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运用弹性力学有限变形基本理论推导出了压电材料双曲壳在外激力和温度场作用下的非线性振动方程和协调方程.通过Bubnov-Galerkin原理,得到该结构的非线性动力学方程.利用Melnikov方法,得到系统产生Smale马蹄变换意义下混沌的条件,用四阶Runge-Kutta法编写程序对系统进行数值求解,并绘制出相应的分岔图、Lyapunov指数图、相轨迹图以及Poincaré截面图,分析了温度场对压电材料双曲壳系统的非线性特性的影响.仿真结果表明,随着温度的升高,系统的混沌与周期区交替出现,温度场的改变可影响和控制系统的振动特性. 相似文献
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在压电网络复合板机电耦合波动方程基础上,首先对在其中传播的弯曲波的波动特性进行了分析,发现压电网络复合板中同时存在两种不同频散特性的弯曲波,电感电阻并联型压电网络复合板中存在的两种弯曲波的频散曲线具有频率转向现象;在频率转向区,弯曲波的衰减常数或达到最大或迅速增大这一结论为压电网络复合板的减振降噪设计提供了参考。对压电网络复合板中的能量分析给出了这一结论的机理:即在频率转向区板中的机械能与电能能够进行最大的能量交换;在波动分析的基础上对压电网络复合板的隔声特性进行了分析,发现压电网络复合板隔声曲线上的低谷随外界电感值的变化能够发生移动或者消失,最后结合压电网络复合板的波动频散特性对复合板的隔声机理进行了分析,为设计压电网络复合板的隔声性能提供了理论参考。 相似文献
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建立压电覆层复合结构中声导波传播模型,结合弱界面“弹簧”模型,推导了压电覆层复合结构存在刚性、滑移联接界面等几种不同界面条件下声导波的广义频散方程,数值计算钛锆酸铅基压电陶瓷覆层复合结构在不同界面条件下声导波的频散曲线,分析了界面特性对导波传播相速度的影响。数值计算和分析表明为了能够有效地评价界面的特性,选择合适的声波模式和声波频率是非常重要的。实验结果验证了界面假设的有效性,为进一步深入研究以多模式声导波参量为基础的压电覆层复合结构界面特性参数反演方法提供了理论基础。 相似文献
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机械波在金属凝固过程中传播的定量计算一直是一个难题,主要原因就是在这个过程中的熔体结构非常复杂.本研究考虑到熔体的变温、非均匀和粘弹性的特点,采用Kelvin粘弹性介质模型,建立了具有粘热损失特性的热粘弹性波动方程,通过隐式有限差分方法对波动方程进行求解,并以ZL203A合金熔体为研究对象,探究了热粘弹波在变温非均匀介质中的传播规律.结果表明:热粘弹波从合金熔体的低温区向高温区传播时,非均匀的温度场对波的传播有较大影响;相反,当波从合金熔体的高温区向低温区传播时,非均匀的温度场对波的传播几乎没有影响.热粘弹波在合金熔体中的衰减系数随频率的增大呈线性增大,而随温度的升高先增大后减小,在熔体的枝晶搭接温度附近达到最大值. 相似文献
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在高强度聚焦超声经颅治疗时,既有纵波又有剪切波,为了保障该治疗方法的安全有效性,有必要分析剪切波对HIFU治疗温度场的影响。该文基于人体头颅CT数据和曲率半径为150 mm的256阵元的半球相控换能器建立三维高强度聚焦超声经颅声波传播模型,利用时域有限差分法结合Westervelt声波非线性传播方程、动量方程、质量守恒方程和Pennes生物热传导方程数值仿真其形成温度场,研究在相同输入功率、不同聚焦角度条件下对应阵元数进行激励时,剪切波对换能器形成温度场的影响。结果表明,随换能器聚焦角度减小,在几何焦点处形成的焦域面积逐渐增大,考虑剪切波形成的温度场达到65?C所需时间逐渐延长,焦点前移程度越大;在相同聚焦角度条件下,考虑剪切波的温度场达到65?C所需时间更短,旁瓣更少,在颅骨处的温度更高,对焦点前移几乎没有影响;随换能器聚焦角度减小,考虑剪切波的模型形成的焦域面积变化范围更大;幂指数函数形式对不同聚焦角度下焦域面积大小的拟合优度高,可预测不同聚焦角度换能器形成的焦域面积。 相似文献
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HUANG Wen-Hua 《理论物理通讯》2008,50(4):827-831
A general solution including three arbitrary functions is obtained for the (2+1)-dimensional higher-order Broer-Kaup equation by means of WTC truncation method. Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution, special types of periodic folded waves are derived. In long wave limit these periodic folded
wave patterns may degenerate into single localized folded
solitary wave excitations. The interactions of the periodic
folded waves and their degenerated single folded solitary waves
are investigated graphically and are found to be completely elastic. 相似文献
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A general solution, including three arbitrary functions, is obtained
for a (2+1)-dimensional modified dispersive water-wave (MDWW)
equation by means of the WTC truncation method. Introducing proper
multiple valued functions and Jacobi elliptic functions in the seed
solution, special types of periodic folded waves are derived. In the
long wave limit these periodic folded wave patterns may degenerate
into single localized folded solitary wave excitations. The
interactions of the periodic folded waves and the degenerated
single folded solitary waves are investigated graphically and found
to be completely elastic. 相似文献
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HUANG Wen-Hua 《理论物理通讯》2008,49(6):1383-1388
Applying the extended mapping method via Riccati equation, many exact variable separation solutions for the (2&1 )-dimensional variable coefficient Broer-Kaup equation are obtained. Introducing multiple valued function and Jacobi elliptic function in the seed solution, special types of periodic semifolded solitary waves are derived. In the long wave limit these periodic semifolded solitary wave excitations may degenerate into single semifolded localized soliton structures. The interactions of the periodic semifolded solitary waves and their degenerated single semifolded soliton structures are investigated graphically and found to be completely elastic. 相似文献
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YANGYong YANZhen-Ya 《理论物理通讯》2002,38(6):657-659
In this letter the three-dimensional nonlinear Helmholtz equation is investigated.which describes electromagnetic wave propagation in a nonlinear Kerr-type medium such that sixteen families of new Jacobi elliptic function solutions are obtained,by using our extended Jacobian elliptic function expansion method.When the modulus m-→1 or 0,the corresponding solitary waves including bright solitons,dark solitons and new line solitons and singly periodic solutions can be also found. 相似文献
