Non-linear Forced Vibration Analysis of Piezoelectric Functionally Graded Beams in Thermal Environment

This work proposes a geometrically non-linear vibratory study of a functional gradation beam reinforced by surface-bonded piezoelectric fibers located on an arbitrary number of supports, subjected to excitation forces and thermoelectric changes. The non-linear formula is based on Hamilton's principle combined with spectral analysis and developed using Euler-Bernoulli's beam theory. In the case of a non-linear forced response, numerical results of a wide range of amplitudes are given based on the approximate multimodal method close to the predominant mode. In order to test the methods implemented in this study, examples are given and the results are very consistent with those of the literature. It should also be noted that the thermal charge, the electrical charge, the volume fraction of the structure, the thermal properties of the material, the harmonic force and the number of supports have a great influence on the forced non-linear dynamic response of the piezoelectrically functionally graded structure