非局部理论的裂纹纳米谐振梁振动特性

Vibration Characteristics of a Cracked Resonant Nano-Beam Considering the Nonlocal Effect

以两端固支纳米谐振梁为研究对象,考虑非局部效应、非线性轴向拉伸应力以及裂纹建立其物理模型并推导出运动控制方程。将裂纹等效为连接两段纳米梁的扭转弹簧,研究非局部效应、裂纹参数对系统自由振动固有频率以及振动模态的影响。采用非线性静电力和非线性轴向拉伸应力模型,用多尺度的数值方法研究系统主谐波共振响应的非线性刚度硬化现象与非局部效应系数以及裂纹各参数的关系。数值结果表明,非局部效应系数越大,系统固有频率越小,主共振非线性强度越大。对于两端固支谐振梁系统,裂纹位置对系统固有频率以及主共振非线性强度的影响存在着三个分界点,分别是纳米梁中点以及距离两端四分之一的两个点。研究结果可在微纳米器件的设计、性能改进及健康检测中得到应用。

Characteristics of free transverse vibration and forced vibration of a cracked resonant nano-beam with both ends fixed are studied. The nonlocal effect, nonlinear axial stretching force and the crack effect are considered. The cracked nano-beam is modeled as two segments connected by a massless rotational spring located in the crack section. Dynamic equations of the nano-beam are derived and its nonlinear response is investigated by using the multiple scales method. The influence of the nonlocal effect and the crack position on the vibration nonlinearity is discussed. The numerical results show that enlarging the nonlocal effect coefficient can decrease the values of the natural frequencies and strengthen the nonlinearity of the resonant vibration. The effects of the crack parameters on the vibration characteristics are complicated.This study may be of interest for the design, performance improvement and health monitoring of nano-devices.