弹性纵波垂直通过非线性结构面的傅里叶级数分析法

发布时间：2018-09-04 20:55

【摘要】：利用傅里叶级数计算任意函数形式的弹性纵波垂直通过非线性结构面的透射波和反射波的速度波形。采用双曲模型描述结构面的变形特性,基于位移不连续模型,结合波振面处动量守恒定律,推导了弹性纵波垂直通过非线性结构面的基本方程。假设应力波在含结构面岩体中传播时,结构面的存在不改变应力波波形函数的最小正周期,运用傅里叶级数理论和周期延拓方法,得到了任意函数形式的弹性纵波垂直入射时透射波和反射波速度波形的傅里叶级数解,并验证了傅里叶级数解是合理的。利用傅里叶级数解,分析了单一频率的正弦谐波入射至结构面时,透射波中各阶谐波的振幅和相位与谐波阶数的关系。研究结果表明,各阶谐波的振幅与阶数呈负指数关系衰减,前7阶谐波振幅的衰减指数为谐波阶数的二次函数,当谐波阶数大于7时,衰减指数为谐波阶数的一次函数;各阶谐波的相位与谐波阶数呈线性关系。
[Abstract]:Fourier series is used to calculate the velocity waveforms of the elastic longitudinal waves perpendicular to the nonlinear structural plane in the form of arbitrary functions. The hyperbolic model is used to describe the deformation characteristics of the structural plane. Based on the discontinuous displacement model and the conservation law of momentum at the wave surface, the basic equation of the vertical passage of elastic longitudinal wave through the nonlinear structural plane is derived. Assuming that the existence of stress wave in rock mass with structural plane does not change the minimum positive period of stress wave waveform function, the Fourier series theory and periodic continuation method are used. The Fourier series solutions of the velocity waveforms of the transmitted and reflected waves are obtained when the elastic longitudinal waves of arbitrary functions are incident vertically, and it is proved that the Fourier series solutions are reasonable. By using the Fourier series solution, the relationship between the amplitude and phase of each harmonic in the transmission wave and the harmonic order is analyzed when the sinusoidal harmonic of a single frequency is incident to the structure surface. The results show that the amplitudes of each order harmonic attenuate in a negative exponential manner. The attenuation exponent of the first seven harmonic amplitudes is a quadratic function of the harmonic order, and when the harmonic order is greater than 7, the attenuation exponent is a first order function of the harmonic order. The phase of each harmonic is linearly related to the number of harmonics.
【作者单位】：江西理工大学建筑与测绘工程学院;江西理工大学工程研究院;
【基金】：国家自然科学基金(No.41462009,No.51104069) 江西理工大学科研基金(No.NSFJ2014-G06)
【分类号】：TU45

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