Finite Element Analysis for Coupled Vibrations of an Elastic Block Supported by a Nonlinear Spring (Investigation under Weak Nonlinearity)

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