【作者】 李鹏；

【导师】 张淑仪；

【作者基本信息】 南京大学 ， 声学， 2012， 硕士

【摘要】 电路系统和振动动力学系统虽属于不同的领域,但在数学上往往归结为相同形式的微分方程。振动动力学系统可以通过简单低廉的电路分析,直观地、迅速地分析出系统的工作状态和特点,而不必求解复杂的微分方程。本文主要致力于强超声脉冲激励下板非线性振动现象的电子电路模拟的研究,通过电路仿真得到板的超谐波、次谐波和混沌等非线性振动现象。本文研究工作的基础是超声红外热像技术,在第一章中简单介绍了该技术的背景和原理,以及超声红外热像技术检测板试样时产生非线性振动现象的研究意义和存在的问题。此外,概述了电路系统在振动动力学系统中的应用以及本文研究电路系统仿真振动动力学系统的目的和优点。在第二章中,简要分析了板的非线性振动理论、板的单自由度近似方法及碰撞接触力模型。在此基础上,系统研究了两自由度的碰撞-振动机械模型的理论。在模型中,超声换能器变幅杆与板分别简化为碰撞振子Mh和Mp,并用弹簧阻尼接触力模型模拟变幅杆与板之间的接触碰撞相互作用过程,得到了相应的运动方程。在第三章中,根据电路系统与振动动力学系统运行原理的相似性,本文提出了由基本电路组成的电子电路系统来模拟上述振动动力学系统,并逐个分析了电路系统中基本运算电路的特性,最终建立了完整的研究强超声脉冲激励下板非线性振动现象的电子电路系统。在第四章中,通过选择合理的参数,进行波形的时间序列和频谱分析,可以得到强超声脉冲激励下板非线性振动的超谐波、次谐波及混沌等现象。由于所有数据均通过电路中模拟电压波形来表示,仿真数据的计算以及采集更为简单快速。电路仿真结果表明,对于超谐波,变幅杆与板周期性的接触碰撞作用是产生超谐波的主要原因,并且相邻接触碰撞时间间隔等于激励周期。次谐波产生的主要原因是在接触碰撞振动的过程中换能器变幅杆与板之间的间歇性接触力脉冲,不同的弹跳碰撞周期导致板出现不同分频比的次谐波振动现象。而板的混沌振动是由变幅杆和板之间不稳定且无规律的接触力作用引起的。在仿真模拟中将计算参数连续变化时,对金属板的速度频谱响应进行了分析,可以看到超谐波、次谐波以及混沌等在参数变化时出现相互转化的现象。最后对全文的研究工作进行了总结。在附录中,给出在研究生学习期间,对基于热传导理论而建立的激光辐照无限长移动平板的三维模型的研究工作,并采用有限元方法数值计算了平板表面瞬态温度场分布,得到了研究的初步结果。其中,在研究移动平板上下表面瞬态温度场的基础上,考虑板材料的热物理参数依赖于温度、板表面的热辐射及对流等因素,计算了上述因素及移动速度对温度场的影响,并进一步讨论了激光半径对温度场的影响。更多还原

【Abstract】 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.更多还原