论文标题
机械系统的相共振非线性模式
Phase resonance nonlinear modes of mechanical systems
论文作者
论文摘要
当发生频率响应的幅度发生局部最大值（振幅共振）或相位滞后正交正交（相位共振）时，强制动力学系统的共振会发生。这项研究的重点是遭受单点谐波激发的非线性机械系统的相共振。在这种情况下，本文的主要贡献是开发一个计算框架，该框架可以预测相共振的模式形状和振荡频率。所得的非线性模式称为相共振非线性模式（PRNMS）。 PRNM的一个关键特性是，除了初级共振外，它们还可以准确地表征超谐音，亚谐波和超矛盾的共振，如本文所示，共振的相位滞后可能与pi/2不同。使用具有立方非线性的一级和两度自由系统的系统证明了所提出的发展。
The resonances of forced dynamical systems occur when either the amplitude of the frequency response undergoes a local maximum (amplitude resonance) or phase lag quadrature takes places (phase resonance). This study focuses on the phase resonance of nonlinear mechanical systems subjected to single-point, single-harmonic excitation. In this context, the main contribution of this paper is to develop a computational framework which can predict the mode shapes and oscillation frequencies at phase resonance. The resulting nonlinear modes are termed phase resonance nonlinear modes (PRNMs). A key property of PRNMs is that, besides primary resonances, they can accurately characterize superharmonic, subharmonic and ultra-subharmonic resonances for which, as shall be shown in this paper, phase lags at resonance may be different from pi/2. The proposed developments are demonstrated using one- and two-degree-of-freedom systems featuring a cubic nonlinearity.
