Modeling and Analysis of Thermoelastic Damping in a Piezoelectro-Magneto-Thermoelastic Imperfect Flexible Beam

This research addresses the phenomena of thermoelastic damping (TED) and frequency shift (FS) of a thin flexible piezoelectro-magneto-thermoelastic (PEMT) composite beam. Its motion is constrained by two linear flexible springs attached to both ends. The novelty behind the proposed study is to mimic the uncertainties during the fabrication of the beam. Therefore, the equation of motion was derived utilizing the linear Euler–Bernoulli theory accounting for the flexible boundary conditions. The beam’s eigenvalues, mode shapes, and the effects of the thermal relaxation time ( t 1 ), the dimensions of the beam, the linear spring coefficients ( K L 0 and K L L ), and the critical thickness ( C T ) on both TED and FS of the PEMT beam were investigated numerically employing the Newton–Raphson method. The results show that the peak value of thermoelastic damping ( Q p e a k − 1 ) and the frequency shift ( Ω ) of the beam increase as t 1 escalates. Another observation was made for the primary fundamental mode, where an increase in the spring coefficient K L L leads to a further increase in Ω . On the other hand, the opposite trend is noted for the higher modes. Indeed, the results show the possibility of using the proposed design in a variety of applications that involve damping dissipation.