Effect of free vibration on mechanical characteristics of Bi-directional functionally graded beams under hygrothermal effect

Abstract

ABSTRACT The effect of free vibration on mechanical characteristics of bi-directional functionally graded material (BDFGM) beams under the influence of hygrothermal effects involves the application of the harmonic differential quadrature method (HDQM). The material parameters are supposed to vary in both axial and thickness directions. The temperature distribution is employed along the length direction of the BDFGM beams while maintaining a constant moisture concentration. An exponential law with axial thermal variation under moisture effect is investigated to analyse vibration behaviour in the BDFGM beams using the HDQM. Hamilton’s principle is used to obtain governing equations. Three kinds of temperature distribution profile were considered i.e. uniform (UTR), linear (LTR) and nonlinear temperature rise (NLTR). Free vibration analysis is performed using the HDQM. The precision of the HDQM is validated by comparing it with prior studies. Various configurations of boundary conditions, including supported, clamped, and free, are considered. Parametric results are investigated to explore the effect of the exponent parameters, temperature profile and constant humidity content. Results indicate that temperature, constant moisture content, material properties, and different end conditions significantly influence natural frequency. The outcomes can be applied to designing two or more directional FGM structures for different environmental conditions.