Electronic Circuit Simulation Of Nonlinear Vibrations In Plates Excited By Intensive Ultrasonic Pulses

Although in different science fields, electronic circuit systems and vibration dynamical systems are generally attributed to the same form of differential equations in mathematics. The status and characteristics of vibration dynamical systems can be intuitively and quickly analyzed by the simple and inexpensive circuit without solving complex differential equations. This thesis is mainly devoted to the studies on the electronic circuit simulation of nonlinear vibrations in plates excited by intensive ultrasonic pulses. The nonlinear vibration phenomena including superharmonics, subharmonics and chaos in plates are observed in the simulation.In the first chapter, the background and mechanism of ultrasonic infrared imaging technique, which is the basis of our research, are briefly introduced. The significance and the problems of researching the nonlinear vibration phenomena in plates are presented. In addition, the overview including the purpose and advantages of the electronic circuit systems applied in dynamical systems is provided.In the second chapter, the principles of the nonlinear vibration in plates, the single-degree-of-freedom approximation method for plates and different contact force modeling are briefly analyzed. Then, based on the above analysis, a two-degree-of-freedom vibro-impact dynamical model is analyzed to simulate the nonlinear vibration phenomena in plates excited by intensive ultrasonic pulses. In the model, the ultrasonic transducer horn and the plate are simplified as two oscillators Mh and Mp, respectively, and a continuous nonlinear damping contact force model is used to simulate the contact impact process between the horn tip and the plate surfaces. The equations of motion are obtained.The electronic circuit systems applied in vibration dynamical systems have attracted a great attention because both systems are with the similar operation principles. In this paper, based on the vibro-impact mechanical system, an electronic circuit model is presented to calculate the differential equations of dynamical systems. The characteristics of the circuits are individually analyzed. As a result, the complete electronic circuit system is obtained which can simulate the process of nonlinear vibrations in plates excited by intensive ultrasonic pulses.In the fourth chapter, the analyses of the waveforms (time series) and frequency spectra are performed to characterize nonlinear vibrations in the electronic circuit simulations. The simulation results show that the superharmonics and subharmonics, as well as chaos, of the nonlinear vibration systems are observed. The simulation calculation and data collection are simple and fast owing to the electronic signals can be directly displayed by the analog voltage waveforms. In the simulation, for the superharmonic vibrations, the periodic contact between the ultrasonic transducer horn and the plate is considered as the main mechanism for generating the superharmonic vibrations, and the interval of the two adjacent impacts is equal to the ultrasonic excitation period. The subharmonic vibration is generated by the intermittent contact forces in the impact process between the ultrasonic transducer horn and the plate. Different impact periods will lead to the subharmonic vibration with different fractional ratios. In addition, it can be found that the chaotic vibration of the plate is caused by the irregular and unstable contact forces between the two oscillators. In further calculation research, the frequency response of the oscillators under continuously varying parameters is also analyzed, in which the transition between the superharmonic, subharmonic and chaos can be observed.Finally, the work of this thesis is summarized.In the appendix, as an added work during my graduated study, based on heat conduction theory, a finite element method is introduced to investigate the three-dimensional transient temperature fields in a moving plate irradiated by a laser beam with Gaussian distribution, in which the plate is considered as infinite along the motion direction. Considering the thermal physical parameters depended on temperature, convection and radiation factors of the surfaces, and motion of the plate, the temperature fields on the upper and bottom surfaces of the plate are obtained.