valid solutions for large perturbation parameters.

2025, JOURNAL OF MECHANICAL ENGINEERING AND SCIENCES

Paths of vehicles under restricted conditions are of technological interest in navigation engineering. One such restriction may be to fix one of the velocity components during motion. For objects moving in a two-dimensional vertical space, the differential equations determining the paths of the objects for which one of the velocity components remains constant are derived. First, the no thrust force case is investigated. The two paths in which the velocity components remain constant are determined by finding exact solutions of the associated differential equations. While the constant x-component case produces the wellknown parabolic solution, the constant y-component case reveals a new solution called the 2/3 rule. Then, the differential equations for an object moving with constant x and y velocity components are derived separately for the constant-magnitude thrust force case. Since the equations inherit high nonlinearities, exact analytical solutions cannot be obtained for the constant-magnitude thrust force case. Instead, approximate solutions obtained by the Perturbation Iteration Method are compared with the Runge-Kutta numerical solutions. Within the range of validity, the approximate solutions can be employed to determine the path instead of the numerical solutions. The approximate analytical solutions would reduce the computational cost of integrating the original numerical solutions. The study may find applications in determining the paths of flying objects such as projectiles, rockets, and aerial vehicles.

2025, Romanian Journal of Acoustics and Vibration

Free and forced damped vibrations of a Duffing equation with cubic nonlinearities is considered. The damping, nonlinearity and external excitation parameters are assumed to vary slowly in time. Using the Method of Multiple Scales, a perturbation technique, the amplitude and phase modulation equations are derived in its most general case. First, the free vibration case is treated. Decaying, built-up and harmonically varying functions are taken to model the slow variations of the parameters in time. The amplitude and phase modulation equations can be integrated to obtain closed form solutions in general for free vibrations. For the forced vibrations, a resort to the numerical techniques is required for the integration of the amplitude and phase modulation equations. It is shown that slow variations on the coefficients may lead to substantial changes in the dynamics of the problem.

2025

In this paper, a distributed parameter model is used to study the pull-in instability of cantilever type nanomechanical switches subjected to intermolecular and electrostatic forces. In modeling of the electrostatic force, the fringing field effect is taken into account. The model is nonlinear due to the inherent nonlinearity of the intermolecular and electrostatic forces. The nonlinear differential equation of the model is transformed into the integral form by using the Green's function of the cantilever beam. Closed-form solutions are obtained by assuming an appropriate shape function for the beam deflection to evaluate the integrals. The pull-in parameters of the switch are computed under the combined effects of electrostatic and intermolecular forces. Electrostatic microactuators and freestanding nanoactuators are considered as special cases of our study. The detachment length and the minimum initial gap of freestanding nano-cantilevers, which are the basic design parameters for NEMS switches, are determined. The results of the distributed parameter model are compared with the lumped parameter model.

2025, Master thesis patient MBAYO

Le défi actuel en maintenance est de pouvoir détecter une avarie sur une machine avant qu’elle ne soit grave, et ne provoque son arrêt, ou celui du système de production tout entier. La détection précoce des défauts par apprentissage... more

2025

Rolling bearings are one of the most important uproar and vibration generator into mechanical constructions. According to that, it is very important to know ascendancy of rolling bearing construction to main parameters which determine level of uproar and vibrations produced inside machines. This paper present new mathematical model of dynamic behavior of rigid rotor inside the rolling bearing. The new model is experimentally validated on a vibration test of rotor.

2024

Anatoly Mykhailovych Samoilenko was born on January 2, 1938 in the village of Potiivka (Zhytomyr Region, Ukraine) to the family of Mykhailo Grygorovych and Mariya Vasylivna Samoilenko. Somewhat later, his family moved to the city of Malyn (Zhytomyr Region). In 1955, he finished school and entered the Geological Faculty of the Shevchenko Kyiv State University. Quite soon he understood that mathematics is his vocation and continued his education at the Faculty of Mechanics and Mathematics of the same university and graduated from this faculty with honors in 1960. By the invitation of Academician Yu.O. Mitropolsky, Anatoly Samoilenko entered a the post-graduate course at the Institute of Mathematics of the Ukrainian Academy of Sciences, where he became a member of the Krylov–Bogolyubov Kyiv Scientific School. In 1961, he published his first scientific works. In 1963, he defended his Candidate–Degree Thesis “Application of Asymptotic Methods to the Investigation of Nonlinear Differentia...

