Numerical and experimental study of impact dynamics of bistable buckled beams

Abstract

Bistable systems have been of great research interest due to their rich dynamics arising from a variety of excitations. This study presents an investigation into the nonlinear dynamics of a continuous bistable beam subjected to a form of vibro-impact forcing. A fixed–fixed Euler–Bernoulli beam, precompressed to achieve bistability, is considered, while a shaker with sinusoidally-prescribed velocity applies transverse impact forcing. By varying excitation parameters such as frequency and amplitude, the system response can be tuned. The study begins by employing a Galerkin expansion to the continuous equation of motion, using the buckling modes to remove buckling level dependence and ensure equilibrium symmetry. A Hertzian contact law is chosen to model the collision between the shaker and the buckled beam. The rich dynamics of this system are then explored through numerical and experimental analyses. The focus lies on investigating the emergence of intrawell and interwell dynamics that arise with varying excitation frequency, amplitude, and location. Moreover, we evaluate the significance of including higher-order modes in the modeling of bistable beam dynamics, particularly near snapthrough. This research provides valuable insights into the behavior of continuous bistable structures under vibro-impact forcing, contributing to the understanding and control of such systems in engineering applications.