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Application of higher-order KdV——mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere
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Higher-order Korteweg-de Vries (KdV)-modified KdV (mKdV) equations
with a higher-degree of nonlinear terms are derived from a simple
incompressible non-hydrostatic Boussinesq equation set in atmosphere
and are used to investigate gravity waves in atmosphere. By taking
advantage of the auxiliary nonlinear ordinary differential equation,
periodic wave and solitary wave solutions of the fifth-order
KdV--mKdV models with higher-degree nonlinear terms are obtained
under some constraint conditions. The analysis shows that the
propagation and the periodic structures of gravity waves depend on
the properties of the slope of line of constant phase and atmospheric
stability. The Jacobi elliptic function wave and solitary wave
solutions with slowly varying amplitude are transformed into
triangular waves with the abruptly varying amplitude and breaking
gravity waves under the effect of atmospheric instability. 相似文献
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A. H. Khater M. M. Hassan E. V. Krishnan Y. Z. Peng 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2008,50(2):177-184
New several classes of exact solutions are obtained in terms of the
Weierstrass elliptic function for some nonlinear partial
differential equations modeling ion-acoustic waves as well as dusty
plasmas in laboratory and space sciences. The Weierstrass elliptic
function solutions of the Schamel equation, a fifth order dispersive
wave equation and the Kawahara equation are constructed. Moreover,
Jacobi elliptic function solutions and solitary wave solutions of
the Schamel equation are also given. The stability of some periodic
wave solutions is computationally
studied. 相似文献
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Yan-Ze Peng 《Pramana》2005,65(2):177-183
By means of the singular manifold method we obtain a general solution involving three arbitrary functions for the (2+1)-dimensional
KdV equation. Diverse periodic wave solutions may be produced by appropriately selecting these arbitrary functions as the
Jacobi elliptic functions. The interaction properties of the periodic waves are investigated numerically and found to be nonelastic.
The long wave limit yields some new types of solitary wave solutions. Especially the dromion and the solitoff solutions obtained
in this paper possess new types of solution structures which are quite different from the basic dromion and solitoff ones
reported previously in the literature. 相似文献
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A transformation is introduced for generalized mKdV (GmKdV for short) equation and Jacobi elliptic function expansion method is applied to solve it. It is shown that GmKdV equation with a real number parameter can be solved directly by using Jacobi elliptic function expansion method when this transformation is introduced, and periodic solution and solitary wave solution are obtained. Then the generalized solution to GmKdV equation deduces to some special solutions to some well-known nonlinear equations, such as KdV equation, mKdV equation, when the real parameter is set specific values. 相似文献
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DOU Fu-Quan SUN Jian-An DUAN Wen-Shan LU Ke-Pu 《理论物理通讯》2007,48(4):584-590
Based on the multi-linear variable separation approach, a class of exact, doubly periodic wave solutions for the (3+1)-dimensional Jimbo-Miwa equation is analytically obtained by choosing the Jacobi elliptic functions and their combinations. Limit cases are considered and some new solitary structures (new dromions) are derived. The interaction properties of periodic waves are numerically studied and found to be inelastic. Under long wave limit, two sets of new solution structures (dromions) are given. The interaction properties of these solutions reveal that some of them are completely elastic and some are inelastic. 相似文献
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In this letter the three-dimensional nonlinear Helmholtz equation is investigated, which describes electro-magnetic wave propagation in a nonlinear Kerr-type medium such that sixteen families of new Jacobi elliptic functionsolutions are obtained, by using our extended Jacobian elliptic function expansion method. When the modulus m → 1or0, the corresponding solitary waves including bright solitons, dark solitons and new line solitons and singly periodicsolutions can be also found. 相似文献