Thermo-electro-mechanical dynamic and free vibration analysis of FGPM nanobeam with initial stress

Abstract

Currently, nanostructures such as nanobeams, nanomembranes and nanoplates have been a hot area of research triggering. The contribution of this research article deals with both the effect of the free and dynamic vibration of a nanobeam as well as the use of the FGM material by integrating the piezoelectric effect. In fact, incorporating the initial stress for a nanoscale beam has not been considered yet. This paper displays an analysis of dynamic and free vibration of power-law functionally graded piezoelectric materials (FGPM) subjected to thermal-electro-mechanical loads with initial stress. The model was resolved based on nonlocal Timoshenko beams theory. The dimensionless fundamental frequency gradually improved with the new configuration of the FGPM nanobeam by 5% compared to the FGM nanobeam. The accuracy of this model is highlighted via numerical examples for different boundary conditions. To solve the governing equations, the polynomial differential quadrature method (PDQM) was elaborated and resolved numerically using MATLAB. For various configurations of the FGPM nanobeams, the effect of scaling parameters, volume fraction and slenderness ratios were discussed. In addition, for different edge conditions, variations of the first four frequencies with volume fraction indices and for different scaling parameters were set forward. This study corroborated that the power exponent, nonlocal parameter, slenderness ratio and thermo-electro-mechanical loads have significant effects on the dimensionless frequencies of various FGPM nanobeams. The present work provides an enlightening as guideline for the draft of a nanoscale beams based thermo-electro-mechanical actuators.