共查询到19条相似文献,搜索用时 62 毫秒
1.
Quasi-Green's function method for free vibration of simply-supported trapezoidal shallow spherical shell 总被引:1,自引:1,他引:0
The idea of quasi-Green's function method is clarified by considering a free vibration problem of the simply-supported trapezoidal shallow spherical shell. A quasi- Green's function is established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the prob- lem. The mode shape differential equations of the free vibration problem of a simply- supported trapezoidal shallow spherical shell are reduced to two simultaneous Fredholm integral equations of the second kind by the Green formula. There are multiple choices for the normalized boundary equation. Based on a chosen normalized boundary equa- tion, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcome. Finally, natural frequency is obtained by the condition that there exists a nontrivial solution to the numerically discrete algebraic equations derived from the integral equations. Numerical results show high accuracy of the quasi-Green's function method. 相似文献
2.
The quasi-Green’s function method is used to solve the free vibration problem of clamped thin plates on the Winkler foundation.
Quasi-Green’s function is established by the fundamental solution and the boundary equation of the problem. The function satisfies
the homogeneous boundary condition of the problem. The mode-shape differential equation of the free vibration problem of clamped
thin plates on the Winkler foundation is reduced to the Fredholm integral equation of the second kind by Green’s formula.
The irregularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary
equation. The numerical results show the high accuracy of the proposed method. 相似文献
3.
《应用数学和力学(英文版)》2017,(6)
Nonlinear stability of sensor elastic element — corrugated shallow spherical shell in coupled multi-field is studied. With the equivalent orthotropic parameter obtained by the author, the corrugated shallow spherical shell is considered as an orthotropic shallow spherical shell, and geometrical nonlinearity and transverse shear deformation are taken into account. Nonlinear governing equations are obtained. The critical load is obtained using a modified iteration method. The effect of temperature variation and shear rigidity variation on stability is analyzed. 相似文献
4.
Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single inclined concentrated force at an interior point. The complex potentials are obtained based on a superposition principle, which provide the solutions to the plane problems of elasticity. The regular parts of the potentials are extracted in an asymptotic analysis. Based on the regular parts, Gre... 相似文献
5.
V. A. Postnov 《Mechanics of Solids》2010,45(1):51-56
We present a method for solving nonlinear inverse problems, which also include identification problems for elastic systems.
The problems whose initial data contain an error are usually solved by regularization methods [1–5]. In the present paper,
we give preference to Tikhonov’s regularization method, which has been widely used in the recent years in practice to increase
the stability of computational algorithms for solving problems in various areas of mechanics [6–9]. 相似文献
6.
The physical content of Maklakoffs tonometric (based on the loading of the cornea) method of measuring the intraocular pressure, widely used in medical practice, is discussed. For this purpose, we employ both the results of physical modeling of the eye described in the literature and the results of our own mathematical modeling based on the representation of the eyeball as a thin shell. The effect of the physical properties of the shell on the results of the modeling is investigated. Qualitative conclusions that follow from our study and may be of practical interest in measuring the intraocular pressure are discussed.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 24–39. Original Russian Text Copyright © 2005 by Bauer, Lyubimov, and Tovstik. 相似文献
7.
《International Journal of Solids and Structures》2003,40(9):2101-2119
The problem of a point force acting in a composite, two-dimensional, isotropic elastic half-plane is considered. An exact solution is obtained, using Mellin transforms and the Melan solution for a point force in a homogeneous half-plane. 相似文献
8.
In this paper the dynamics of solitary waves governed by Gardner’s equation for shallow water waves is studied. The mapping
method is employed to carry out the integration of the equation. Subsequently, the perturbed Gardner equation is studied,
and the fixed point of the soliton width is obtained. This fixed point is then classified. The integration of the perturbed
Gardner equation is also carried out with the aid of He’s semi-inverse variational principle. Finally, Gardner’s equation
with full nonlinearity is solved with the aid of the solitary wave ansatz method. 相似文献
9.
《International Journal of Solids and Structures》2004,41(3-4):871-884
This paper is concerned with the force-induced vibrations of linear elastic solids and structures. We seek a transient distribution of actuating stresses produced by additional eigenstrain, such that the vibrations produced by a given set of imposed forces are exactly compensated. This problem, known as dynamic shape control problem in structural engineering, or as dynamic displacement compensation problem in automatic control, is inverse to the usual direct problem of determining displacements due to imposed forces and actuation stresses. In the present paper, we extend a method, which was introduced by F.E. Neumann for demonstrating the uniqueness of direct elastodynamic problems. We use this extended Neumann method in order to show that the distribution of the actuating stresses for shape control must be equal to any statically admissible stress distribution that is in temporal equilibrium with the imposed forces. We furthermore discuss the role of stresses corresponding to this class of solutions in some detail, emphasizing the non-unique nature of a statically admissible stress. As an analytical justification of our formulations, we show that our method reveals some static results by J.M.C. Duhamel and by W. Voigt and D.E. Carlson. Particularly, our method can be interpreted as a dynamic extension of the Duhamel body-force analogy. We moreover present numerical results for a dynamically loaded, irregularly shaped domain in a state of plane strain. These finite element computations give excellent evidence for the validity of the presented method of shape control for both, the case of a step-input and the case of a harmonic excitation. 相似文献
10.
