共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, an orthogonal function method is presented based on the idea to suppose periodic solution with the method of
harmonic balance. The displacement is expressed in the form of trigonometric functions, a group of simplified eigenequations
are obtained by the use of orthogonarity of trigonumetric functions and linear modes. The method overcomes the difficulty
of a drift term existing ht systems with quadratic nonlinearities. The calculation examples show that the method has the advantages
of high calculation precision, high convergence speed and little calculation work. 相似文献
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钱伟长 《应用数学和力学(英文版)》1989,10(5):385-397
This paper gives the theorems concerning the summation of trigonometric series with the help of Fourier transforms. By means of the known results of Fourier transforms, many difficult and complex problems of summation of trigonometric series can be solved. This method is a comparatively unusual way to find the summation of trigonometric series, and has been used to establish the comprehensive table of summation of trigonometric series. In this table 10 thousand series are given and most of them are new. 相似文献
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《International Journal of Non》1987,22(2):89-98
The Galerkin method is an approximate method which finds wide application in solving differential and integral equations. But a large amount of computation is needed in order to get a high order approximation by using the method. Applying the FFT technique to form a so-called fast Galerkin method, we can reduce the computation work greatly, when taking trigonometric functions as characteristic functions. Taking the periodic solution of non-linear oscillators as an example, we illustrate the procedure and the efficiency of the method. Moreover, with some modifications we extend the applicability of the method, so that not only periodic solutions with known periods, but also those with unknown periods, as well as subharmonics, combination tones, etc., can be treated with the method. Some techniques are described which can be used to simplify the computation. 相似文献
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《应用数学和力学(英文版)》2019,(6)
A trigonometric series expansion method and two similar modified methods for the Orr-Sommerfeld equation are presented. These methods use the trigonometric series expansion with an auxiliary function added to the highest order derivative of the unknown function and generate the lower order derivatives through successive integrations. The proposed methods are easy to implement because of the simplicity of the chosen basis functions. By solving the plane Poiseuille flow(PPF), plane Couette flow(PCF), and Blasius boundary layer flow with several homogeneous boundary conditions,it is shown that these methods yield results with the same accuracy as that given by the conventional Chebyshev collocation method but with better robustness, and that obtained by the finite difference method but with fewer modal number. 相似文献
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M. A. Abdou 《Nonlinear dynamics》2008,52(3):277-288
The improved F-expansion method with a computerized symbolic computation is used to construct the exact traveling wave solutions
of four nonlinear evolution equations in physics. As a result, many exact traveling wave solutions are obtained which include
new soliton-like solutions, trigonometric function solutions, and rational solutions. The method is straightforward and concise,
and it holds promise for many applications. 相似文献
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加权残数配点法解正交各向异性板的积分方程 总被引:1,自引:0,他引:1
本文推导了一般各向异性板弯曲的积分方程,运用加权残数配点法求解了正交各向异性板弯曲的积发方程,本文将部分配点取在边界上,另一部分配点取在域外,只用关于找度的基本积分方程,而不用关于转角的补充积分方程,简化了方程求解和计算程序,由于正交各向异性板没有争析形式的、实用的基本解,本文提出了两种新的近似基本解;加权双三角级数;广义各向同性板解析形式的基本解和加权双三角级数的叠加,算例表明,本文提出的解法和近似基本解适用于各类边界条件的正交各向异性板,具有简单、可靠、精度高等优点。 相似文献
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Sypniewska-Kamińska Grażyna Awrejcewicz Jan Kamiński Henryk Salamon Robert 《Meccanica》2021,56(4):963-980
Meccanica - The nonlinearities of geometric nature that is characteristic for pendulum-type systems are expressed by the trigonometric functions. In order to apply the method of multiple scales in... 相似文献
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N. A. Veklich 《Mechanics of Solids》2013,48(6):673-681
The integro-differential equation of small transverse vibrations of a rectilinear elastic pipeline filled with a transported fluid is obtained. The pipeline vibrations are described in the linear setting in the beam approximation. The mutual dynamic influence of motions of the pipeline and the filling fluid is taken into account. A complete trigonometric series method is presented for solving problems with various boundary and initial conditions for the pipeline deflection. 相似文献
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爆炸参量对爆破地震反应谱的影响 总被引:2,自引:0,他引:2
利用在地震工程中广泛应用的反应谱理论对爆破地震效应进行研究。根据单自由度体系反应谱理论,采用计算量少、精确度高的三角插值解析公式法取代常用的分段线性插值法进行反应谱数值计算。结合大量工程爆破地震监测资料,对不同爆炸参量下产生的爆破振动信号进行反应谱分析。结果表明,结构体对爆破震动的响应特征与爆炸参量有着密切的关系。为综合研究爆破机理和爆破地震波,特别是为将来构建爆破振动速度 频率相关安全准则提供了一种实用的分析技术。 相似文献
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采用同时具有三角函数良好逼近特性和小波多分辨率与局部特性的Hermite插值型三角小波,基于二维张量积三角小波,推导了求解各种不同边界条件下的矩形弹性薄板的弯曲、振动和屈曲问题的统一列式,同时给出了两种提高计算精度的方法一升阶法和多分辨率法。数值算例表明,三角小波法求解弹性薄板的弯曲、振动和屈曲问题时,能方便地处理各类边界条件,计算效果良好;自振特性分析更具优势,升阶法和多分辨率法能有效地提高分析精度。 相似文献
14.
