一种利用复阻尼理论计算结构自由振动响应的数值方法

A numerical method for analyzing the structural free vibration responses based on complex damping theory

复阻尼理论的运动方程通解中包含有发散项,导致结构自由振动响应不能稳定收敛。在复阻尼理论的频域微分方程基础上,修正阻尼项,进而得到滞变阻尼理论表达式,可保证结构自由振动时程计算结果的稳定性。针对滞变阻尼理论的特点,本文依据正弦函数的希尔伯特变换,提出了相应的时程计算方法,可有效计算滞变阻尼理论下结构的自由振动响应。算例分析表明:基于滞变阻尼理论的结构自由振动响应是稳定收敛的,且与黏性阻尼理论计算结果近似相等;相比基于滞变阻尼理论的直接积分法,本文方法具有计算过程简单和计算量小的优点。

The inclusion of divergent items in general solution to the motion equation via the complex damping theory makes the structural free vibration response not stably convergent.Based on frequency domain differential equation of the complex damping theory,a hysteretic damping theory can be obtained.The hysteretic damping theory has the advantage that energy consumption is not related to external excitation frequencies in every cycle.It also guarantees the stability of the structural time-history calculation.The time-history calculation method is put forward,according to the characteristics of hysteretic damping theory and Hilbert transform of sine function.Themethod can effectively calculate structural free vibration responses via hysteretic damping theory.The analysis results of examples show that structural free vibration responses based on hysteretic damping theory are stably convergent.The calculation results are approximately equal to the results based on viscous damping theory.Compared with the direct integral method based on hysteretic damping theory,the suggested method has the advantages that calculation process is simple and calculation cost is small.