Flexural response of thermoelastic thin beam resonators due to thermal and mechanical loads

• The flexural vibration of generalized thin beam due to loads has been investigated.
• Laplace transforms and ADM solutions have been found to be consistent.
• The effects of thermal and mechanical material parameters have been examined.
• The effects of Fourier and non-Fourier processes of heat conduction have been analyzed.
• The response ratio of the system has also been evaluated.

The flexural vibrations of homogeneous, transversely isotropic, generalized (non-Fourier) thermoelastic simply-supported thin beam resonators due to thermal and mechanical loads have been investigated under Euler–Bernoulli hypothesis. The model equation governing the transverse vibrations has been solved by using double Laplace transform technique (LTT) with respect to space and time. A mesh-less computational method, Adomian decomposition method (ADM), has also been employed to solve the model equation in the space domain for the comparison purpose. The inversion of the transformed solution has been carried out by using Durbin׳s technique in order to obtain the results in physical time domain. The natural frequencies and the corresponding mode shapes of the beam have been computed. The effects of thermal variations and other parameters on the deflection and temperature profiles of the thin beam have been studied. The effect of thermal relaxation time (second sound) on the vibration characteristics of beam has also been observed. The results computed by using LTT and ADM have been compared and are found to be in good agreement. It is noticed that ADM is an accurate, computer friendly and provides a unified, systematic powerful mathematical tool for solving the static and dynamic vibration problems for the considered beams.