粘弹性基底上功能梯度压电纳米梁波传播特性

Wave Propagation Characteristics of Functionally Graded Piezoelectric Nanobeams on Viscoelastic Substrates

本文利用非局部应变梯度理论(NSGT)探究了含粘弹性基底的功能梯度压电(FGP)纳米梁的波传播特性.基于NSGT,建立含粘弹性基底的Euler梁波传播模型及考虑剪切效应的Timoshenko梁模型,利用哈密顿原理推导出波传播控制方程;通过引入两种梁变形理论对应的波传播通解方程,对运动方程组进行求解,探讨了剪切效应、尺度参数、粘弹性参数、FG指数等对波传播频率及相速度的影响.研究表明:尺度参数对波传播频率的影响与波数密切相关;电压与梯度指数对两种梁波传播特性影响程度不同;粘弹性基底参数对波传播频率有明显的影响,且其影响程度与波数密切相关.

This paper investigates the wave propagation characteristics of functionally graded piezoelectric(FGP)nanobeams on viscoelastic substrates using nonlocal strain gradient theory(NSGT).Based on NSGT,wave propagation model of Euler and Timoshenko beam model considering shear effect are established.Then the governing equations of wave propagation are derived by Hamilton principle.By introducing the general equations of wave propagation corresponding to two beam deformation theories,the equations of motion are solved.Moreover the effects of shear effect,scale parameter,viscoelastic parameter,and FG index on wave propagation frequency and phase velocity are discussed numerically.The results indicate that the effect of scale parameters on wave propagation frequency is closely related to wave number,and the influences of voltage and gradient index on the propagation characteristics for two kinds of beam waves are different.In addition,the viscoelastic base parameters have obvious influence on the wave propagation frequency,and the degree of influence is closely related to wave number.