Dynamic analysis of linear and bilinear oscillators with rate-independent damping

Energy loss in many materials is essentially independent of the exciting frequency and can be modeled as rate-independent damping. However, the model of rate-independent damping is only available for calculating the steady-state response of harmonic excitation. The transient response of the rate-independent damping model is noncausal. A procedure to ensure that the calculated response of the rate-independent damping model conforms to the prescribed condition at the initial time is proposed in this paper. At first, response functions excited by unit initial displacement change and unit initial velocity change, respectively, are derived in the frequency domain. A free-vibration response composed by these unit response functions is then superposed on the steady-state response solved by the discrete Fourier transform, so that the calculated transient response can satisfy the initial condition. Because the bilinear elastoplastic system can be treated as a combination of multiple linear-model stages, the proposed method is extended to calculate the transient response of the bilinear model with rate-independent damping.