Nonlinear Vibration of a Heated Rectangular Thin Plate with Two Stick-slip-stop Boundaries

Abstract

This study deals with the nonlinear dynamics of a uniformly heated and simply-supported rectangular thin plate in the presence of two adjacent in-plane stick-slip-stop boundaries in order to release the thermal stresses in the plate. The analysis of linear vibration of the plate shows that the natural frequency of mode (2, 1) decreases with an increase of temperature and may coincide with the natural frequency of mode (1, 1) if the assembly forces on the in-plane movable boundaries are not very strong. Hence, the study focuses on the one-to-one internal resonance of the plate subject to weak assembly forces and temperature rise. Both analysis and numerical examples show that the one-to-one internal resonance happens for different combination of excitation amplitude and assembly forces, and exhibits a great variety of periodic, quasi-periodic and chaotic vibrations.