A nonlinear oscillator with history dependent forces
by
Ketema, Y., R. L. Fosdick and J. H. Yu
in
International Journal of Nonlinear Mechanics, 33, 447-459, 1998.
Category: Journal Article
Keywords: viscoelasticity, oscillator, history material, Melnikov’s method, subharmonic orbits,
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Abstract:
We study the dynamics of a non-linear damped one-degree-of-freedom oscillator whose response force is dependent on the history of the motion and is of the relaxing type. Such an oscillator may serve as a simple model for mechanical applications where viscoelastic materials are used for the purpose of vibration damping and/or isolation. In the simplest cases history dependent forces are characterized by two parameters: the relaxation modulus @a and the relaxation time y. Through the use of a version of Melnikov’s method we show how the two parameters govern the existence of non-linear subharmonic orbits. We suggest an experimental method for determining both parameters.
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