Effects of internal resonance on the nonlinear acoustic radiation induced by axial and bending vibration of hyperelastic cantilever beams

Abstract

This paper provides a numerical nonlinear vibro-acoustic study of a slender hyperelastic cantilever beam with 2:1 internal resonance condition. The model of beam includes geometric and material nonlinearities, while the model of acoustics includes the Arbitrary Lagrangian-Eulerian frame and the perfectly matched layers. The finite element method and the time integration method are used to discretize the structure and acoustic field. A loosely coupled serially staggered procedure is used to compute the variable values of structure and acoustic field. The results show that the transition from the axial mode to the bending mode of beam can be excited by the axial mode excitation. This leads to the alteration of acoustic directivity pattern and frequency components. Besides, due to the weak or strong coupling effects of axial and bending modes of beam, the symmetric or asymmetric acoustic directivity patterns can be witnessed in different frequency components.