2024, Packaging Technology and Science

Polymer foams are commonly used in the protective packaging of fragile products. Cushion curves are commonly used within the packaging industry to characterize a foam's impact performance. These curves are two‐dimensional representations of the deceleration of an impacting mass versus static stress. Cushion curves are currently generated from exhaustive experimental test data. This study represents the first time that the physics of the mass‐cushion impact have been analysed by modelling the foam as nonlinear, continuous rod. Using a single mode of vibration and excluding the effects of damping, the maximum displacement during the impact can be obtained from a polynomial describing the maximum elastic energy in the foam. The displacements can be used to recover the amplitude of the deceleration shock pulse. Numerical and analytical analysis of the model with damping is considered in its ability to predict the shock pulse shape, duration, and amplitude at various static stresses,...

2024, Springer eBooks

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2024, Journal of Applied and Computational Sciences in Mechanics

n this study, the free vibration analysis of a functionally graded rotating double tapered beam is performed. The analysis is based on Euler-Bernoulli beam theory. The Material properties of the beam vary continuously in the thickness direction according to the power-law function. The governing differential equation of motion is derived using the Hamilton’s principle. Natural frequencies are obtained using differential transformation (DTM) technique. The effects of the taper ratios, nondimensional rotational speed, nondimensional hub radius and material volume fraction index on the natural frequencies are discussed. Numerical results are tabulated in several tables and figures. To verify the present analysis, the results of this study are compared with the available results from the existing literature. It is shown that the natural frequencies of a functionally graded rotating double tapered Euler-Bernoulli beam can be obtained with high accuracy by using DTM. It was observed that nondimensional rotational speed, height taper ratio and power-law exponent significantly affect the natural frequency. The effects of hub radius and breadth taper ratio on the natural frequencies are negligible.

2024, Journal of Applied and Computational Sciences in Mechanics

In this research, effects of various system parameters on nonlinear response of transverse vibrations of beam-like fluid conveying microtube with fixed simply supported boundary conditions under axial magnetic parametric resonance condition is investigated. Reddy’s first order shear deformation theory and Eringen nonlocal elasticity theory are used to derive microtube nonlinear equations of transverse motion considering nonlinear geometric terms of von-Karman. For fluid flow velocities more than flutter critical velocity, behavior of 2 DoF nonlinear system is studied under parametric magnetic resonance condition. By deriving nonlinear response curves, effects of various parameters including magnetic excitation amplitude, parameter of excitation frequency and nonlocal stress parameter on resonance amplitude is investigated and discussed.

2024

A new class of modern smart materials such as piezoelectric polymers and ceramics, electrorheological fluids, optical fibers and shape memory alloys have a great number of possible applications in many industrial and engineering fields. This number grows constantly encouraging scientists and engineers to study and analyze the behavior of the materials, range and ways of their best use. Shape memory alloy reinforced composites are an extremely versatile class of materials. Shape memory alloys are characterized by: large internal forces, unique ability of changing its material properties, wide range of operational temperature, excellent damping properties and high durability. Mechanical and physical properties of SMA strongly depend on temperature and initial stresses. Changes in temperature and initial stresses involve changes in the volume fraction of martensite in the alloys. During the martensite transformation recovery stresses appear. These recovery stresses are not only a funct...

2024, International Journal of Fluid Mechanics Research

The equation of motion of the axially moving carbon nanotube conveying fluid is obtained in order to investigate the effect of the velocity of axially moving CNT and internal flowing fluid on the vibrational behavior of the system. To this end, the nonlocal continuum theory is used to consider the small-scale effect and the Knudsen number is employed to create the nanoflow as a fluid passing through the CNT. The equation of motion is obtained by using Hamilton's principle and the Galerkin method is used to discretize and solve it. The results indicate that the small-scale parameter plays a key role in determining the critical velocity values and the occurring instabilities of the system. It is obvious that for the eigenfunction in the higher modes, the imaginary parts of the eigenvalues reach zero at a lower critical velocity in longitudinal vibration of the axially moving CNT conveying fluid. Moreover, it can be found that the stability of the system decreases when the axially moving CNT conveying fluid is considered with the constant axial movement velocity of the CNT, the constant fluid velocity, and the case in which both velocities are the same, respectively. Also, the existence of the fluid could cause an approximately 0.2% reduction in the magnitude of the system critical velocity, and then the system's stability decreases.

