Date of Award
Doctor of Philosophy (PhD)
Dr. Mohammed F. Daqaq, Committee Chair
Dr. Ardalan Vahidi
Dr. Gang Li
Dr. Phanindra Tallapragada
This dissertation investigates the response of Duffing oscillators to bi-harmonic ex-citations consisting of a soft resonant component and a hard high-frequency non-resonant component. To this end, the dissertation uses approximate analytical solutions, numerical simulations, and an especially-designed experimental module to detail the influence of non-resonant excitation on the resonant response for oscillators with symmetric/asymmetric, mono and bi-stable potential energy functions. For mono-stable Duffing oscillators, we demonstrate that the high-frequency excitation has a substantial influence on the shape of the potential energy function associated with the slow dynamics. In specific, we show that the hard excitation stiffens the slow response for oscillators with a symmetric potential energy function. For asymmetric potential energy functions, we clearly illustrate that the high-frequency excitation tends to symmetrize the potential function, therewith reducing the softening nonlinear behaviour of the system. In such case, we also demonstrate that the high-frequency excitation can be the effectively utilized to change the effective nonlinearity of the slow dynamics from the softening to the hardening type. Therefore, by choosing the proper parameters, the hard excitation can be used to locally linearize the resonant dynamics of an asymmetric mono-stable Duffing oscillator. We also demonstrate that by reducing the depth of the potential wells and bringing them closer together, a high-frequency hard excitation can influence the effective properties of the slow dynamics of a bi-stable Duffing oscillator. This has the effect of amplifying the intra-well response. The reduction of the depth of the potential wells also causes the wells to become more asymmetric which increases the softening nonlinearity of the slow dynamics. Furthermore, once the magnitude of the non-resonant excitation exceeds a certain threshold, the potential function loses its bi-stable properties and becomes mono-stable. In summary, this dissertation highlights many interesting effects of the hard excitation on the qualitative properties of the slow resonant response. Such effects can be utilized as an effective open-loop tool to alter the resonant behaviour of the system, which, in turn, can be useful in various application problems including, but limited to, vibration mitigation, sensor sensitivity enhancement, and system identification. Here, we present one illustration where we exploit the hard excitation for parametric system identification of a nonlinear mono-stable oscillator. We present the proposed methodology and apply it successfully to identify the nonlinear parameters of several experimental systems.
Abusoua, Abdraouf, "Some Interesting Effects of High-Frequency Non-Resonant Harmonic Excitations on the Slow Response of Duffing Oscillators" (2018). All Dissertations. 2234.