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1.
Analytic nonlinear three-dimension solutions are presented for axially symmetrical homogeneous isotropic circular plates and multilayered plates with rigidly clamped boundary conditions and under transverse load.The geometric nonlinearily from a moderately large deflection is considered.A developmental perturbation method is used to solve the complicated nonlinear three-dimension differential equations of equilibrium.The basic idea of this perturbation method is using the two-dimension solutions as a basic form of the corresponding three-dimension solutions,and then processing the perturbation procedure to obtain the three-dimension perturbation solutions.The nonlinear three-dimension results in analytic expressions and in numerical forms for ordinary plates and multilayered plates are presented.All of the plate stresses are shown in figures.The results show that this perturbation method used to analyse nonlinear three-dimension problems of plates is effective. 相似文献
2.
周焕文 《应用数学和力学(英文版)》1981,2(5):519-528
In this paper, we analyzed some problems of nonlinear circular plates by means of perturbation method. The perturbation parameters chosen here are obtained from solving the equations and are not certain mechanical quantities given precedently. This is an extension of W. Z. Chien’s perturbation method, which uses the central deflection as the perturbation parameter. 相似文献
3.
A generalized hyperbolic perturbation method is presented for homoclinic solutions of strongly nonlinear autonomous oscillators,in which the perturbation procedure is improved for those systems whose exact homoclinic generating solutions cannot be explicitly derived.The generalized hyperbolic functions are employed as the basis functions in the present procedure to extend the validity of the hyperbolic perturbation method.Several strongly nonlinear oscillators with quadratic,cubic,and quartic nonlinearity are studied in detail to illustrate the efficiency and accuracy of the present method. 相似文献
4.
《International Journal of Solids and Structures》2005,42(18-19):4958-4970
The study was intended to evaluate the range of dynamic responses of structures with uncertain-but-bounded parameters by using the parameter perturbation method. The uncertain parameters were modeled as an interval vector. The first-order perturbation quantities of responses of the perturbed system were obtained through the parameter perturbation method, and then taking advantage of interval mathematics a new algorithm to estimate the response interval was presented. Comparisons between the parameter perturbation method and the probabilistic approach from mathematical proofs and numerical simulations were performed. The numerical results are in agreement with the mathematical proofs. The response range given by the parameter perturbation method encloses that obtained by the probabilistic approach. The results also show good robustness of the proposed method. 相似文献
5.
Static and Dynamic Analysis of Non-Linear Uncertain Structures 总被引:2,自引:0,他引:2
The procedures usually adopted in the evaluation of the stochastic response of structures with uncertain parameters, the so-called stochastic structures, are affected by some limits. Namely, the major drawbacks are: the conspicuous computational time required for the analysis of many degree of freedom systems and the loss of accuracy in the case of large uncertainty in the parameters. A method able to reduce the previous inconveniences was recently introduced in the study of statically loaded linear structures. The method, named improved perturbation method, was also extended to the field of linear dynamics. In both cases, the improved perturbation method provides a good approximation, even in the case of moderately large deviation of the uncertain parameters, and the computational time required is comparable to conventional first order perturbation. The present paper intends to apply the improved perturbation method in the second order analysis of geometrically non-linear uncertain systems subjected to static and dynamic deterministic forces. 相似文献
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8.
Periodic Traveling Waves for Diffusion Equations with Time Delayed and Non-local Responding Reaction 总被引:6,自引:0,他引:6
We develop a singular perturbation technique to study the existence of periodic traveling wave solutions with large wave speed
for a class of reaction-diffusion equations with time delay and non-local response. Unlike the classical singular perturbation
method, our approach is based on a transformation of the differential equations to integral equations in a Banach space that
reduces the singular perturbation problem to a regular perturbation problem. The periodic traveling wave solutions then are
obtained by the use of Liapunov-Schmidt method and a generalized implicit function theorem. The general result obtained has
been applied to a non-local reaction-diffusion equation derived from an age-structured population model with a logistic type
of birth function. 相似文献
9.
摄动有限元法在结构动力模型修改中的应用 总被引:3,自引:2,他引:3
本文将摄动理论与有限元法相结合,提出了用于小变参数结构分析的摄动有限元法(P-FEM),导出了在结构参数发生小变化的情况下,结构摄动单元矩阵的一般公式及结构的动特性随结构参数变化的二阶渐近展开式,并将这一结果运用于结构的动力模型修改中,提出了一种新的适合于工程应用的结构动力模型修改方法,把这一方法应用于实际的复杂结构动力模型修改中,获得了十分满意的结果. 相似文献
10.
Lie symmetries,symmetrical perturbation and a new adiabatic invariant for disturbed nonholonomic systems 总被引:1,自引:0,他引:1
For a nonlinear nonholonomic constrained mechanical system with the action of small forces of perturbation, Lie symmetries,
symmetrical perturbation, and a new type of non-Noether adiabatic invariants are presented in general infinitesimal transformation
of Lie groups. Based on the invariance of the equations of motion for the system under general infinitesimal transformation
of Lie groups, the Lie symmetrical determining equations, constraints restriction equations, additional restriction equations,
and exact invariants of the system are given. Then, under the action of small forces of perturbation, the determining equations,
constraints restriction equations, and additional restriction equations of the Lie symmetrical perturbation are obtained,
and adiabatic invariants of the Lie symmetrical perturbation, the weakly Lie symmetrical perturbation, and the strongly Lie
symmetrical perturbation for the disturbed nonholonomic system are obtained, respectively. Furthermore, a set of non-Noether
exact invariants and adiabatic invariants are given in the special infinitesimal transformations. Finally, one example is
given to illustrate the application of the method and results. 相似文献
11.