2024, International Journal of Fluid Mechanics Research

The transverse vibration and instability of the axially moving carbon nanotube (CNT) conveying fluid were studied. To this end, the nonlocal continuum theory and Knudsen number were utilized to consider the small-scale effect of the nanostructure and nanoflow, respectively. The Hamilton's principle was employed to obtain the governing equation of motion for the axially moving CNT with and without fluid passing through it, and the analysis was carried out using the Galerkin weighted residual method. In addition, to consider the small-size effect of nanoflow through the CNT, the Knudsen number is introduced. The results indicate that the resonant frequencies in which the instabilities emerge can be influenced by the fluid flow passing through the CNT more than the axially traveling CNT speed. In addition, it can be observed that the axially moving CNT conveying fluid, while the axially CNT velocity is constant, is more stable. This demonstrates, however, that the stationary CNT conveying fluid is more stable than all cases of the axially moving CNT conveying fluid.

2024, Latin American Journal of Solids and Structures

Many authors have shown that the effective design of viscoelastic systems can be conveniently carried out by using modern mathematical models to represent the frequency-and temperaturedependent behavior of viscoelastic materials. However, in the quest for design procedures of real-word engineering structures, the large number of exact evaluations of the dynamic responses during iterative procedures, combined with the typically high dimensions of large finite element models, makes the numerical analysis very costly, sometimes unfeasible. It is especially true when the viscoelastic materials are used to reduce vibrations of nonlinear systems. As a matter of fact, which the resolution of the resulting nonlinear equations of motion with frequency-and temperature-dependent viscoelastic damping forces is an interesting, but hard-to-solve problem. Those difficulties motivate the present study, in which a time-domain condensation strategy of viscoelastic systems is addressed, where the viscoelastic behavior is modeled by using a four parameter fractional derivative model. After the discussion of various theoretical aspects, the exact and reduced time responses are calculated for a three-layer sandwich plate by considering nonlinear boundary conditions.

2024, Journal of Theoretical and Applied Mechanics

A nonlocal Dynamic Stiffness Model (DSM) for free vibration analysis of Functionally Graded Material (FGM) stepped nanostructures based on the Nonlocal Elastic Theory (NET) is proposed. An exact solution to the equation of motion of a nanobeam element according to the Timoshenko beam theory, NET, and taking into account position of the neutral axis is constructed. Nondimensional frequencies and mode shapes of complete FGM stepped nanostructures are easily obtained using the nonlocal DSM. Numerical results are presented to show significance of the material distribution profile, nonlocal effect, and boundary conditions on free vibration of nanostructures.

2024, IFAC Proceedings Volumes

2024

The ability of mesh design in arbitrary Lagrangian-Eulerian finite element method (ALE-FEM) makes it a generally efficient device for simulating engineering problems. In this paper, ALE-FEM is used to model the static deflection and instability of beam-type cantilever nano-actuators using plain element. Effects of electrostatic fields are taken into account through first-order fringing field corrected model. In addition, the influence of quantum vacuum fluctuations is considered via attractive Casimir and van der Waals force depending on the range of application. The instability parameters, i.e. pull-in voltage and deflection of the nano-actuator are computed. The obtained results are compared with those reported in literature using numerical method as well as Lagrangian FEM. The findings indicate that ALE method can be used as a powerful technique for modeling beam type nano-actuator.

2024

This work presents a numerical model developed to simulate the dynamics and vibrations of a multistage tractor gearbox. The effect of time varying mesh stiffness, time varying frictional torque on the gear teeth, lateral and torsional flexibility of the shafts and flexibility of the bearings were included in the model. The model was developed by using the Lagrangian method, and it was applied to study the effect of three design variables on the vibration and stress levels on the gears. The first design variable, module, had little effect on the vibration levels but a higher module resulted to higher bending stress levels. The second design variable, pressure angle, had little effect on the vibration levels, but had a strong effect on the stress levels on the pinion of a high reduction ratio gear pair. A pressure angle of 25o resulted to lower stress levels for a pinion with 14 teeth than a pressure angle of 20o. The third design variable, contact ratio, had a very strong effect on b...

