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1.
含多种尺寸缺陷岩体中的弹性波散射   总被引:4,自引:0,他引:4  
研究了含多种尺寸扁平椭圆缺陷的岩体中弹性波散射规律.细观上应用Green函数方法,考虑了入射波与基本的扁平椭圆缺陷相互作用,宏观上采用线性叠加原理,得到了缺陷岩体的频散和衰减规律.频散曲线中特征频率与裂纹尺寸负相关.含几种不连续尺寸裂纹的岩体中其频散曲线呈“阶梯跳跃”形,其衰减曲线也有不同的峰值;而含“均匀分布”与“正态分布”裂纹尺寸的岩体,与含单一尺寸缺陷的岩体相比,其频散曲线具有较宽的特征频率段.结合两个声波测试实例,讨论了这一理论模型的合理性与可行性.  相似文献   

2.
给出了包含宏观应变和微形变的全部二次项以及宏观应变三次项的一种新的自由能函数.利用新自由能函数并根据Mindlin微结构理论,建立了描述微结构固体中纵波传播的一种新模型.利用近来发展的奇行波系统的动力系统理论,分析了系统的所有相图分支,并给出了周期波解、孤立波解、准孤立尖波解、孤立尖波解以及紧孤立波解.孤立尖波解和紧孤立波解的得到,有效地证明了在一定条件下,微结构固体中可以形成和存在孤立尖波和紧孤立波等非光滑孤立波.此结果进一步推广了微结构固体中只存在光滑孤立波的已有结论.  相似文献   

3.
将傅立叶级数方法推广应用于矩形截面梁中波传播的精确分析.不仅试着直接从三维弹性动力学方程出发,导出了矩形截面梁中波传播的一般解析解,而且给出了弹性波在自由矩形截面梁中的传播特性.波传播精确模型的提出,为实现梁波的耦合控制奠定了坚实基础.  相似文献   

4.
纤维复合材料中弹性波散射与动应力   总被引:1,自引:0,他引:1  
基于弹性波动理论,对纤维增强复合材料结构中弹性波多重散射与动应力集中问题进行了分析研究,给出了介质各区域弹性波分析解的表达式.根据位移与应力在各区界面处的连续条件,确定了未知弹性波模式系数.采用Hankel函数的加法定理,将不同局部坐标系中散射波场的表达式变换到了同一个局部坐标系中,以给出弹性波模式系数和动应力集中因子的表达式.分析了多相纤维基体中两个散射体的间距、界层区材料性质以及界层区和纤维核区截面尺寸的变化,对各区界面动应力集中系数的影响.分析表明,两个散射体的间距、界层区材料性质和结构尺寸的变化对复合材料的力学特性具有显影响.作为算例,给出了纤维增强复合材料结构中各区界面动应力集中系数的数值结果,并对其进行了分析讨论.  相似文献   

5.
研究了在应力自由和刚性固定边界条件下,无能量耗散的均匀、各向同性微极热弹性无限板的轴对称自由振动波的传播,导出了相应的对称和斜对称模态波传播的闭合式特征方程和不同区域的特征方程.对短波的情况,应力自由热绝缘和等温板中对称和斜对称模态波传播的特征方程退化为Rayleigh表面波频率方程.根据导出的特征方程得到了热弹性、微极弹性和弹性板的结果.在对称和斜对称运动中计算了板的位移分量幅值、微转动幅值和温度分布,给出了对称和斜对称模式的频散曲线,并示出了位移分量和微转动幅值和温度分布的曲线.能够发现理论分析和数值结论是非常一致的.  相似文献   

6.
弹塑性杆在刚性块轴向撞击下的动力屈曲   总被引:4,自引:0,他引:4  
基于能量原理,对弹塑性杆在刚性块轴向撞击下的动力屈曲问题进行了讨论.用特征线法分析了刚性块轴向撞击是塑性直杆时应力波传播的过程.考虑了弹塑性应力波传播对屈曲的影响,建立了该问题横向扰动方程.用幂级数解法,理论上给出了该问题的级数解.分析解的性质,得到了发生屈曲时的临界条件.通过理论分析和数值计算,得到了临界速度与冲击质量、临界长度及线性强化模量间的关系.  相似文献   

