HAMILTONIAN-BASED FREQUENCY-AMPLITUDE FORMULATION FOR NONLINEAR OSCILLATORS

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.

A Novel Megastable Hamiltonian System with Infinite Hyperbolic and Nonhyperbolic Equilibria

The dimension of the conservative chaotic systems is an integer and equals the system dimension, which brings about a better ergodic property and thus have potentials in engineering application than the dissipative systems. This paper investigates the phenomenon of megastability in a unique and simple conservative oscillator with infinite of hyperbolic and nonhyperbolic equilibria. Using traditional nonlinear analysis tools, we found that the introduced oscillator possesses an invariable energy and displays either self-excited or hidden dynamics depending on the stability of its equilibria. Besides, the conservative nature of the new system is validated using theoretical measurement. Furthermore, an analog simulator of the oscillator is built and simulated in the PSpice environment to confirm that the previous results were not artifacts.

A more accurate solution of nonlinear conservative oscillator by energy balance method

Purpose The purpose of this paper is to present an analytical approximate technique to solve nonlinear conservative oscillator based on the He’s energy balance method (improved version recently presented by Khan and Mirzabeigy). The method is illustrated by solving double well Duffing oscillator. Design/methodology/approach The Duffing equation with a double-well potential (with a negative linear stiffness) is an important model of a mass particle moving in a symmetric double well potential. This form of the equation also appears in the transverse vibrations of a beam when the transverse and longitudinal deflections are coupled (Thompsen, 2003). Findings The approximate solutions obtained by the present technique have good agreement with the numerical solution and also provide better results than other existing methods. Originality/value The results are more accurate than those obtained by other existing methods. The relative errors obtained by the present paper are less than those obtained by other existing methods. Therefore, the present technique is very effective and convenient for solving nonlinear conservative oscillator.