2024, Innovative Systems Design and Engineering

This work presents a numerical model developed to simulate and optimize the dynamic stress of multistage spur gears. The model was developed by using the Lagrangian energy method and modified Heywood method, and applied to study the effect of three design variables on the dynamic stress on the gears. The first design variable considered was the module, and the results showed that increasing the module resulted to increased dynamic stress levels. The second design variable, pressure angle, had a strong effect on ...

2024, The Proceedings of the International Conference on Nuclear Engineering (ICONE)

2024, Thin-Walled Structures

Previous work by Li et al. in the area of axial vibrations of bellows dealt with fixed end conditions. However, it is seen on several occasions that bellow ends are welded to a small pipe spool that has a lumped mass such as a valve or an instrument. Hence, the present paper aims at finding out the effect of elastically restrained ends on the axial natural frequencies. The analysis considers finite stiffness axial restraints on the bellows, i.e. solving the set of equations with non-homogeneous boundary conditions. Two bellow specimens are considered for comparison having the same dimensions as taken by Li in his analysis. The transcendental frequency equation deduced is accurate as the first, second and third mode frequencies computed are in close agreement to the ones obtained by Li.

2024, Applied Mathematical Modelling

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights  The mechanical behavior of a clamped-clamped microbeam with middle paddle is analyzed.  The pull in voltage declines and the deflection enlarges as the intermolecular forces increase.  Presence of the electrostatic force accelerated the instability resulting from the capillary force.  Fringing field effect considerably affected determination of the bifurcation points.

2024, Mechanics and advanced technologies

A method for detecting excitations leading to the damage of the gears and bearings working surfaces has been developed by means of experimental study of the dynamic characteristics of the gearbox of metro tunnel escalator drive in normal and bad performance. The technique is based on the acquisition and analysis of low and high resolution spectra. The technique is tested during the analysis of vibration spectra of a standard three-stage, four-shaft gearbox of tunnel escalator drive. The vibration analysis was performed using the kinematic excitation frequencies generated by the gears and rolling bearings in the zones of resonance vibrations of the gearbox elements. According to the results of the analysis, the presence of variable stiffness of the teeth in one of the gears and damage of the inner ring of the ball bearing of the intermediate shaft cover is established.

2024, Anali PAZU

This paper treats the adaptation of the Extended Lindstedt-Poincare Method with multiple time scales (EL-PM) for analysis of stationary and nonstationary resonances of harmonically excited Duffing oscillator with time delay feedback control. The fundamental and ⅓ subharmonic resonance, respectively of Duffing oscillator with feedback control are analyzed in details. The comparison of stationary resonances with nonstationary resonances due to the slowly varying excitation frequency is presented by means of examples, which are computed by programming tool Mathematica®.

2024, Sound and Vibration

The free vibration analysis of simply supported box-girder bridges is carried out using the finite element method. The fundamental frequency is determined in straight, skew, curved and skew-curved box-girder bridges. It is important to analyse the combined effect of skewness and curvature because skew-curved box-girder bridge behaviour cannot be predicted by simply adding the individual effects of skewness and curvature. At first, an existing model is considered to validate the present approach. A convergence study is carried out to decide the mesh size in the finite element method. An exhaustive parametric study is conducted to determine the fundamental frequency of box-girder bridges with varying skew angle, curve angle, span, span-depth ratio and cell number. The skew angle is varied from 0°to 60°, curve angle is varied from 0°to 60°, span is changed from 25 to 50 m, span-depth ratio is varied from 10 to 16, and single cell & double cell are used in the present study. A total of 420 bridge models are used for parametric study in the investigation. Mode shapes of the skew-curved bridge are also presented. The fundamental frequency of the skew-curved box-girder bridge is found to be more than the straight bridge, so, the skew-curved box-girder bridge is preferable. The present study may be useful in the design of box-girder bridges.

