Analysis of Damped Vibration for Viscoelastic Blocks Connected by a Nonlinear Spring with Linear Hysteresis Using FEM Described by Normal Coordinate

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This paper describes a vibration analysis study using the finite element method (FEM) for two viscoelastic blocks connected by a nonlinear concentrated spring. One of these blocks is supported by a linear concentrated spring. The restoring force of the spring is expressed as a power series of the relative displacement between the blocks. This restoring force includes linear hysteresis damping. Therefore, a complex spring constant is introduced for the linear component of the restoring force. The finite elements for the spring are expressed and they are attached to the viscoelastic structures, which are modeled as linear solid finite elements. The discrete equations in terms of physical coordinates are transformed into nonlinear ordinary coupled equations using normal coordinates corresponding to the linear natural modes. These transformed equations are then computed to obtain the nonlinear frequency responses with a fairly small degree of freedom. The effectiveness of this analysis is checked using a basic mass-spring model. Moreover, the influences of the storage modulus of the blocks on the nonlinear responses are clarified. Further, the influences of the dissipated energy on the nonlinear frequency responses of the viscoelastic blocks are investigated.