Time-domain calculation method of improved hysteretic damped system based on frequency-dependent loss factor

Abstract

Hysteretic damping model is consistent with experiment results within a wide frequency range, and is usually employed in structural dynamic analysis. However, hysteretic damping time-domain model has the two shortcomings, namely damped natural frequency increases with the increase of structural loss factor and the vibration response is non-causal. In order to overcome the two shortcomings, an improved hysteretic damping time-domain model based on frequency-dependent loss factor (IHDT) is proposed. Combined with strain energy method, a mode superposition method based on IHDT is further proposed, then an approximately linear time-domain calculation method (RIHDT) can be realized for multi-degree-of freedom hysteretic damped system. Shaking table test is conducted for cantilever plates composed of host and damping layers to validate the proposed method. Structural vibration responses under random excitations are obtained in the test, which are compared with the corresponding simulation results obtained by RIHDT and the time-domain method based on Rayleigh damping model (RT), respectively. The calculation results of RIHDT and RT are both similar to the test results under external excitation within low vibration frequencies. However, compared with RT, the calculation results of RIHDT are unique and the problem of choosing reasonable modes is avoided. For the test results of external excitation within high vibration frequencies, the computational accuracy of RIHDT is higher than the corresponding one of RT, since the contributions of higher vibration modes are not underestimated by RIHDT. Besides, RIHDT is based on the damping properties of materials, which makes the calculation process simple.