A generic time domain implementation scheme for non-classical convolution damping models

A generic time domain integration formulation for linear systems with non-classical convolution damping models is presented. The non-classical damping force is assumed to depend on the past history of velocity through a convolution integral over a causal dissipative kernel function. The time domain implementation formulation is developed using the Newmark constant average acceleration framework. To emphasize the accuracy of the proposed scheme, numerical comparisons are made for a three-degrees-of-freedom system and an axially vibrating rod problem reported in literature. The generality of the formulation is shown by simulating the response of a cantilever beam enhanced with two known standard dissipation functions: the exponential and the Gaussian model. The implementation of the proposed scheme is also presented.