Reformulated Strain Gradient (Rsg) Elasticity Theory for Free Vibration of Thermal Bi-Directional Fg Microbeam

Abstract

This research examines the vibrational response of a micro-scale Euler beam made from two-directional functionally graded (2D-FG) materials and subjected to thermal effects. By employing a reformulated strain gradient elasticity (RSGE) approach, the equations of motion using Hamilton’s principle for clamped -clamped and clamped-simply boundary conditions are derived and solved them using Galerkin's approach. The investigation explores the impact of temperature, gradient index, and parameters length scale materials on the bidirectional graded microbeam's dynamic characteristics. Furthermore, the normalized frequency, as based on the current reformulated strain gradient elasticity microbeam model, consistently emerges as higher than that derived from the classical model.