单自由度系统强迫振动下Kelvin模型和Maxwell模型的比较

A Comparison Study on Kelvin and Maxwell Model for a Forced Single Degree-of-freedom System

以Kelvin模型和Maxwell模型为对象,研究了单自由度系统强迫振动下2种模型的系统响应。首先,将单自由度强迫振动分为简谐激励下的强迫振动、偏心质量引起的强迫振动和支承运动引起的强迫振动3种情况,分别在这3种情况下建立了2种模型的运动微分方程,并得到了系统的解析解。随后,通过解析解得到了振幅放大因子和相位差的解析式,研究了系统的幅频响应曲线和相频响应曲线。通过比较2种模型的幅频响应曲线,发现在偏心质量和支承运动引起的强迫振动情况下Maxwell模型在小阻尼时振动控制效果远优于Kelvin模型。

Considering the Kelvin and Maxwell model as the research objects, the system responses for the two models are studied based on forced vibration of single degree-of-freedom system. First, the forced vibration is divided into three conditions, such as forced vibration under harmonic excitation, eccentric quality and supporting motion. Under the three conditions, the analytical solutions of the two models are obtained based on the established motion differential equation. Then the analytical formula of amplitude magnification factor and phase difference are obtained, and the amplitude-frequency response curve and phase-frequency response curve are drawn out respectively. By comparing the amplitude-fre- quency response curves of the two models, it could be concluded that the control performance of Max- well model is much better than that of the Kelvin model in the ease of small damping, which is useful to the design and revision of vibration system.