Active tuning and maximization of natural frequency in three-dimensional functionally graded shape memory alloy composite structures using meshless local Petrov–Galerkin method

Abstract

A mesh-less method based on the local Petrov–Galerkin approach is developed and numerically implemented for active tuning and three-dimensional (3D) analysis of free vibration response of functionally graded (FG) shape memory alloy (SMA) sandwich composites. The local symmetric weak formulation is derived based on the 3D equilibrium equations of elasticity and the field variables are interpolated using the moving-least squares approach. Two main goals are followed. Firstly, free vibration analysis of a sandwich plate made of a SMA fiber reinforced composite core and two FG face sheets are presented. A parametric study is performed to investigate the influences of design parameters on the fundamental natural frequency (FNF) of composite structure and also maximize that. Secondly, SMA wires are embedded to fiber reinforced (FR) composite structures to enable precisely active control of their dynamic characteristics and change that in a required manner. To increase the controllability level and tune the complex exhibits, functionally graded shape memory alloys are considered which have the advantage of combining the functionalities of the shape memory effect and those of FG structures. This paper uses multi-layer activation patterns and the polynomial graded orientation angle of SMA wire along the structure thickness to furnish the FR composite designer with a powerful free vibration control tool. Finally, two activation techniques of SMA wires, the active property tuning (APT) and the active strain energy tuning (ASET) techniques, are compared. It is concluded from all investigated cases that the obtained FNF of ASET technique is always larger than the APT technique.