Thermoviscoelastic Vibrations of a Micro-Scale Beam Subjected to Sinusoidal Pulse Heating

Abstract

In this article, we studied the vibrational effects of a viscoelastic micro-scale beam induced by sinusoidal pulse heating based on Euler-Bernoulli beam theory. The formulation of the present problem is applied to the generalized thermoelasticity with phase lags. The deflection, temperature, axial displacement, and bending moment of the micro-scale beam are determined by using the Laplace transform method. The system of governing equations is reduced to a novel six-order thermoelastic differential equation in either deflection or temperature. The numerical results in case of silicon material are presented with the help of Mathematica programming software. Some plots are illustrated to investigate the effects of the phase-lags and the width of the sinusoidal pulse parameters. The effect of the viscosity on the micro-scale beam resonator is also investigated.

Response of thermoviscoelastic microbeams affected by the heating of laser pulse under thermal and magnetic fields

“…• The amplitude of the field quantities decreased significantly for the viscous states compared to the non-viscous field, due to the presence of the viscosity term in the presented model with phase lags, confirming the results obtained in [13,52]. • One important fact is that all the field quantities vanish identically with the increase of the length x.…”

“…In order to investigate the obtained results, some numerical results and different cases will be presented and displayed graphically. The material properties for thermoviscoelastic material (copper) are taken as [51,52] ( ) The values of the constants R a and d 0 are taken as 0.5, 0.01. Without loss of generality, we take = -L 10 J m .…”

Thermoviscoelastic response of an axially loaded beam under laser excitation and resting on Winkler’s foundation

“…According to this figure, it is visible that all the studied field variables are very sensitive to the time size parameter t 0 . This result is in good agreement with the results obtained in (Zenkour and Abouelregal, 2014a; Mashat et al , 2017). From Figure 4(a)–(d), we can see that an increase of time size parameter t 0 increases the value of field variables in all three values of t 0 .…”

“…Hooke’s law can be approximated for many materials, for example, polycrystalline metals and high polymers by the theory of viscoelasticity. Using the generalized models of thermoelasticity, many authors have taken several thermoviscoelastic problems into consideration (Chang et al , 1992; Habibi et al , 2016; Hilton and Dong, 1964; Mashat et al , 2017). The viscous model, named Kelvin–Voigt model, comprises a dashpot and a spring in parallel.…”

The Response of Nanobeams with Temperature-Dependent Properties Using State-Space Method via Modified Couple Stress Theory

“…Careful analysis of different consequences of resonator features, for instance, resonant frequencies and quality factors, is vital to designing the component's high performance. Several authors have studied the process of heat transfer and the behavior of vibrations of microbeams [10][11][12][13][14][15][16][17][18][19][20][21].…”