2024, Sound&Vibration

2024, Journal of Mechanical Science and Technology

In this paper, the Homotopy Analysis Method (HAM) with two auxiliary parameters and Differential Transform Method (DTM) are employed to solve the geometric nonlinear vibration of Euler-Bernoulli beams subjected to axial loads. A second auxiliary parameter is applied to the HAM to improve convergence in nonlinear systems with large deformations. The results from HAM and DTM are compared with another popular numerical method, the shooting method, to validate these two analytical methods. HAM and DTM show excellent agreement with numerical results (the maximum errors in our calculations are about 0.002%), and they additionally provide a simple way to conduct a parametric analysis with different physical parameters in Euler-Bernoulli beams. To show the benefits of this method, the effect of different physical parameters on the amplitude is discussed for a cantilever beam with a cyclically varying axial load.

2024, Journal of Mechanical Science and Technology

2024, Вестник Самарского государственного технического университета. Серия «Физико-математические науки»

Предложен алгоритм решения задач о нелинейном динамическом поведении осесимметричных неразветвленных мягкооболочечных конструкций, основанный на использовании метода дифференцирования по параметру. Алгоритм не накладывает каких-либо ограничений на диапазон деформаций и перемещений, свойства материала, условия закрепления или форму меридиана конструкции. При этом уравнения движения в частных производных сводятся к нелинейным обыкновенным дифференциальным уравнениям с использованием метода прямых. Полученная система уравнений дифференцируется по календарному параметру. В результате решение задачи сводится к решению двух взаимосвязанных задач -- квазилинейной многоточечной краевой задачи и нелинейной задачи Коши с правой частью специального вида. Особенности использования данного алгоритма применительно к задачам динамики мягких оболочек проявляются при его программной реализации и описаны в работе. Тестирование алгоритма выполнено на примере решения задачи динамического раздувания шар...

2024, Mechanics of Advanced Materials and Structures

This paper infer the transient vibration of piezoelectric sandwich nanobeams, In present work, the flexoelectric effect on the mechanical properties of vibration piezoelectric sandwich nanobeam with different boundary conditions is investigated. According to the Nonlocal elasticity theory in nanostructures, the flexoelectricity is believed to be authentic for such size-dependent properties. The governing equations are derived by Hamilton's principle and boundary condition solved by Galerkin-based solution. This research develops a nonlocal flexoelectric sandwich nanobeam supported by Winkler-Pasternak foundation. The results of this work indicate that natural frequencies of a sandwich nanobeam increase by increasing the Winkler and Pasternak elastic constant. Also, increasing the nonlocal parameter at a constant length decreases the natural frequencies. By increasing the length to thickness ratio (L/h) of nanobeam, the nonlocal frequencies reduce.

2024

A model is proposed to study the dynamic response of cargo like pendulum vibration under three dimension vehicle hull motions. A nonlinear two degree-of-freedom model of the cargo inside vehicle hull is developed and analyzed. Equations of pendulum motion are obtained by first order Lagrange equations using Lagrange multiplier for constrained system with one constraint equation. One or two independent bumpers of the securing cargo are considered in the model. In model of two bumpers between them is right angle. Bumpers forces are represented by a special stiffness and damping as a function of the displacement and motion velocity. Investigation was made for three kinds of pendulum motion: transient motion from free initial conditions without hull vibrations; stationary motion exciting from constrained string or hull bumpers vibrations; jointly transient and exciting motion. The investigation was made for one, two and tree component harmonica motion of hull. Additional investigation o...

2024, First Conference on Mechanical Behavior Modeling of Materials

In the present study, the non-linear vibration of micro rotating shafts is studied based on the modified couple stress. By utilizing the Hamilton principle, the governing equations of motion are derived in the form of partial differential equations with consideration of the geometrical nonlinearity, internal damping and the shaft eccentricity. Then with the aid of the Galerkin method, those are converted into infinite ordinary differential equations. In the next step, the multiple scale method is employed to solve the non-linear ODEs and obtain the natural frequencies in both the backward and forward motion. The effects of different parameters, including the non-dimensional length scale parameter and the rotational speed, on the first two modes in forward and backward whirling are investigated.