7.
本文讨论地球流体运动浅水波模式中间断周期解与间断孤立波解。在系统的非平衡点即奇点附近考虑轨线性质时,我们发现只要引入广义解的概念(分片光滑连续解),就会产生间断周期解并得到了间断周期解的条件。当系统在退化的过程中,发现系统此时会产生间断的孤立波解,与此同时其它物理量也产生了间断。这里我们发现,一般认为在超高速情况下解会产生间断,然而在非超高速时也会产生间断现象。本文讨论了上述一系列问题得到了间断解的解析解表达式,并把这一事实与飑线的实例进行比较,得到了不少类似之处。  相似文献   

8.
考虑固体材料的宏观尺度立方非线性效应、微尺度立方非线性效应以及微尺度频散效应并根据修正的Mindlin理论,建立了一维微结构固体中纵波传播的一种新模型.用动力系统的定性分析方法,证明了适当条件下立方非线性微结构固体中可存在对称钟型孤立波和反钟型孤立波,并给出了两种孤立波的存在条件.用数值方法分析了微尺度立方非线性效应对钟型与反钟型孤立波的影响,结果显示随着微尺度非线性效应的增强(或负增强),两种孤立波的宽度变窄(或变宽)而幅度保持不变.  相似文献   

9.
本文首先给出了等温大气中点源重力波的解析解.然后,在此基础上建立了水平等温分层大气中点源重力波的计算机模式.从而解决了在真实大气中对点源重力波传播的数值计算问题.对大气中点源声波的传播过程也可以借助本计算机模式进行数值计算.  相似文献   

10.
讨论了一类具有大Reynolds数且弱频散性的KdV-Burgers方程, 在数学上表示为一类奇摄动KdV-Burgers方程.KdV-Burgers方程中含有的非线性项与频散项互补作用形成稳定向前传播的孤立子.通过数学分析, 描述了孤立子的传播途径和传播速度等物理量的发展变化规律.通过奇摄动展开方法, 构造了该问题的渐近解.首先,用Riemann-Earnshaw方法求得退化解, 得到了简单波, 该简单波波形中的任意一点与初始点都存在一个传播速度差, 这使得波在传播过程中波形不断畸变, 最终形成冲击波面, 即间断面, 在它的两侧质点的速度有一个跳跃, 且随时间不断变化;其次, 在退化解的间断曲面处做变量替换, 构造一种修正的行波变换, 得到了内解展开式的孤子解, 并证明了内外解的存在性与唯一性;最后,通过一致有界逆算子的存在性做了余项估计, 并得到渐近解的一致有效性.结果表明, KdV-Burgers方程在大Reynolds数且弱频散性的性质下,扰动集中在退化解的间断面附近,孤立子链接两侧质点,其传播途径不是时间与空间的线性形式,而是沿着退化解的间断面附近传播,形成稳定的波形.  相似文献   

11.
The plane wave expansion (PWE) and the extended plane wave expansion (EPWE) formulations are derived in order to obtain the complex dispersion relation of flexural waves in a metamaterial Mindlin-Reissner thick plate with multiple periodic resonators. These new formulations are useful to obtain more accurate results at higher frequencies than those based on Kirchhoff-Love thin plate theory. Multiple periodic resonators with multiple degrees of freedom (M-DOF) attached to metamaterial thick plates broaden the applications for wave attenuation in high frequencies.  相似文献   

12.
Within the framework of a piecewise homogeneous body model, with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies, the propagation of torsional waves in prestressed multilayered circular cylinders is investigated. The elasticity relations for cylinder components are given through the Murnaghan potential. The influence of variations in the geometric and mechanical parameters of the cylinders on the dispersion curves is analyzed.  相似文献   

13.
Under a plane-strain state in a half-plane covered with a homogeneous prestressed layer, the Rayleigh-wave propagation along the layer is investigated. The investigations are carried out within the framework of a piecewise homogeneous body model with the use of the three-dimensional linearized theory of elasticity. Complete and incomplete contact conditions between the layer and half-plane are considered. Numerical results relating to the dispersion of the waves are obtained for the case where the layer and half-plane are isotropic and homogeneous.  相似文献   

14.
Based on the equivalent elasticity theory for layered materials, the micro-mechanics equivalent models for single and dual damascene structures were established. The equivalent elastic constant of the patterned structure was introduced, to establish the propagation model for the surface acoustic waves propagating in the layered structure of the patterned film/ substrate, and the theoretical dispersion curves of the surface acoustic waves were calculated with Green’s function and the matrix method. The finite element method was used to calculate 24 numerical examples of damascene structures with different volume ratios, and the results were compared with those of the strain energy method. The results show that, the average relative errors of the equivalent Young’s moduli of the 300 nm-thick dual damascene film and the 100 nm-thick single damascene film are 2.06% and 2.27%, respectively. The research verifies the correctness of the equivalent patterned structure model and the feasibility of the surface acoustic wave method to characterize the mechanical properties of patterned films, and provides a reference for the development of suitable chemico-mechanical polishing technologies for patterned films under low pressure. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.  相似文献   

