A modal projection-based reduction method for transient dynamic responses of viscoelastic systems with multiple damping models

Abstract Large and complex engineering systems are usually assembled by subcomponents with different energy dissipation levels. Therefore, these systems often contain multiple damping models, which may lead to great difficulties in analyzing efficiently. In this paper, an efficient modal projection-based reduction method, which accounts for transient dynamic responses of structural system with multiple damping models, is proposed in the framework of a modified precise integration method. Two robust modal reduction bases, namely multi-model method (MM) and modal strain energy by first-order correction method (MSEC), are introduced to reduce the order of the original system. Based on the reduced system and a general damping model (GDM), a reduced state-space formalism for the structural system with multiple damping models is developed. Finally, the transient dynamic responses are derived using a modified precise integration method on the reduced stage. The numerical stability, accuracy and complexity are discussed. Two numerical examples are illustrated to assess the performances of the computational accuracy and efficiency. The results indicate that the proposed method is more efficient than other methods and most suitable for large-scale problems with rather good accuracy.