Resonances of a forced van der Pol equation with parametric damping

被引：7

作者：

Afzali, Fatemeh ^{[1
]}

Kharazmi, Ehsan ^{[2
]}

Feeny, Brian F. ^{[1
]}

机构：

[1] Michigan State Univ, E Lansing, MI 48824 USA

[2] Brown Univ, Providence, RI 02912 USA

来源：

NONLINEAR DYNAMICS | 2023年 / 111卷 / 06期

基金：

美国国家科学基金会;

关键词：

Parametrically excited van der Pol oscillator; Parametric damping; Method of multiple scales;

D O I：

10.1007/s11071-022-08026-w

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

This work entails an analysis of secondary resonances in the parametrically damped van der Pol equation, with and without external excitation. A potential application of this system is a vertical-axis wind-turbine blade, which can have cyclic damping, aeroelastic self-excitation, and direct excitation. We analyze the system using the method of multiple scales and numerical solutions. For the case without external excitation, the analysis reveals nonresonant phase drift (quasiperiodic responses) and subharmonic resonance with possible phase drift or phase locking (periodic responses). The case of external excitation consists of a constant load and a harmonic load with the same frequency as the parametric term. Hard excitation is treated for nonresonant conditions and secondary resonances. Subharmonic and superharmonic resonances show possible phase drift and phase locking. Primary resonance is observed but not analyzed here.

引用

页码：5269 / 5285

页数：17

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