A Galerkin-type state-space approach for transverse vibrations of slender double-beam systems with viscoelastic inner layer

A free interface component mode synthesis method for viscoelastically damped systems

“…Some research approaches are devoted to efficiently solving the eigenvalue problem. One of these approaches is the state-space approach [28,[33][34][35][36][37][38]62,63] which constructs a linear eigenvalue problem by introducing some internal variables. Also, some approximate approaches [38][39][40][41][42][43][44][45] are presented to solve the eigenvalue problem for the exponential-like viscoelastic damping models.…”

“…Some researchers [33][34][35][36][37][38][39][40][41][42][43][44][45] developed methods to efficiently solving the viscoelastic damping models and most of these methods considered the viscoelasitcally damped structure as a whole. In practice, a large or complicated structure is usually composed of several parts which may have different levels of energy dissipation, thus making the viscoelastic damping models differ from each other.…”

Direct Time-Domain Integration Approach for Viscoelastic Systems Involving Various Damping Models

“…The system matrices are given by 10 The eigenvalues and eigenvectors of the four DOF system are list in paper [32]. However, for large-scaled problems, it is often unnecessary and impossible to obtain all the eigenpairs of the system, the high-order mode truncation problem is frequently encountered and leads to errors [33][34][35][36].…”

“…In recent years, researchers have considered the dynamic responses of nonviscous damping models. Some authors developed exact state-space approaches [4][5][6][7][8][9][10][11][12] based on internal variables. Others proposed approximated approaches [13][14][15][16][17][18][19][20] and model reduction methods [21][22][23][24][25][26] to solve the eigenproblem for the exponential-like damping models.…”

Dynamics of structural systems with various frequency-dependent damping models

“…In general, these approaches of solving these nonlinear eigenvalue problems can be split into state-space approaches [20,21,[33][34][35][36][37] and real modes based approaches [38][39][40][41][42][43][44][45][46]. These state-space approaches transform the nonlinear eigenvalue problem into a linear eigenvalue problem by using some additional internal dissipation variables.…”