Analysis of damped vibration for a viscoelastic block supported by a nonlinear concentrated sping using FEM

This paper describes vibration analysis using finite element method for a viscoelastic block supported by a nonlinear concentrated sping. The restoring force of the spring has cubic nonlinearity and linear hysterisis damping. Finite element for the nonlinear spring is expressed and is connected to the viscoelastic block modeled by linear solid finite elements in consideration with complex modulus of elasticity. 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 share of dissipated energy on nonlinear frequency responses for the viscoelastic block are clarified.