The paper outlines a method of analyzing layered anisotropic shells of revolution for stability using complex Fourier series.
This simplifies the derivation of the basic equations compared with complete trigonometric Fourier series. Anisotropic shells
in the form of a torus segment are analyzed for stability. This method allows optimizing the structure of the material and
the geometry of the shell 相似文献
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汪克让 《应用数学和力学(英文版)》1990,11(9):869-879
In this paper an accurate solution for the thick rectangular plate with free edges laid onelastic foundation is presented.The superposition method of trigonometric series is used.The method can solve this kind of plates directly and simply.Its results completely satisfythe boundary conditions of the four free edges and nicely agree with the solutions by WangKe-lin and Huang Yi. 相似文献
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卢文达 《应用数学和力学(英文版)》1980,1(3):385-411
The equations of equilibrium of shallow shells with rectangular base elastically supported with edge arched beams are obtained through the variational principle together with corresponding boundary conditions and corner conditions. It is assumed that edge arched beams are of narrow plate form, so that only the rigidities in their own planes are taken into consideration, torsional rigidities and bending rigidities out of their own planes are neglected. In this paper, two kinds of corner conditions are discussed. First of these is pinned corner conditions. Second of these is simply supported corner conditions, such that the corner can be moved freely in horizontal directions. The former corresponds to the conditions of those with heavy tension beams, in which the tension rigidities of the rods can be assumed infinite. The latter corresponds to the conditions of elastically supported edge arched beams without tension rods. In the former case, the edge tangential displacement of shallow shells is assumed to be zero everywhere, so that the vertical displacement of the edge arched beams gives the only elastic supported forces. This kind of supporting conditions is a good approximation for practical roof design.In this paper, the solutions of the problem of shallow spherical shell of square base supported elastically by edge arched beams and tie-rods under the conditions, such that the corners are restricted, are solved by the method of double trigonometric series. The edge conditions are integrated along their respective edge, and the conditions at corner are satisfied by proper choices of integral constants. The integrated edge conditions are then used to determine the unknown constants in the double trigonometric series. The result of this paper gives the tension in the tie-rods directly, which is an important quantity in the shell roof design practice.The method of integrated form of boundary conditions used in this paper in general is useful for the treatment of problem of plates and shells elastically supported by edge frames and tie-rods or by other means.This paper also gives the results of numerical calculation based upon the method of double trigonometric series on the problem of shallow spherical shell with square bases elastically supported by arched beams. The corner are pinned supported or simply supported. The calculated results for =11.5936 show that the trigonometric series converges rapidly. The effect of elastic deformation in the arched beams to the components of membrane tensions, moments, and deflections of the shell are given. 相似文献
18.
鉴于整周模糊度的快速解算是GPS载波相位测姿的一个主要技术难题,从系统实时性、动态性要求出发,给出了一个整周模糊度的快速解算的新方法。其主要特点为:利用三角函数约束条件减少模糊度搜索范围,优选指标不受基线运动状态影响,可利用多历元动态基线数据进行平差。实验结果验证了该算法的有效性。 相似文献
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Some properties of the wavelet transform of trigonometric function, periodic function and nonstationary periodic function have been investigated. The results show that the peak height and width in wavelet energy spectrum of a periodic function are in proportion to its period. At the same time, a new equation, which can truly reconstruct a trigonometric function with only one scale wavelet coefficient, is presented. The reconstructed wave shape of a periodic function with the equation is better than any term of its Fourier series. And the reconstructed wave shape of a class of nonstationary periodic function with this equation agrees well with the function. 相似文献
20.
R. Abazari 《Journal of Applied Mechanics and Technical Physics》2013,54(3):397-403
In this paper, the (G′/G)-expansion method is used to obtain exact solitary-wave and periodic-wave solutions for nonlinear evolution equations arising in mathematical physics with the aid of symbolic computations, namely, the Klein-Gordon equation with quintic nonlinearity. Our work is motivated by the fact that the (G′/G)-expansion method provides not only more general forms of solutions, but also periodic and solitary waves. As a result, hyperbolic function solutions and trigonometric function solutions with parameters are obtained. The method is straightforward and concise, and its application is promising for other nonlinear evolution equations in mathematical physics. 相似文献