共查询到12条相似文献,搜索用时 15 毫秒
1.
Polyakov V. A. Shlitsa R. P. Khitrov V. V. Zhigun V. I. 《Mechanics of Composite Materials》2002,38(3):223-232
The wave process arising in a sandwich panel with a free back surface under the action of a short-term dynamic load on the front surface of the upper layer (plane deformation) is investigated. The calculation procedure for displacements, rates, and stresses under a rectangular short-time pulse, whose duration does not exceed the double time of wave travel within a layer, is based on the representation of the solution to the one-dimensional wave equation in terms of characteristics. The transmission and reflection coefficients of the pressure pulses on the contact surfaces of layers with different physical properties are determined. The expressions for tensile stresses in the panel face layers and filler, which are responsible for the material failure by spalling, are presented. The stresses in relation to the geometry and dynamic parameters of the sandwich structure are analyzed. In the case of a symmetric panel structure, the stress pattern in the midlayer and on its contact boundaries is given, which takes into account the branching and superposition of pulses. 相似文献
2.
Polyakov V. A. Shlitsa R. P. Khitrov V. V. Zhigun V. I. 《Mechanics of Composite Materials》2004,40(5):365-378
The interaction of plane tension/compression waves propagating within a plate perpendicularly to its surface is considered. The analytic solution is obtained by a modified method of characteristics for the one-dimensional wave equation used in problems on an impact of a rigid body on the surface of a plate. The displacements, velocities, and stresses in the plate are determined by the edge disturbance caused by the initial velocity and the stationary force field of masses of the striker and the plate. The method of analytic continuation in time put forward allows a stress analysis for an arbitrary time interval by using finite expressions. Contrary to a stress analysis in the frequency domain, which is commonly used in harmonic expansion of disturbances, the approach advanced allows one to analyze the solution in the case of discontinuous first derivatives of displacements without calculating jumps in summing series. A generalized closed-form solution is obtained for stresses in an arbitrary cycle n(t), which is determined by the multiplicity of the time of wave travel across the double thickness of the plate. A method of recurrent solution based on calculating the convolution of repeated integrals of the initial form of disturbance at t = 0 is elaborated. The procedure can be used for evaluating the maximum stress and the contact time in a plane impact on the surface of a plate. 相似文献
3.
In this paper, we consider a general problem of Goursat type for third-order hyperbolic equations of general form with dominated lower terms. We study the influence of the lower terms contained in the equation, as well as those in the boundary conditions, on the well-posedness of the problem under consideration. 相似文献
4.
血液动力学问题是生物力学心血管系统中的重要研究课题.血管内斑块处,血管截面和血管壁的材质发生变化,对血液流动产生重要影响.血液流动中基本波及其相互作用对探究血液流动的规律、生理学意义及与疾病的关系有着重要的意义.本文研究血液动力学血液流动简化数学模型的基本波的相互作用.血管流模型是3×3非严格双曲型方程组.构造性地得到了初值为三段常状态时,血管流问题的解,即解决了激波与驻波的相互作用问题.特别地,给出四种后前激波与驻波的相互作用的结果. 相似文献
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6.
静脉系统是心血管系统的重要组成部分.脉搏波在血液流动中有着突出的重要性.本文主要研究静脉血流动力学模型基本波的相互作用.血流动力学模型是2×2严格双曲型方程组,其基本波包括疏散波和激波,属于血液流动中的脉搏波.基本波相互作用后血管截面面积和血流速度发生相应的变化. 相似文献
7.
关于构造数学物理中非线性发展方程组孤波解的一种新算法 总被引:2,自引:0,他引:2
根据改进的sine-cosine法和吴文俊消元法,给出了一种构造非线性发展方程组孤波解的新算法。这种算法比已知的双曲函数法有更好的结论,并且在使用的过程中更简单。借助于MATH-EMATICA软件,这一算法能够在计算机上实现。 相似文献
8.
Fumihiro Chiba Teruo Ushijima 《Journal of Computational and Applied Mathematics》2009,233(4):1155-1174
Our fundamental solution method gives an analytic representation of the approximate solution for the reduced wave problem in the exterior region of a disc. The asymptotic behavior of this representation yields an approximate formula for the scattering amplitude. An error estimate for this formula is given. We add two numerical tests: the numerical estimate of errors; and profiles of scattering cross sections and the far-field coefficient. Both tests include cases of high wave numbers. 相似文献
9.
A. V. Gasnikov 《Computational Mathematics and Mathematical Physics》2008,48(8):1376-1405
The time asymptotic behavior of a solution to the initial Cauchy problem for a quasilinear parabolic equation is investigated. Such equations arise, for example, in traffic flow modeling. The main result of this paper is the proof of the previously formulated conjecture that, if a monotone initial function has limits at plus and minus infinity, then the solution to the Cauchy problem converges in form to a system of traveling and rarefaction waves; furthermore, the phase shifts of the traveling waves may depend on time. It is pointed out that the monotonicity condition can be replaced with the boundedness condition. 相似文献
10.
Zhi-Qiang Shao 《Journal of Mathematical Analysis and Applications》2007,330(1):511-540
This work is a continuation of our previous work [Z.-Q. Shao, D.-X. Kong, Y.-C. Li, Shock reflection for general quasilinear hyperbolic systems of conservation laws, Nonlinear Anal. TMA 66 (1) (2007) 93-124]. In this paper, we study the global structure instability of the Riemann solution containing shocks, at least one rarefaction wave for general n×n quasilinear hyperbolic systems of conservation laws in the presence of a boundary. We prove the nonexistence of global piecewise C1 solution to a class of the mixed initial-boundary value problem for general n×n quasilinear hyperbolic systems of conservation laws on the quarter plane. Our result indicates that this kind of Riemann solution mentioned above for general n×n quasilinear hyperbolic systems of conservation laws in the presence of a boundary is globally structurally unstable. Some applications to quasilinear hyperbolic systems of conservation laws arising from physics and mechanics are also given. 相似文献
11.
《Mathematical Methods in the Applied Sciences》2018,41(8):3117-3137
We study a generalized time‐harmonic transport equation, which appears in the Goldstein equations and allows us to model the acoustic radiation in a flow. We investigate the well‐posedness of this transport problem. The result will be established under the assumption of a Ω‐filling flow, which, in 2D, is simply equivalent to a flow that does not vanish. The approach relies on the method of characteristics, which leads to the resolution of the transport equation along the streamlines, and on general results of functional analysis. The theoretical results are illustrated with numerical results obtained with a Streamline Upwind Petrov‐Galerkin finite element scheme. 相似文献
12.
R. C. Brown 《Proceedings of the American Mathematical Society》2004,132(8):2273-2280
Using a recent result of Chernyavskaya and Shuster we show that the maximal operator determined by on , -\infty$">, where and the mean value of computed over all subintervals of of a fixed length is bounded away from zero, shares several standard ``limit-point at " properties of the case. We also show that there is a unique solution of that is in all , .