Analysis of Forced Vibrations in Micro-Scale Anisotropic Thermo-Elastic Beams Due to Concentrated Loads

Abstract

This article is devoted to model and analyze the transverse deflection and thermal moment of transverse vibrations in a transversely isotropic, thermo-elastic beam resonator under the action of time harmonic concentrated load. The governing equations of flexural vibrations and thermal moment in a transversely isotropic, thermo-elastic Euler–Bernoulli beam have been derived in a closed form. A time harmonic point load is assumed to act on the beam at a given distance from the origin. The beam is assumed to be at either clamped-clamped (CC), simply supported-simply supported (SS), clamped-simply supported (CS), or clamped-free (CF) conditions at its ends. The Laplace transform technique has been used to find the transverse deflection and thermal moment in the transform domain due to the action of concentrated load in a beam under above conditions in case of both free and forced vibrations. The analytic expressions obtained in the physical domain after inversion of Laplace transforms have been computed numerically with the help of MATLAB software for silicon material beam. The results for coupled thermo-elastic, elastic, and isotropic beams have been deduced as special cases. The computer-simulated results have been presented graphically. The study may find applications in development and design of resonators (sensors), precision thermometers, and energy harvesters.

Keywords:

• Anisotropy
• Euler-Bernoulli Beam
• Laplace transforms
• MEMS
• Resonators

ACKNOWLEDGMENTS

The authors are grateful to the Council of Scientific and Industrial Research (CSIR), New Delhi, for providing financial assistance via Grant Nos. 09/918(0002)2010-EMR-I and 25(0184)/10/EMR-II to complete this work.