HAMILTONIAN-BASED FREQUENCY-AMPLITUDE FORMULATION FOR NONLINEAR OSCILLATORS

Ji-Huan He, Wei-Fan Hou, Na Qie, Khaled A. Gepreel, Ali Heidari Shirazi, Hamid Mohammad- Sedighi

DOI Number
10.22190/FUME201205002H
First page
199
Last page
208

Abstract


Complex mechanical systems usually include nonlinear interactions between their components which can be modeled by nonlinear equations describing the sophisticated motion of the system. In order to interpret the nonlinear dynamics of these systems, it is necessary to compute more precisely their nonlinear frequencies. The nonlinear vibration process of a conservative oscillator always follows the law of energy conservation. A variational formulation is constructed and its Hamiltonian invariant is obtained. This paper suggests a Hamiltonian-based formulation to quickly determine the frequency property of the nonlinear oscillator. An example is given to explicate the solution process.


Keywords

He’s frequency formulation, Ancient Chinese mathematics, Semi-inverse method, Periodic solution

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References


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