EXACT NON-ORTHOGONAL MODAL SUPERPOSITION SOLUTIONS OF TRANSIENT RESPONSE OF MDOF DISSIPATION STRUCTURES WITH GENERAL LINEAR VISCOELASTIC DAMPERS

The exact non-orthogonal modal superposition solutions of transient response of MDOF dissipation structures with general linear viscoelastic dampers including elastomeric isolators are studied systematically. By using the general integral models of viscoelastic dampers, which are the most general exact models of linear viscoelastic dampers, the exact dynamic integral-differential response equations in original structural space for MDOF dissipation structures with general linear viscoelastic dampers are established. Then, by using transfer matrix method, the exact non-orthogonal modal superposition solutions in original structural space for displacement and velocity transient response of MDOF dissipation structures with general linear viscoelastic dampers due to arbitrary exterior forcing loadings and initial conditions are obtained. It is verified that these exact solutions are correct, general, simple, direct, and provide better physical insights through solutions in comparison with three kinds of more general typical dissipation structures. These exact solutions in original structural space are similar to the classical modal superposition results for proportionally damped structures usually obtained using the mode-orthogonality relationships, and can exactly discover the vibration characteristics of viscoelastic dissipation structures, namely: though the dissipation structural modes are not orthogonal, the dynamic equations can not be decoupled by using structural modes, the structural transient response can be exactly expressed in terms of a superposition of individual modal response. Therefore, by using above characteristics, it may be possible to extend the existing modal superposition response spectrum method, structural identification, model updating, optimization, and control algorithms available for viscously damped structures to general viscoelastically damped structures.