Behavior of one-dimensional elastic waves at a unilateral contact interface between two piezoelectric solids
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摘要: 弹性波与压电材料接触界面的相互作用问题是工程应用中常见而复杂的问题，入射波足够强会引起界面出现滑移和分离，但滑移和分离的边界未知，边界条件具有非线性特性。通过Fourier分析，将混合边值问题的求解转化为非线性代数方程，利用软件通过迭代修正的方法进行了求解；给出3种状态边界的求解，分析入射波强度、外加应力及电场对界面状态的影响，并对高频谐波的特性进行分析，通过实例对理论推导进行验证，结果显示：入射波强度、外加荷载和电场的大小及摩擦因数均会影响到界面，通过改变这些条件可以控制界面状态，另外检测高频谐波的信号也可以反映界面状态。Abstract: The behavior of one-dimensional elastic waves at a unilateral frictional contact piezoelectric material interface was studied theoretically in this thesis. When the incident wave is strong enough, the contact interface will separate or slip in local interface areas and non-linearity (boundary non-linearity) will pose as a serious problem, and high harmonics will be generated due to this non-linearity, thus not only causing difficulties in mathematics but giving rise to some new phenomena in physics. In this paper one-dimensional problems were discussed in details using the Fourier analysis, and the mix-boundary value problems with unknown regions were converted to a set of non-linear algebraic equations for a one-dimensional case. An iterative method was developed to determine the extent and location of the separation, slip and stick regions which vary with the external mechanical-electrical loads. The interface tractions, relative slip velocities and the amplitudes of the reflected and refracted high harmonics due to the boundary non-linearity were calculated. Their variation with the applied mechanical-electrical loads was discussed. It was found that, due to the mechanical-electrical coupling, the non-linearity of mechanical parameters would induce the non-linearity of electrical parameters, and the applied electrical fields would influence the interface states by changing the mechanical loads. The present research may enrich the wave theory of piezoelectricity and facilitate its practical application. For instance, we could evaluate the contact state and modulate an interface by detecting the mechanical or electrical information carried by high harmonics.
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Key words:
- piezoelectric material /
- frictional contact /
- elastic waves /
- high frequency harmonics /
- separation zones /
- slip zones
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图 1 一维弹性波透过压电介质摩擦接触界面的传播
Figure 1. Propagation of one-dimensional elastic wave through a frictional contact interface between two piezoelectric media
图 2 界面张开位移与参数关系
Figure 2. Relation between the interface opening displacement and the parameter
图 5 P波入射，分离状态分布区间与Pz/A3(0)的变化关系
Figure 5. Distribution of separation zones for different －Pz/A3(0) when the incident wave is P wave
图 6 P波入射，分离、滑移和黏着状态分布区间随Tx/A3(0)的变化关系
Figure 6. Distribution of separation, slip, stick state zones for different Tx/A3(0)when the incident wave is P wave
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