Nonlinear dynamics of contact interaction porous size-dependent Euler-Bernoulli beams resonators with clearance: Numerical analysis of the stability problem

Abstract

In this study, a new mathematical model is developed to study the contact interactions of nano- and micro-electro-mechanical (NEMS/MEMS) beam resonators. The structural elements are considered as porous, size-dependent Euler-Bernoulli beams subjected to a variable transverse load. The beams resonators are located one above the other with minimal clearance. The analysis includes interactions between beams of both linear elastic and physically nonlinear materials, following the approach of Professor B. Ya. Kantor. Modified Coupled Stress Theory (MCST) is used to account for size-dependent effects. Hamilton's principle is applied to derive new size-dependent equations of motion together with the corresponding boundary and initial conditions. This study presents a new approach to the analysis of the chaotic dynamics of the contact interaction of porous, size-dependent Euler-Bernoulli beams. They are considered as systems with an "almost" infinite number of degrees of freedom. This innovative approach uses Principal Component Analysis (PCA) and Wavelet Analysis to filter out noise from signals. In addition, different beam interaction scenarios are classified including static Euler and Rayleigh instabilities as well as interactions between Koning-Taub and Richtmeyer-Meshkov instabilities. A significant discovery of this investigation is the chaotic behaviour of nonlinear vibrations during the contact interaction of these closely positioned beams. This demonstrates the complex dynamics involved in these high technology mechanical systems.