Abstract
Complex mechanical systems usually include nonlinear interactions between their components which can be modeled by nonlinear equations that describe the sophisticated motion of the system. In order to interpret the nonlinear dynamics of these systems, it is necessary to compute their nonlinear frequencies more precisely. 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.