Equivalent One-Dimensional Spring-Dashpot System Representing Impedance Functions of Structural Systems with Non-Classical Damping

Abstract

This paper describes the transformation of impedance functions in general structural systems with non-classical damping into a one-dimensional spring-dashpot system (1DSD). A transformation procedure based on complex modal analysis is proposed, where the impedance function is transformed into a 1DSD comprising units arranged in series. Each unit is a parallel system composed of a spring, a dashpot, and a unit having a spring and a dashpot arranged in series. Three application examples are presented to verify the applicability of the proposed procedure and the accuracy of the 1DSDs. The results indicate that the 1DSDs accurately simulate the impedance functions for a spring-dashpot-mass structure, a truss frame structure, and a plate structure. The 1DSD transformation offers compatibility with complex modal analysis: a large number of units associated with high modes beyond a target frequency region can be removed from the 1DSDs as an approximate expression of impedance functions. The accuracy of the approximated 1DSDs can be improved by incorporating an additional unit associated with the residual stiffness that compensates for the effect of high modes. A marked decrease in the computational domain size and time with the use of the 1DSDs is of great scientific and engineering importance in diverse technological applications.