一维复合波入射的固-固界面接触特性分析
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摘要
基于弹性波理论,针对接触面非线性相互作用,建立了一个非线性刚度模型,利用接触应力描述非线性刚度特性。引入包含基波和谐波的一维复合波入射,在二阶微扰近似以及非线性边界条件下,给出了界面的反射波和透射波的表达式,得到反射系数和透射系数。结合界面线性刚度和接触应力的幂律关系,定义了四个非线性系数。通过数值计算分析了固-固界面的非线性特性以及谐波对于接触应力的依赖性。
Based on the theory of the one-dimensional nonlinear interaction between elastic wave and contact surface, a nonlinear stiffness model using contact pressure to describe nonlinear stiffness characteristics is established. One-dimensional composite wave incidence including fundamental and harmonic waves is introduced, the expressions of reflection wave and transmission wave at the interface are derived by the second order perturbation approximation and under the nonlinear boundary condition, and the reflection and transmission coefficients are obtained. By the power-law relationship between the linear stiffness of interface and the contact pressure, four nonlinear parameters are defined. The nonlinear characteristics of solid-solid contact surface and the dependency of the harmonic waves on the contact pressure are analyzed by numerical calculation.
Based on the theory of the one-dimensional nonlinear interaction between elastic wave and contact surface, a nonlinear stiffness model using contact pressure to describe nonlinear stiffness characteristics is established. One-dimensional composite wave incidence including fundamental and harmonic waves is introduced, the expressions of reflection wave and transmission wave at the interface are derived by the second order perturbation approximation and under the nonlinear boundary condition, and the reflection and transmission coefficients are obtained. By the power-law relationship between the linear stiffness of interface and the contact pressure, four nonlinear parameters are defined. The nonlinear characteristics of solid-solid contact surface and the dependency of the harmonic waves on the contact pressure are analyzed by numerical calculation.
引文
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[3]XIANG Y X,DENG M X.Cumulative second-harmonic generation of Lamb waves propagating in a two-layered solid plate[J].Chinese Physics B,2008,17(11):4232-4241.
[4]王成会,林书玉.超声波作用下气泡的非线性振动[J].力学学报,2010,42(6):1050-1059.WANG Chenghui,LIN Shuyu.The nonlinear oscillation of bubbles in the ultrasonic field[J].Acta Mechanica Sinica,2010,42(6):1050-1059.
[5]SHUI Y,SOLODOV I Y.Nonlinear properties of Rayleigh and Stoneley waves in solids[J].Journal of Applied Physics,1988,64(11):6155-6165
[6]肖齐.固体粗糙界面与超声的非线性相互作用的研究[D].南京:南京大学,2014.XIAO Qi.Study the nonlinear interaction of solid rough interface with ultrasound[D].Nanjing:Nanjing University,2014.
[7]LEN K S,SEVERIN F M,SOLODOV I Y.Experimental observation of the influence of contact nonlinearity on the reflection of bulk acoustic waves and the propagation of surface acoustic waves[J].Sov.Phys.Acoust.,1991,37(6):610-612.
[8]BREAZEALE M A,THOMPSON D O.Finite-amplitude ultrasonic waves in aluminum[J].Appl.Phys.Lett.,1963,3(1):77-78.
[9]THOMPSON R B,BUCK O,THOMPSON D O.Higher harmonics of finite amplitude ultrasonic waves in solids[J].J.Acoust.Soc.Am.,1976,59(5):1087-1094.
[10]HIRSEKORN S.Nonlinear transfer of ultrasound by adhesive joints-a theoretical description[J].Ultrasonics,2001,39(1):57-68.
[11]BIWA S,NAKAJIMA S,OHNO N.On the acoustic nonlinearity of solid-solid contact with pressure-dependent interface stiffness[J].Journal of Applied Mechanics,2004,71(4):508.
[12]RICHARDSON J M.Harmonic generation at an unbonded interface:i.planar interface between semi-infinite elastic media[J].Int.J.Eng.Sci.,1979(17):73-85.
[13]LOMBARD B,PIRAUX J.Propagation of compressional elastic waves through a 1-D medium with contact nonlinearities[M]//Ultrasonic Wave Propagation in Non Homogeneous Media.Springer Berlin Heidelberg,2009:183.
[14]DRINKWATER B W,DWYER-JOYCE R S,CAWLEY P.Astudy of the interaction between ultrasound and a partially contacting solid-solid interface[J].Proc.R.Soc.London,Ser.A,1996,452(1995):2613-2628.