碳纳米管和梁受电压激励非线性动力学研究

发布时间：2018-11-13 14:39

【摘要】：碳纳米材料因本身巨有潜大的优越性,越来越多的学者也开始关注它的特性和结构,并其对它进行广泛的研究。它具有弹性高、密度低、绝热性好及强度高等优点。这些特殊性能可以广泛应用于纳米器件、传感器和纳米机械等。因此,研究碳纳米梁和管的动力学特性是很有意义的。分别以碳纳米材料矩形和环形的横截面积受电压激励梁与管为研究对象,应用经典的拉格朗日方程—麦克斯韦方程建立非线性动力学模型,采用多尺度法和MLP法进行非线性振动分析:1)应用多尺度法研究碳纳米梁和碳纳米管受电压激励的影响,分析了02W=w和0W=w的参强联合共振、主共振、主参数共振、0次近似解和一次近似解。结果表明:增大梁的长度和交流电压的幅值,可以增大共振振幅和共振区,增大梁与极板之间的距离和阻尼系数的幅值,可以减小共振振幅和共振区。随着碳纳米管长度和交流电压的增加,不稳定区间逐渐增大,振幅增加;随着碳纳米管半径和极板距离的增大,不稳定区间逐渐减小,振幅减小,但当σ接近零时,振幅几乎不随系统参数变化而变化。2)应用MLP法研究矩形横截面碳纳米梁受电压激励强非线性振动问题,分析了激频和倍频的主共振、三分之一次亚谐、三次超谐、二分之一次亚谐、二次超谐、0次近似解和一次近似解。结果表明:增大梁的长度和交流电压的幅值,可以增大共振振幅和共振区,增大梁与极板之间的距离,可以减小共振振幅和共振区。
[Abstract]:Due to its potential advantages, more and more scholars have begun to pay attention to its characteristics and structure, and it has been widely studied. It has the advantages of high elasticity, low density, good adiabatic and high strength. These special properties can be widely used in nano-devices, sensors and nano-machinery. Therefore, it is of great significance to study the dynamics of carbon nanobeams and tubes. Taking the rectangular and annular cross-sectional beams and tubes of carbon nanomaterials as research objects, the classical Lagrange equation-Maxwell equation is used to establish a nonlinear dynamic model. The nonlinear vibration analysis is carried out by using multi-scale method and MLP method. 1) the influence of voltage excitation on carbon nanobeam and carbon nanotube is studied by using multi-scale method. The parametric resonance and main parameter resonance of 02W=w and 0W=w are analyzed. The 0-order approximate solution and the first-order approximate solution. The results show that increasing the length of beam and the amplitude of AC voltage can increase the resonance amplitude and resonance region, increase the distance between beam and plate and the amplitude of damping coefficient, and reduce the resonance amplitude and resonance region. With the increase of carbon nanotube length and AC voltage, the instability region increases gradually and the amplitude increases. With the increase of the radius of carbon nanotubes and the distance between the plates, the instability region gradually decreases and the amplitude decreases, but when 蟽 is close to 00:00, The amplitude hardly varies with the system parameters. 2) the MLP method is used to study the strong nonlinear vibration of the rectangular cross-section carbon nanobeam excited by voltage. The main resonance, 1/3 subharmonic, cubic super harmonic of the stimulated frequency and the double frequency are analyzed. The subharmonic of order 1/2, the subharmonic of order 2, the approximate solution of order 0 and the solution of order one. The results show that increasing the length of beam and the amplitude of AC voltage can increase the resonance amplitude and resonance region, increase the distance between beam and plate, and decrease the resonance amplitude and resonance region.
【学位授予单位】：华北理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O322;TB383.1

【共引文献】