Fast Finite Element Analysis of Frequency Responses for Elastic Block Supported by Plural Nonlinear Springs

Abstract

A fast computational method is proposed to calculate nonlinear vibration characteristics for elastic blocks supported by plural nonlinear concentrated springs using finite element method. The restoring force of the springs is expressed as power series of displacement. Finite elements for the nonlinear springs are added to the nodal force of elastic blocks modeled by linear solid finite elements. Further, the discretized equations in physical coordinate are transformed into nonlinear ordinary coupled equations using normal coordinate corresponding to linear natural modes. First, the proposed method for the case having plural nonlinear springs is verified. Next, as a numerical example, influences of Young's modulus on nonlinear frequency responses for the elastic blocks with nonlinear springs are demonstrated.