Direct perturbation solution procedures to non-linear systems are developed from variational statements derived from the principle of invariance of the action integral under infinitesimal transformations. Solution procedures that are the variational equivalent of the classical perturbation methods of strained parameters, the KBM method of averaging and the method of multiple time scales are presented. 相似文献
12.
ON SOLVING HIGH-ORDER SOLUTIONS OF CHIEN’S PERTURBATION METHOD TO STUDY CONVERGENCE BY COMPUTER 总被引:2,自引:0,他引:2
In this paper, we have obtained the analytical formula of arbitrary n-th order perturbation solution which perturbation parameter is central deflection for circular thin plate under a concentrated load by means of its integral equation. All unkown constants of every perturbation solution can be determined by computer. Hence higher order perturbation solution is obtained. Based on the solution of higher order perturbation, asymptotical property and suitable interval of Chien’s perturbation method are also discussed. 相似文献
13.
针对振动陀螺仪单向时滞耦合系统,研究了角速度、耦合强度、耦合时滞与系统输出信号之间的关系,着重关注耦合时滞对待检测角速度测量结果的影响.本文采用摄动法对振动陀螺仪单向时滞耦合系统进行理论分析,得到了系统输出信号、系统振动边界和待检测角速度的近似表达式,并将数值和近似计算结果进行了对比.理论分析结果与数值结果比较吻合,验证了运用摄动法分析振动陀螺仪单向时滞耦合系统的有效性,也表明了在运用摄动法分析系统时具有局限性. 相似文献
14.
陈山林 《应用数学和力学(英文版)》1986,7(7):633-641
In this paper, the least square method of determination of the perturbation parameter is presented when the perturbation technique is used in the solution of large deflection of axisymmetrical plates and shallow shells. The examples of circular plates are calculated and compared with the exact solution and other perturbation solutions. The results show the best agreement with the exact solution among those perturbation solutions. 相似文献
15.
A Universal Matrix Perturbation Technique for Complex Modes 总被引:1,自引:0,他引:1
IntroductionMatrixperturbationmethodsforthedynamicreanalysisofself_adjointsystemshavebeenwelldeveloped[1] .However,manysystemsgiverisetogeneralnon_self_adjointformulations.Importantexamplesareaeroelasticstabilityofsystems,arbitrarilydampedorgyroscopicsys… 相似文献
16.
Reductive Perturbation Method of Super KdV Equations 总被引:1,自引:1,他引:0
IntroductionSuperKdVequationsareut-buux 3hhx uxxx =0 ,ht-buhx-ahux chxx =0 ,( 1 )wherea ,b,c(c≠ 0 )areconstants.Thesimilarsolutionsof ( 1 )weregivenin [1 ]bydirectmethodpresentedbyClarksonandKruskal.Inthispaper,( 1 )arechangedintoordinaryKdVequationsbyreductiveperturbationm… 相似文献
17.
In the problems of large deflection of clamped circular plates under uniformly distributed loads, various perturbation parameters
relating to load, deflection, slope of deflection, membrane force, etc, are studied. For a general perturbation parameter,
the variational principle is used for the solution of such a problem. The applicable range of these perturbation parameters
are studied in detail. In the case of uniformly loaded plate, perturbation parameter relating to central deflection seems
to be the best among all others. The method of determination of perturbation solution by means of variational principle can
be used to treat a variety of problems, including the large deflection problems under combine loads.
This paper is completed under the guidance of Prof. Chien Wei-zang. 相似文献
18.
The free-parameter perturbation method is applied to solve the problems of nonlinear stability of spherical shallow shells under uniform load. As a modified perturbation method, the free-parameter perturbation method enables researchers to obtain all characteristic relations without choosing the certain perturbation parameter. Some examples were discussed to study the variety regulations of deflections and stress of shells in the process of buckling, and the results were compared with those of other researchers. 相似文献
19.
Using the perturbation method, the axial laminar flow of Non-Newtonian fluid through an eccentric annulus is studied in the present paper. The relative eccentricity ε is taken as a perturbation parameter, and the first order perturbation solutions of the problem, such as velocity field, limit velocity and pressure gradient, are all obtained. 相似文献
20.
The perturbation method for the reanalysis of the singular value decomposition(SVD)of general real matrices is presented in this paper.This is a simple but efficientreanalysis technique for the SVD,which is of great worth to enhance computationalefficiency of the iterative analysis problems that require matrix singular valuedecomposition repeatedly.The asymptotic estimate formulas for the singular values and thecorresponding left and right singular vectors up to second-order perturbation componentsare derived.At the end of the paper the way to extend the perturbation method to the case ofgeneral complex matrices is advanced. 相似文献