A generalized complex eigenvector method for dynamic analysis of heterogeneous viscoelastic structures

A generalized complex eigenvector method which can be used to a linear dynamic analysis of viscoelastic structures is described. Here dynamic analysis is understood as transient analysis and frequency response analysis. The generalized complex eigenvector method is based on nite element discretization of structure, approximation of viscoelastic properties by di erential operators and mode superposition technique. Coe cients of di erential operator are de ned from the condition of best coincidence of complex characteristic of viscoelastic material and complex characteristic of di erential operator in preset frequency range. Advantage of this method is that it allows to take into account the real changes of the viscoelastic property in frequency range. Also, the generalized complex eigenvector method permit to describe a viscoelastic properties by two functions (complex Youngʹs modulus, complex Poissonʹs ratio). The method is veri ed with the help of comparing with solutions obtained by complex modulus method. An in uence of viscoelastic Poissonʹs ratio on transient and frequency responses of structure is demonstrated