2024, Composite Structures

In the present study, an accurate Bézier based multi-step method is developed and implemented to find the nonlinear vibration and post-buckling configurations of Euler-Bernoulli composite beams reinforced with graphene nano-platelets (GnP). The GnP is assumed to be randomly and uniformly dispersed in the composite mixproportion, with a random checkerboard configuration. Therefore, a probabilistic model together with an efficient simulation technique is proposed to find the effective moduli of a matrix reinforced GnP. It is worth noting that the presented micro-mechanics model found by the employed Monte-Carlo simulation matches exactly the experimental data and predicts the composite elastic constants more accurate than that found from other common methods, including the Halpin-Tsai theory. Also, for mathematical simplification, the composite beam in-plane inertia is neglected. The presented multi-step method is based on Burnstein polynomial basis functions while shows interesting potential to provide robust solutions for various initial and boundary value problems. It is found that adding a relatively low content of GnP would drastically increase the composite elastic constants, particularly in the transverse direction to fiber. In addition, the numerical results are compared with those provided by exact analytical solutions, where the stability of results suggests the effectiveness of the presented methodology.

2024, Journal of Solid Mechanics

Buckling strength of composite latticed cylindrical shells is one of the important parameters for studying the failure of these structures. In this paper, new governing differential equations are derived for latticed cylindrical shells and their critical buckling axial loads. The nested structure under compressive axial buckling load was analyzed. Finite Element Method (FEM) was applied to model the structure in order to verify the analytical results. The obtained results were validated based upon the results of previous case studies in literature. For the squared type of lattice composite shells, a new formula for the buckling load was developed and its value was compared to the critical load, using FEM with 3D beam elements. The processes were carried out for three different materials of Carbon/Epoxy, Kevlar/Epoxy and EGlass/Epoxy.

2024, Journal of Solid Mechanics

2023, Shock and Vibration

In this paper we study the periodic solutions of free vibration of mechanical systems with third and fifth-order nonlinearity for two examples using He's Frequency-Amplitude Formulation (HFAF).The effectiveness and convenience of the method is illustrated in these examples. It will be shown that the solutions obtained with current method have a fabulous conformity with those achieved from time marching solution. HFAF is easy with powerful concepts and the high accuracy, so it can be found widely applicable in vibrations, especially strong nonlinearity oscillatory problems.

2023, Latin American Journal of Solids and Structures

In this paper, variational iteration (VIM) and parametrized perturbation (PPM) methods have been used to investigate non-linear vibration of Euler-Bernoulli beams subjected to the axial loads. The proposed methods do not require small parameter in the equation which is difficult to be found for nonlinear problems. Comparison of VIM and PPM with Runge-Kutta 4th leads to highly accurate solutions.

2023

This article attempts to investigate the dynamical analysis of beam vibrations in the presence of preload discontinuity and proposes an innovative accurate equivalent function for this well-known nonlinearity. This approach enables us to overcome the inherent computational difficulty of the preload nonlinearity in the analytical investigations. At first, the nonlinear equation of beam vibration with preload boundary condition is considered and analytical solution is obtained using He's parameter expanding method. The precision of the proposed equivalent function has been elucidated by comparison of our results with the obtained solutions using numerical method. Finally, the accuracy of the obtained results in the vibration analysis of suspension bridges as a realistic problem, verifies the strength of the presented modeling.

2023, Journal of Theoretical and Applied Mechanics

The dynamic response of an initially flat viscoelastic membrane is investigated. The viscoelastic model is described with fractional order derivatives. The membrane is subjected to surface transverse and inplane dynamic loads. The governing equations are three coupled second order nonlinear partial FDEs (fractional differential equations) of hyperbolic type in terms of the displacement components. These equations are solved using the BEM for fractional partial differential equations developed recently by Katsikadelis. Without excluding other viscoelastic models, the herein employed material is the Kelvin-Voigt model with a fractional order derivative. Numerical examples are presented which not only demonstrate the efficiency of the solution procedure, but also give a better insight into this complicated but very interesting response of structural viscoelastic membranes. It is worth noting that in case of resonance, phenomena similar to those of the Duffing equation are observed.

