Substructure Synthesis Methods for Viscoelastic Structures

摘要

Viscoelastic damping models are necessary for accurate dynamic analysis offlexible aerospace structures. The method of substructure synthesis is extended to systems with general linear viscoelastic damping. The stationary variational principles for discrete symmetric and nonsymmetric viscoelastic systems are first developed in parallel for the time, Laplace, and frequency domain. The corresponding substructure synthesis methods are then formulated. On the basis of the Rayleigh-Ritz method, each substructure is represented by a set of admissible trial vectors. Real trial vectors, such as eigenvectors and Lanczos vectors of the corresponding undamped substructure as well as Ritz vectors obtained by spatial discretization of simple functions, are recommended. The geometric compatibility between substructures can be approximated by a weighted residual method, and the traditional state space formulation is avoided. The effort involved in the reduction process is almost independent of the complexity of viscoelastic models. Beam and plate examples are presented to illustrate the effectiveness of the substructure synthesis method in terms of reducing the size of final equations to obtain accurate solutions of eigenvalues, frequency responses, and transient responses for viscoelastic symmetric systems.