A Time-History Analysis Algorithm of a Non-viscously Damped System Using Gauss Precise Integration

Time-history analysis of a multiple-degree-of-freedom system with non-viscous damping was considered. It was assumed that the non-viscous damping forces depend on the past history of velocities via convolution integrals over exponentially decaying kernel functions. By transforming the equation of motion into a first-order extended state-space representation and combining the Gauss-Legendre quadrature with the calculation technique of matrix exponential function in the precise time-integration method, a more applicable time-history analysis method of this system was proposed. The main virtues of the proposed method were the avoidance of matrix inversion, the high efficiency and the selectable accuracy. A numerical example was given to demonstrate the validity and efficiency of the method.