Thermoelastic damping in nonlocal nanobeams considering dual-phase-lagging effect (original) (raw)
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This article constructs a new model of nonlocal thermoelasticity beam theory with phase-lags considering the thermal conductivity to be variable. A nanobeam subjected to a harmonically varying heat is considered. The nonlocal theories of coupled thermoelasticity and generalized thermoelasticity with one relaxation time can be extracted as limited and special cases of the present model. The effects of the variable thermal conductivity parameter, the nonlocal parameter, the phase-lags and the angular frequency of thermal vibration on the lateral vibration, the temperature, the displacement, and the bending moment of the nanobeam are investigated.
Applied Mathematics and Computation, 2014
For small volumes at the micrometer and nanometer level, classical continuum mechanics cannot be used to capture experimentally observed phenomena, such as size effects. Moreover, dissipation is much less pronounced than that in the case of macroscopic volume elements. To remedy the situation, generalized continuum mechanics theories should be used as an alternative to molecular dynamics simulations which do provide physical insight, but may not be suitable for engineering applications and the formulation of related boundary value problems. The present contribution is an example in this direction. An Euler-Bernoulli beam model is constructed to study the vibration of a nanobeam subjected to ramp-type heating. A generalized thermoelasticity theory with non-local deformation effects and dual-phase-lag (DPL) or time-delay thermal effects is used to address this problem. An analytical technique based on Laplace transform is employed. The inverse of Laplace transform is computed numerically using Fourier expansion techniques. The effects of nonlocality, DPLs, and the ramping-time parameter on the lateral vibration, the temperature, the displacement and the flexural moment of the nanobeam are discussed. The results are shown quantitatively in corresponding graphs.
Microsystem Technologies
This paper deals with a new nonlocal model based on Eringen's nonlocal elasticity and generalized thermoelasticity. A study was carried out on magnetothermoelastic waves in a thermoelastic isotropic conducting finite rod subjected to a moving heat sources permeated by a primary uniform magnetic field and rotating with a uniform angular velocity. The Laplace transform technique has been used to solve the resulting non-dimensional coupled field equations. Expressions for nonlocal thermal stress, temperature, and displacement in the physical domain are obtained using a numerical inversion technique. The effects of nonlocal parameter, rotating, magnetic field and the speed of the heat source on the physical fields are detected and illustrated graphically. The results obtained in this work should be useful for researchers in nonlocal material science, lowtemperature physicists, new material designers, as well as to those who are working on the development of the theory of nonlocal thermoelasticity.
Mathematics
In this article, a nonlocal thermoelastic model that illustrates the vibrations of nanobeams is introduced. Based on the nonlocal elasticity theory proposed by Eringen and generalized thermoelasticity, the equations that govern the nonlocal nanobeams are derived. The structure of the nanobeam is under a harmonic external force and temperature change in the form of rectified sine wave heating. The nonlocal model includes the nonlocal parameter (length-scale) that can have the effect of the small-scale. Utilizing the technique of Laplace transform, the analytical expressions for the studied fields are reached. The effects of angular frequency and nonlocal parameters, as well as the external excitation on the response of the nanobeam are carefully examined. It is found that length-scale and external force have significant effects on the variation of the distributions of the physical variables. Some of the obtained numerical results are compared with the known literature, in which they ...
Thermo-elastic Damping in Nano-beam Resonators Based on Nonlocal Theory
International Journal of Engineering, 2012
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.
Applied and Computational Mechanics, 2019
In this study, the second type of Green and Naghdi's thermoelasticity theory is applied to present the vibration of a nanobeam subjected to rectified sine wave heating based upon the nonlocal thermoelasticity theory. Both Young's modulus and thermal conductivity are considered to be linear functions of the temperature. The Laplace transform domain is adopted to solve the governing partial differential equations using the state space approach. Numerical computations are carried out using the inverse of Laplace transforms. The effects of nonlocal parameter and angular frequency on the thermal vibration quantities are discussed. The results of all quantities are illustrated graphically and investigated.
Thermoelastic Vibrations of Nonlocal Nanobeams Resting on a Pasternak Foundation via DPL Model
Applied and Computational Mechanics, 2020
The present work introduces the thermoelastic vibrations of nonlocal nanobeams resting on a two-parameter foundation. The governing equations are formulated for linear Winkler–Pasternak foundation type based on the generalized dual-phase-lag heat conduction and nonlocal beams theories. The nanobeam is subjected to a temperature ramping function. The coupled equations of the problem are formulated and solved by Laplace transform technique. The effects of the nonlocal parameter and different foundation parameters on the field variables are illustrated graphically and discussed. The results obtained are consistent with previous analytical and numerical results.
2020
A theoretical nonlocal thermoelastic model for studying the effects of the thermal conductivity variability on a rotating nanobeam has been described in the present article. The theory of thermal stress is employed using the Euler–Bernoulli beam model and generalized heat conduction with phase lags. It is believed that the thermal conductivity of the current model varies linearly according to temperature. Due to variable harmonic heat, the considered nanobeam excited and was subjected to a time-varying exponential decay load. Using the Laplace transform process, the analytical solutions for displacement, deflection, thermodynamic temperature and bending moment of rotating nanobeams are provided in final forms and a numerical example has been taken to address the problem. A comparison of the stated results was displayed and additionally, the influences of non-local parameters and varying load were analyzed and examined. We also investigate how the linear changes in the temperature of...
Vibration of FG nanobeams induced by sinusoidal pulse-heating via a nonlocal thermoelastic model
Acta Mechanica, 2014
In this study, the second type of Green and Naghdi's thermoelasticity theory is applied to present the vibration of a nanobeam subjected to rectified sine wave heating based upon the nonlocal thermoelasticity theory. Both Young's modulus and thermal conductivity are considered to be linear functions of the temperature. The Laplace transform domain is adopted to solve the governing partial differential equations using the state space approach. Numerical computations are carried out using the inverse of Laplace transforms. The effects of nonlocal parameter and angular frequency on the thermal vibration quantities are discussed. The results of all quantities are illustrated graphically and investigated.