Nonlinear isolation of transverse vibration of pre-pressure beams

Abstract

Research on nonlinear isolation has always focused on the vibration of discrete systems. The elastic vibration of the main structure itself is always ignored. In order to study the influence of the multimodal elastic vibration of the main structure on the nonlinear isolation effect, nonlinear isolation of the transverse vibration of a pre-pressure elastic beam is studied in this paper. Three linear springs are utilized to build a nonlinear isolation system, in which horizontal springs are utilized to provide non-linearity and to achieve quasi-zero stiffness. The transverse vibration of the beam is isolated by the elastic support at the two ends. The Galerkin truncation method (GTM) is used to solve the response of the forced vibration. The isolation effect of the primary resonance of the pre-pressure beam is presented. The effects of the axial pre-pressure and nonlinear isolation system on vibration transmission are explored. Results of the GTM are confirmed by utilizing the finite difference method (FDM). It also illustrates the effectiveness of the proposed difference method for nonlinear support structures. The numerical results demonstrate that under certain conditions, the quasi-zero stiffness isolation system may increase the transmission of high-order modal vibration of the elastic continuum. Furthermore, this work finds that the initial axial pre-pressure could be beneficial to vibration isolation of elastic structures.