Nonlinear Multimode Vibration Attenuation Using Passive Circuits

A Master of Science thesis in Mechanical Engineering by Khaled Kadri entitled, “Nonlinear Multimode Vibration Attenuation Using Passive Circuits”, submitted in December 2024. Thesis advisor is Dr. Samir Emam. Soft copy is available (Thesis, Completion Certificate, Approval Signatures, and AUS Archives Consent Form).

Abstract

The reduction of the mass of a structure lead to many engineering benefits such as reducing the material used, increasing efficiency, and increasing effectiveness. However, the decrease in mass results in a structure that is more subjected to the effects of vibration. Vibration absorbers have been used to supress vibration from structures. Piezoelectric materials connected to shunted circuits are being utilized as vibration absorbers to attenuate the excess vibration of a structure. The piezoelectric material, in most cases a patch, is connected to the structure that is to be controlled. The use of shunted circuits provides a more convenient way of implementation than the typical spring mass damper absorbers, known as the vibration absorber, as they are easier to design and less likely to detune. Linear single-mode attenuation, nonlinear single-mode attenuation, and linear multimode attenuation using shunted circuits have been well developed and studied in the literature. The aim of this thesis is to develop a system for nonlinear multimode vibration attenuation. A mathematical model is developed to simulate the vibration response of a cantilever beam. Different force amplitudes will be simulated in order to observe the nonlinearity in the system. The nonlinearity in the cantilever beam is of cubic nature. A MATLAB optimization function is used for finding the optimal shunted circuit component values. Two different criteria for optimization were used: minimize the area under the frequency response plot and minimize the peak of the frequency response plot. Furthermore, optimal placement of the piezoelectric patch is also explored. The model is able to match the performance of current tuning methods used for linear and nonlinear single mode systems. Current Blocking technique is used for multimode vibration attenuation. A comparison is made between using linear and nonlinear circuit elements for nonlinear attenuation.