On the Dynamic Instability of an Imperfect Microbeam under Magnetic and Thermal Excitations
Abstract
Magnetoelastic microbeams play a major role in various remote sensing and biomechanical applications. However, electromagnetic and thermal interactions are considered key challenges in magneto-solids mechanics. To this end, this research paper investigates the regions of dynamic instability and the transient response of a microbeam subjected to periodic transverse magnetic fields and thermal loads. The study employs a magnetoelastic model of a micro-beam with an imperfection represented by a half-sine rise. The material is characterized as nonlinear thermoelastic, incorporating nonlinear strain. The governing partial differential equation of motion is obtained as a nonlinear, time-dependent Mathieu’s equation, employing Galerkin’s method and considering the first mode shape. The investigation of dynamic instability is conducted utilizing the incremental harmonic balance method. The effect of the variations in the initial rise, temperature increment, and amplitude on the dynamic instability are illustrated and analyzed. In addition, the transient midspan vibration is studied under various cases involving alterations in transverse magnetic field strength, temperature increment, and oscillating transverse magnetic field excitation frequency, with and without initial rise. Finally, deliberate variations in the excitation frequency are selected to examine the system dynamic transitions across the instability boundary, revealing the presence of beating and pseudo-unstable phenomena.