期刊
JOURNAL OF LOW FREQUENCY NOISE VIBRATION AND ACTIVE CONTROL
卷 42, 期 1, 页码 89-109出版社
SAGE PUBLICATIONS LTD
DOI: 10.1177/14613484221118177
关键词
He's frequency formula; nonlinear oscillation; Toda oscillator; Helmholtz-Duffing oscillator; Zhiber-Shabat oscillator; tangent oscillator; nonlinear singular oscillator
类别
The main focus of this work is the comprehensive formularization of the frequency-amplitude formula, covering higher powers of the restoring force. Three equivalent styles of the generalized frequency amplitude have been proposed, along with the formulation of three forms of non-secular forces for the first time. These advances have been applied to the linearized Duffing oscillator, enriching the analysis and providing advantages for high nonlinearity vibration.
The comprehensive formularization of the frequency-amplitude formula is the main interest in this work to cover higher powers of the restoring force which are not limited to cubic powers. Three equivalent styles of the generalized frequency amplitude have been performed. In addition, the restoring force is not restricted to an odd function in which the non-secular forces are included. Three forms of the non-secular forces have been formulated for the first time and treated as non-homogenous of the linearized Duffing oscillator. The modified style of He's formula has been applied to the singular oscillator using the enhanced potential function. The simplicity of the present approach provides extra advantages for high nonlinearity vibration. This method enriches the analysis with more details in new dimensions.
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