A method to formulate the equations of motion of viscoelastic substructures in terms of constant mass, damping and stiffness matrices, similar to those of elastic structures, is presented. Classical Generalized Maxwell spring-dashpot model is used for modeling the constitutive relationship of viscoelastic materials. This formulation enables reduction techniques to be used to efficiently represent the viscoelastic behavior in generalized coordinates and the removal of rigid body modes in dissipation coordinates. Consequently, many solution techniques and tools for linear elastic structures can be used for complex structures with viscoelastic materials. When the substructure consists of only one element, the substructure degenerates into a viscoelastic finite element. This enables stiffness and damping matrices of viscoelastic elements to be derived directly from the corresponding elastic element stiffness matrix. An example of vibration analysis of a beam with elastic and viscoelastic materials, and an example of a beam element formulation are presented.
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