On a Class of Periodic Inputs That Passively Quench the Superharmonic Resonance of a Symmetric Duffing Oscillator

Mohammed F. Daqaq
J. Comput. Nonlinear Dynam. January 2025, 20(1): 014501.
https://doi.org/10.1115/1.4066659

​The symmetric monostable Duffing oscillator exhibits a superharmonic resonance of order three when excited harmonically at an excitation frequency that is one third its linear natural frequency. In this letter, it is shown that a certain class of periodic excitations can inherently quench the superharmonic resonance of order three. The Fourier series expansion of such excitations yields a harmonic component at the natural frequency whose magnitude can be properly tuned to completely quench the effect of the superharmonic component. Based on this understanding, the parameters of a piecewise periodic function and the modulus of the cosine Jacobi elliptic function are intentionally designed to passively suppress the superharmonic resonance. Such periodic functions can be used to replace single-frequency harmonic excitations whenever the effects of the superharmonic resonance are to be passively mitigated.

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