考虑形状参数的分数黏弹性振子频响特性

FREQUENCY RESPONSE OF FRACTIONAL VISCOELASTIC OSCILLATOR CONSIDERING GEOMETRIC FACTOR

黏弹性振子为描述黏弹性减振降噪结构的基本物理单元。针对传统黏弹性振子整数阶模型较差的试验拟合性和无几何标度性,提出了考虑形状参数的分数黏弹性振子模型及建立其动力学方程的一般方法,并推导出频响函数。以其中典型分数黏弹性振子(SFVEO)为例研究了频响特性及参数影响性。数值算例表明,幅频响应存在谐峰值,相频响应存在转折频率,两者均受系统参数(固有频率、分数阶数、形状参数和阻尼比)影响;固有频率、阻尼比和形状参数均在低频段对幅频响应有显著影响,分数阶数则在高频段存在明显影响;各参数对相频响应在低频段有明显作用。为黏弹性缓冲减振结构的设计和多目标优化提供理论参考。

Viscoelastic oscillator （VEO） is a basic physical element used to characterize viscoelastic damper. To address the common drawbacks of the conventional integer derivative model of VEO, the fractional VEO considering geometric factor is proposed and its frequency response function is derived. The SFVEO, one of the representative VEOs, is adopted as the study case for investigating the frequency characteristics and parameter influence. The numerical results show that there are harmonic peaks in the amplitude-frequency response and comer frequencies in the phase-frequency response. The harmonic peaks and the comer frequencies are influenced by system parameters including natural frequency, fractional order, geometric factor and damping ratio. Natural frequency, damping ratio and geometric factor exhibit notable impact on the amplitude-frequency response at low frequency-ratio stage, while fractional order strongly affects it at high frequency-ratio stage. All parameters display evident impact on the phase-frequency response at low frequency-ratio stage. This study can provide essential theoretical references for the design and multi-object optimization of the viscoelastic damper.