Nonlinear Oscillators with a Power-Form Restoring Force: Non-Isochronous and Isochronous Case

Abstract:

This work is concerned with single-degree-of-freedom conservative nonlinear oscillators that have a fixed restoring force, which comprises a linear term and an odd-powered nonlinear term with an arbitrary magnitude of the coefficient of nonlinearity. There are two cases of interest: i) non-isochronous, when the system has an amplitude-dependent frequency and ii) isochronous, when the frequency of oscillations is constant (amplitude-independent). The first case is associated with the constant coefficient of the kinetic energy, while the frequency-amplitude relationship and the solution for motion need to be found. To that end, the equation of motion is solved by introducing a new small expansion parameter and by adjusting the Lindstedt-Poincaré method. In the second case, the condition for the frequency of oscillations to be constant is derived in terms of the expression for the position-dependent coefficient of the kinetic energy. The corresponding solution for isochronous oscillations is obtained. Numerical verifications of the analytical results are also presented.

• Periodical: Applied Mechanics and Materials (Volume 430)
• Pages: 14-21
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.430.14
• Online since: September 2013
• Authors: Ivana Kovacic
• Keywords: Amplitude, Frequency, Isochronicity, Nonlinear Oscillator

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