Signal processing techniques for nonlinearity identification of structures using transient response

In this work, an alternate method for determining nonlinearity of vibrating structures is investigated. In contrast to previous approaches, transient vibrations have been used in combination with advanced signal processing techniques to determine hardening or softening effects and strength of nonlinearity. The nonlinear characteristics of a structure can play a significant role in its behavior or response to stimuli. Thus, knowing these characteristics can lead to better design analysis and predictions of system responses.;In order to demonstrate this method's practicality and how transient vibrations can be used to determine nonlinearity, an experiment involving a cantilever beam has been subjected to vibratory analysis. The simple structure of a cantilever beam is used widely in numerous applications. In particular, Micro-Electro-Mechanical Systems (MEMS) devices known as Micromachined Vibratory Gyroscopes (MVG) make use of tuning fork type designs which utilize cantilever beams and thus can be modeled as such. In order to utilize the dynamics of MVGs to measure angular rate, their response to specific stimuli must be known. Specifically, the tuning fork tines will be subjected to parametric excitation and Coriolis forces. An essential aspect of an MVG requires predictability. Hence, knowing the response of the system to these stimuli is crucial for design applications. MVGs require precision design and manufacturing for optimal performance.;In previous works, simulated and experimental parametric excitation of a cantilever beam has been a subject of question, as results are often contradicting. Specifically, determining whether the beam's response is characterized by a hardening or a softening effect has proven to be difficult to obtain. Moreover, theoretical response curves frequently fail to match experimental data.;Within this work, the viability of using transient vibratory analysis to determine the nonlinear characteristics of a cantilever beam has been explored. Experimental data has first been processed by using either a Butterworth 4th order low pass digital filter or the empirical mode decomposition. Furthermore, a novel signal tracking technique, known as the Harmonics Tracking Method, has been used in conjunction with experimental data for signal analysis. This method was then compared to two other more traditional signal tracking techniques, the Teager-Kaiser algorithm and the Hilbert-Huang transform. Through this analysis it has been determined that a nonlinear softening effect exists within the transient response of the cantilever beam. Additionally, the effect of gravity upon the beam's response has been investigated and shown to have a slight hardening effect. It has also been determined that for transient nonlinear analysis, the Harmonics Tracking Method used in conjunction with the empirical mode decomposition yields the best results.