State-space based time integration method for structural systems involving multiple nonviscous damping models

• A direct time integration method for nonviscously damped system is proposed.
• An extended state-space method is developed.
• A general nonviscously damped model is proposed.
• The method is applicable to systems involving multiple damping models.
• Two examples are given to show the accuracy and efficiency of the method.

Engineering structures are often assembled by subsections with various levels of energy dissipation, which lead to great difficulties in analyzing. In this paper, a direct time integration method is proposed to solve the dynamic responses of structural systems involving multiple nonviscous damping models. Based on a general non-viscously damped model, an extended state-space scheme for the damped system is derived. Then, an implicit time integration method using linear approximations is developed built on the extended state-space formalism. The stability and efficiency of the method are discussed by theoretical and numerical analyses. The method is illustrated by two examples.