2007 年 2 巻 3 号 p. 578-589
This paper describes vibration analysis using the finite element method (FEM) for a viscoelastic block supported by a nonlinear concentrated spring. The restoring force of the spring exhibits cubic nonlinearity and linear hysteresis damping. The finite element for the nonlinear spring is expressed and is connected to the viscoelastic block, which is modeled using linear solid finite elements taking into consideration the complex modulus of elasticity. Further, the discretized equations in physical coordinate are transformed into nonlinear ordinary coupled equations using normal coordinate corresponding to the linear natural modes. Note that modal damping is also transformed without inconsistency in this procedure. This transformation can save computational time. Further, by applying the harmonic balance method to the transformed equations, steady-state nonlinear frequency responses are computed with fairly small degree of freedom. The influence of Young's modulus of the blocks on the nonlinear responses is clarified. Moreover, the influences of dissipated energy on the nonlinear frequency responses for the viscoelastic block are clarified.
