The Vibrations of a Piezoelectric Functionally Graded Material (FGM) Beam Have Been Analyzed in a Thermal Field Under Various Boundary Conditions and a Harmonic Moving Force

In this paper, the vibrations of a piezoelectric functionally graded material (FGM) beam have been analyzed in a thermal field under various boundary conditions and a harmonic moving force. In order to achieve the objectives of this study, governing equations of piezoelectric FGM beam dynamics under a thermal field and various boundary conditions were obtained using the Euler-Bernoulli Theory. Furthermore, results were analyzed using Differential Quadrature numerical method, through which various boundary conditions, including double-fixed, fixed-pinned, pinned-fixed and double-pinned were obtained. In addition, properties of the functionally graded composite material were assumed as a function of beam thickness. Results indicated that increasing the volume fraction of functionally graded materials causes an increase in beam displacement. It was also observed that all-steel beams underwent larger displacements, compared to all-ceramic beams. Additionally, the piezoelectric effect reduced system displacement by causing an increase in the stiffness matrix in the governing equation. Results also showed that higher temperature variations caused larger system drifts. On the other hand, increasing force velocity lead to a higher resulting stress, and consequently, larger beam displacements. Moreover, it was deduced that beam displacement is directly correlated to the beam length parameter, such that larger beam spans result in larger system displacements. Reducing the volume fraction of functional material causes an upsurge in the moving force critical velocity. On the other hand, temperature variations are associated with smaller critical velocities of moving forces and the occurrence of critical velocities at smaller amounts. However, piezoelectricity results in higher critical velocities of the moving force; and therefore, critical velocity will occur at higher amounts. Double-pinned boundary conditions resulted in larger displacements, in comparison to other boundary conditions. Changing the boundary conditions resulted in different amounts of displacement; through which higher system stiffness, andhence, smaller system drifts couldbe achieved.