Dynamic analysis of the non-viscously damped structure using the superposition of first-order IIR filters

Abstract The convolution integral of the velocity and the general kernel function in the motion equation of a non-viscously damped structure makes the numerical solution difficult. According to the consistent motion assumption and the linear time-invariant system theory in signal processing, the single-step recursive formulations replacing the convolution integral derive from viewing the kernel function as the superposition of first-order IIR filters. The time integration formulations incorporating the recursive expressions are then derived, and correspondingly a computational scheme is proposed for the dynamic analysis of the structure. Due to introducing the internal support vectors, the one ensures that the computational amount of the non-viscously damped system is nearly in proportion to the needed analysis time and slightly higher than that of the linear viscous-damping system. The scheme stability is studied using the spectral radius theory and proves conditional. The scheme applies to two numerical examples. Consequently, the computational results compare well with those based on other methods, confirming the scheme’s accuracy.