一种不对称滞回受迫振动系统及其分析

Analysis of a Forced Vibration System with Asymmetrical Hysteresis

许多系统或结构在动载荷作用下会表现出非线性滞回行为。通常情况下，人们往往认为滞回环是对称的。但是，在工程实际中还存在一些特殊的、不对称的滞回现象。例如，在对物料进行振动压实的过程中，由于压实机构的压下和回程中物料弹塑性变形规律不同，该振动压实系统存在不对称的滞回恢复力。本文提出用一种不对称模型描述这种不对称滞回性质，该不对称滞回模型由分段曲线组成。文章对这类系统在简谐激励下的响应特征进行了分析，得到一次近似解析解以及特有的直流分量和二次谐波等成分。然后又通过实验和数值模拟分别验证了模型的合理性。

Many systems and structures under dynamic loading usually exhibit nonlinear hysteretic behavior. In practice, most hysteretic loops are considered to be symmetrical. However, there do exist some asymmetrical hysteretis Loops in practice. For example, in the process of vibration compacting of materials, the way of materials elastic plastic deforming when loading is often quite different from the way when unloading. So the vibrator together with the materials(i.e. vibration compacting system) is considered as a nonlinear vibration system with an asymmetrical hysteretic force. Based on experimental results, a piece wise model is proposed to describe such an asymmetrical hysteretic loop. We have also analyzed the steady response of the system excited by a sinusoidal force, and obtained explicitly the first order harmonic component together with direct current component and the second, third harmonics. In addition, numerical simulation data and experiment results have verified that this kind of asymmetrical hysteretic model is much better fit with the real case than other symmetrical models commonly used.