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Subharmonics analysis of nonlinear flexural vibrations of piezoelectrically actuated microcantilevers

机译:压电驱动微悬臂梁的非线性挠曲振动的次谐波分析

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Using the method of multiple scales, an extensive frequency response and subharmonic resonance analysis of the equations of motion governing the nonlinear flexural vibrations of piezoelectrically actuated microcantilevers is performed. Such comprehensive understanding of the nonlinear response and subharmonics analysis of these microcantilevers is, indeed, justified by the applications of piezoelectrically actuated microcantilevers that are increasingly becoming popular in many science and engineering areas including scanning force microscopy, biosensors, and microactuators. Along this line, the method of multiple scales is used to derive the 2× and 3× subharmonic resonances appearing in nonlinear flexural vibrations of a piezoelectrically actuated microcantilever. An experimental examination is performed in order to verify the analytical results. The analytical and experimental results yield the same system response for the fundamental frequency. In addition, the experimental results demonstrate the presence of subharmonic resonances that are supported by numerical simulations of the equations of motion. The experimental mode shapes of these subharmonic frequencies are also measured and compared with fundamental frequency. Keywords Piezoelectrically actuated microcantilevers - Nonlinear vibrations - Method of multiple scales
机译:使用多尺度方法,对控制压电致动微悬臂梁的非线性挠曲振动的运动方程进行了广泛的频率响应和次谐波共振分析。压电驱动的微悬臂梁的应用确实证明了对这些微悬臂梁的非线性响应和亚谐波分析的这种全面理解,这种应用在包括扫描力显微镜,生物传感器和微致动器在内的许多科学和工程领域中越来越受欢迎。沿着这条线,使用了多个尺度的方法来推导在压电致动微悬臂梁的非线性挠曲振动中出现的2x和3x次谐波谐振。为了验证分析结果,进行了实验检查。分析和实验结果对基频产生相同的系统响应。另外,实验结果证明了运动方程数值模拟所支持的次谐波共振的存在。还测量了这些次谐波频率的实验模式形状,并将其与基本频率进行比较。压电致动微悬臂梁非线性振动多尺度方法

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