15.
The present investigation is concerned with the study of extensional wave motion in an infinite homogenous isotropic, thermoelastic plate by using asymptotic method. The governing equation for the extensional wave motions have been derived from the system of three-dimensional dynamical equations of linear coupled theory of thermoelasticity. All coefficients of the differential operator are expressed as explicit functions of the material parameters. The velocity dispersion equation for the extensional wave motion is deduced from the three-dimensional analog of Rayleigh–Lamb frequency equation for thermoelastic plate waves. The approximations for long and short waves and expression for group velocity are also derived. The thermoelastic Rayleigh–Lamb frequency equations for the considered plate are expanded in power series in order to obtain polynomial frequency and velocity dispersion relations whose equivalence is established to that of asymptotic method. The dispersion curves for phase velocity and attenuation coefficient are shown graphically for extensional wave motion of the plates.  相似文献   

16.
本文对无限长常水深平底渠道中一小振幅入射波经由多个间隔相等、透水性能一致的细孔透水板的反射和透射进行了研究,得到了相邻两板间距l为入射波半波长的倍数时的一个特解.结果表明,当无量纲的孔隙影响参数G_0等于透水板个数的一半时消波效果最佳,入射波能量的50%能被消掉.此时反射波与透射波的振幅相等.  相似文献   

17.
Within the framework of the piecewise homogeneous body model with utilization of the three-dimensional linearized theory of elastic waves in initially stressed bodies, the mathematical modeling of the torsional wave propagation in the initially stressed infinite body containing an initially stressed circular solid cylinder (case 1) and circular hollow cylinder (case 2) are proposed. In these cases, it has been assumed that in the constituents of the considered systems there exist only the normal homogeneous tensional or compressional initial stress acting along the cylinder, i.e. in the direction of wave propagation. In the case where the mentioned initial stresses are not present, the proposed mathematical modeling coincides with that proposed and investigated by other authors within the classical linear theory of elastic waves. The mechanical properties of the cylinder and surrounding infinite medium have been described by the Murnaghan potential. The numerical results related to the torsional wave dispersion and the influence of the mentioned initial stresses on this dispersion are presented and discussed.  相似文献   

18.
Effects of initial stresses on the dispersion curves of Lamb and SH waves in multilayered PZT-4/PZT-5A composites are investigated using the polynomial expansion approach. The piezoelectric layers are considered with arbitrary crystal orientations with a result that only Lamb or SH waves may be transmitted. The problem is solved employing the Legendre polynomial approach that poses the advantages of numerically stability and effectiveness over conventional matrix method. The solution is validated by comparing the wave propagation behavior of piezoelectric materials with those reported in literature, and the convergence properties are examined. Numerical results demonstrate that initial stress has profound influences on the guided wave propagation in multilayered PZT-4/PZT-5A laminates. The phase velocity of Lamb and SH waves increases with initial tensile stresses. In addition, the effects of initial stresses rely on the wave mode and thickness of constituent layers and the stacking sequence of the constituent materials. The results are useful for understanding and optimization of new designs for actuator, electromechanical sensor and acoustic wave devices made of PZT-4/PZT-5A composites.  相似文献   

19.
在不同热弹性扩散理论的框架中,无应力作用、恒温/绝热、化学势条件下,研究了均匀、横观各向同性无穷板中热弹性扩散环形峰波的传播.得到了热弹性扩散Lamb型波的色散方程.同时推演出色散方程的一些特例.  相似文献   

20.
The propagation of torsional waves in a prestressed compound (bi-layered) hollow circular cylinder is in vestigated within the frame work of a piecewise homogeneous body model, with the use of a three-dimensional linerized theory of elastic waves in initially stressed bodies. The elasticity relations for components of the compound cylinder are obtained from the Murnaghan potential. Numerical investigations are performed for bronze and steel. According to the results obtained, the effect of variations in the geometric (the ratio between the thickness of the cylinder and its inner radius) and mechanical parameters on the dispersion curves are analyzed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 1, pp. 103–116, January–February, 2008.  相似文献   

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