Frequency Response Analysis of Elastic Blocks Supported by a Nonlinear Spring Using Finite Element Method (Investigation under Weak Nonlinearity)

Abstract

This paper describes vibration analysis using finite element method for an elastic block supported by a nonlinear concentrated spring. This block is connected to another block by a linear concentrated spring. The restoring force of the nonlinear spring has cubic nonlinearity. In this system, resonance responses mainly involve nonlinearity due to two vibration modes. Finite element for the nonlinear spring is expressed. Then the nonlinear spring element and linear spring element are combined to the elastic blocks modeled by linear solid finite elements. Further, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled differential equations using normal coordinate corresponding to linear natural modes. This transformation yields computation efficiency. Influences of Young's modulus on frequency responses are clarifed.