基于闭式解算法的粘弹性振子系统阻尼效应分析

Damping Effect Analysis of Viscoelastic Vibration Based on Closed Solution Algorithm

为了降低大型工程车辆在工作时产生的噪声及振动,以具有流体特性的Maxwell分数阶粘弹性振子作为研究对象,构建粘弹性阻尼缓冲模型。依据粘弹性材料的分数阶本构关系及动力学关系,建立分数阶数学模型,得到系统的动力学方程。并将离散后的Grünwald-Letnikov分数阶微分定义代入系统方程,得到系统的闭式解。对比分析正弦函数和单位冲激函数两种激励下系统参数变化对阻尼效应的影响。结果表明:微分方程的阶数及系数变化均对系统的阻尼效应产生不同程度的影响。该数值方法为工程车辆中粘弹性缓冲结构的阻尼效应分析提供了一种新的思路。

In order to reduce the noise and vibration of large engineering vehicles.By taking Maxwell fractional viscoelastic oscillator with fluid characteristics as the research object,the viscoelastic damping buffer model was constructed.According to the fractional constitutive relation and kinetic relation of viscoelastic materials,the fractional order mathematical model was established and the kinetic equation of the system was obtained.The discrete Grünwald-Letnikov fractional differential definition was taken into the system equation to obtain the closed-form solution of the system.The influence of system parameters on the damping effect under sinusoidal and unit impulse excitation was analyzed.The results show that the order and coefficient of the differential equation have different influence on the damping effect of the system.This numerical method provides a new way to analyze the damping effect of viscoelastic buffer structures in engineering vehicles.