Mathematical Modeling and Analysis of Forced Vibrations in Micro-Scale Microstretch Thermoelastic Simply Supported Beam

The present paper deals with the flexural vibrations
of homogeneous, isotropic, generalized micropolar microstretch
thermoelastic thin Euler-Bernoulli beam resonators, due to
Exponential time varying load. Both the axial ends of the
beam are assumed to be at simply supported conditions. The
governing equations have been solved analytically by using Laplace
transforms technique twice with respect to time and space variables
respectively. The inversion of Laplace transform in time domain
has been performed by using the calculus of residues to obtain
deflection.The analytical results have been numerically analyzed with
the help of MATLAB software for magnesium like material. The
graphical representations and interpretations have been discussed
for Deflection of beam under Simply Supported boundary condition
and for distinct considered values of time and space as well. The
obtained results are easy to implement for engineering analysis and
designs of resonators (sensors), modulators, actuators.

Authors:

• Geeta Partap
• Nitika Chugh

Keywords:

• Microstretch
• deflection
• exponential load
• Laplace transforms
• Residue theorem
• simply supported.

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