A single-step recursive algorithm of the convolution integral for computing non-viscous damping forces in dynamic analyses

The non-viscous damping force features the convolution integral of the velocity and the kernel function, causing the difficulty of the solutions of the system equation of motion due to the nonlocal time dependence. In accordance with the linear time-invariant system theory in signal processing, this paper presents a single-step recursive algorithm of convolution integral for efficiently computing non-viscous damping forces. The algorithm parameters are effectively identified from the discrete responses of the kernel function to the rectangular unit impulse through digital filter technologies. The proposed algorithm is compatible with the solution schemes based on existing time integration methods, which handle the nonlocal dependence using internal recursive support vectors while leaving the order of the equation of motion unchanged. The central difference method, the Newmark-ss method, and the Bathe method are employed to illustrate the use of the algorithm, proving to retain the stability characteristics of time integration methods. The single and multiple DOF examples show that the simulated results based on the compatible solution schemes compare well with those built on other existing methods, verifying high accuracy and efficiency. The proposed algorithm thus extends the application range of existing time integration methods from the viscously damped system to the non-viscously damped one, fully demonstrating its generalizability.