2023, Applied Mathematical Modelling

The main objective of this study is to predict the both subharmonic and superharmonic resonances of the nonlinear oscillation of nanobeams in the presence of surface free energy effects. To this purpose, Gurtin-Murdoch elasticity theory is adopted to the classical beam theory in order to consider the surface Lame constants, surface mass density, and residual surface stress within the differential equations of motion. The Galerkin method together with the method of multiple scales is utilized to investigate the size-dependent response of nanobeams under hard excitations corresponding to various boundary conditions. A parametric analysis is carried out to indicate the influence of the surface elastic parameters on the frequency-response as well as amplitude-response of the nonlinear secondary resonance including multiple vibration modes and interactions between them. It is seen that for the superharmonic excitation, except to the clamped-free boundary condition, the jump phenomenon is along the hardening direction, while in the clamped-free end supports, it is along the softening direction. Moreover, it is revealed that for the subharmonic excitation, within a specific range of the excitation amplitude, the nanobeam is excited, and this range shifts to lower external force by incorporating the surface free energy effects. It is found that in the case of superharmonic excitation, the value of the excitation frequency associated with the bifurcation point at the peak of the frequency-response curve increases by taking the surface free energy effect into consideration.

2023, Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics

The present contribution deals with developing a semi-analytical analysis for studying the free vibration of a shape memory alloy beam with pseudoelastic behavior. The equations of motion are derived using the Hamilton principle and the Euler-Bernoulli theory. Then mathematical processes of non-dimensionalization and numerical integration are performed and finally the obtained partial differential equations are solved using the Galerkin method. A threedimensional phenomenological model for shape memory alloy, which has the capability of identifying the martensite phase transformation, saturated phase transformation, pseudoelasticity and the shape memory effect, is utilized for modeling the shape memory alloy. According to the hysteresis behavior of the shape memory alloy, the energy dissipation characteristic is clearly observed in the early stages of the free vibration. Stress and strain analysis is employed to specify the effect of phase transformation in each layer along the beam. The property of shape memory alloy beam demonstrates its great potential for using in damping applications.

2023, Journal of the Mechanical Behavior of Materials

The focus of this work is to study the influence of flexoelectric phenomenon on the electromechanical response of graphene-reinforced nanocomposite (GNC) nanorods. An analytical model has been derived by utilizing the Timoshenko beam theory and the principle of variational work by incorporating flexoelectric effects. The GNC nanorod is subjected to a concentrated load acting downward for clamped-free and simply supported support types. The GNC is reinforced with a defective graphene sheet as it is known to show enhanced polarization. The elastic properties of defective graphene sheets have been evaluated using molecular dynamic simulations. The outcome of our model shows that the flexoelectric effect must be considered for accurate modeling of nanostructures. Irrespective of the support type, flexoelectric effect improves the stiffness of the nanorod. We also observed that the stiffness of the nanorod is significantly influenced by the support type. This work presents an opportunity...

2023, Applied Surface Science

2023

The angular and radial backlashes due to intensive wear are the most distinctive feature of the cold and hot rolling mills drive trains. It causes nonlinear torsional vibration and significant torque amplification. It leads to equipment failures but it could be used for wear diagnostics in the range of natural frequencies of the drive trains during the transient processes. The static load and dynamic response interrelation, non isochronisms and other nonlinear system features are used for wear diagnostics under the non stationary loads and speeds.

2023, Zenodo (CERN European Organization for Nuclear Research)

The condition monitoring (CM) of heavy-duty mining and metallurgical machines working under non-stationary loading and cyclic (reversal) speed-changing conditions is always accompanied by transient vibrations [1-3]. The presence of impulsive impacts results in false alarms, which cause either downtime for revisions or unexpected failures and significant production losses. The spatial

2023, Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines

This paper intends to describe nonlinear effects occurring in rolling mills dynamics. That is necessarily for vibrations damping and reliable diagnostics of rolling mills equipment under non-stationary working conditions. Three types of nonlinear effects are investigated taking place in drivelines and stands of different design, namely, transient torsional vibrations in hot rolling mills, chatter vibrations in tandem cold rolling mills and parametrical vibrations in high-speed wire and rod rolling mills. The procedure is proposed for natural frequencies identification when short transient torque signals restrict application of the Fourier transform. Examples are given on using nonlinear effects for wear diagnostics and vibrations control based on natural frequencies and modes analysis of multi-body systems.