Based on the nonlinear theory of shallow spherical thick shells and the damage mechanics, a set of nonlinear equations of
motion for the laminated shallow spherical thick shells with damage subjected to a normal concentrated load on the top are
established. According to Hertz law, the contact force acted upon the shells is determined due to the impact of a mass, and
it is related to the mass and initial velocity of the striking object, the geometrical and physical character of the shell.
By using the finite difference method and the time increment procedure, the nonlinear equations are resolved. In the numerical
examples, the effects of the damage, the initial velocity, and mass of the striking object, the shells’ geometrical parameters
on the dynamic responses and dynamic buckling of the laminated shallow spherical thick shells are discussed.
Research of Y. Fu, Z. Gao and F. Zhu was supported by National Natural Science Foundation of China (No. 10572049). 相似文献
11.
12.
This paper is concerned with the direct boundary integral approach to isotropic spherical shell model with the transverse shear deformability taken into account. The validity of the formulation has been proved by example results including comparison with analytical solutions and classical thin shell theory.project supported by State Natural Science Foundation. 相似文献
13.
The problem of axisymmetric nonlinear vibration for shallow thin spherical and conical shells when temperature and strain fields are coupled is studied. Based on the large deflection theories of yon Ktirrntin and the theory of thermoelusticity, the whole governing equations and their simplified type are derived. The time-spatial variables are separated by Galerkin ‘ s technique, thus reducing the governing equations to a system of time-dependent nonlinear ordinary differential equation. By means of regular perturbation method and multiple-scales method, the first-order approximate analytical solution for characteristic relation of frequency vs amplitude parameters along with the decay rate of amplitude are obtained, and the effects of different geometric parameters and coupling factors us well us boundary conditions on thermoelustically coupled nonlinear vibration behaviors are discussed. 相似文献
14.
Green quasifunction method for vibration of simply-supported thin polygonic plates on Pasternak foundation 总被引:1,自引:0,他引:1
A new numerical method—Green quasifunction is proposed.The idea of Green quasifunction method is clarified in detail by considering a vibration problem of simply-supported thin polygonic plates on Pasternak foundation.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the vibration problem of simply-supported thin plates on Pasternak foundation is reduced to two simultaneous Fredholm integral equations of the second kind by Green formula.There are multiple choices for the normalized boundary equation.Based on a chosen normalized boundary equation,a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcome.Finally,natural frequency is obtained by the condition that there exists a nontrivial solution in the numerically discrete algebraic equations derived from the integral equations.Numerical results show high accuracy of the Green quasifunction method. 相似文献
15.
The idea of Green quasifunction method is clarified in detail by considering a free vibration problem of simply-supported trapezoidal shallow spherical shell on Winkler foundation.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the free vibration problem of simply-supported trapezoidal shallow spherical shell on Winkler foundation is reduced to two simultaneous Fredholm integral equations of the second kind by Green formula.There are multiple choices for the normalized boundary equation.Based on a chosen normalized boundary equation, the irregularity of the kernel of integral equations is avoided.Finally, natural frequency is obtained by the condition that there exists a nontrivial solution in the numerically discrete algebraic equations derived from the integral equations.Numerical results show high accuracy of the Green quasifunction method. 相似文献
16.
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17.
This paper deals with nonlinear free vibration of reticulated shallow spherical shells taking into account the effect of transverse shear deformation. The shell is formed by beam members placed in two orthogonal directions. The nondimensional fundamental governing equations in terms of the deflection, rotational angle, and force function are presented, and the solution for the nonlinear free frequency is derived by using the asymptotic iteration method. The asymptotic solution can be used readily to perform the parameter analysis of such space structures with numerous geometrical and material parameters. Numerical examples are given to illustrate the characteristic amplitude-frequency relation and softening and hardening nonlinear behaviors as well as the effect of transverse shear on the linear and nonlinear frequencies of reticulated shells and plates. 相似文献
18.
Based on the large deflection dynamic equations of axisymmetric shallow shells of revolution, the nonlinear forced vibration of a corrugated shallow shell under uniform load is investigated. The nonlinear partial differential equations of shallow shell are reduced to the nonlinear integral-differential equations by the method of Green's function. To solve the integral-differential equations, expansion method is used to obtain Green's function. Then the integral-differential equations are reduced to the form with degenerate core by expanding Green's function as series of characteristic function. Therefore, the integral-differential equations become nonlinear ordinary differential equations with regard to time. The amplitude-frequency response under harmonic force is obtained by considering single mode vibration. As a numerical example, forced vibration phenomena of shallow spherical shells with sinusoidal corrugation are studied. The obtained solutions are available for reference to design of corrugated shells 相似文献
19.
Based on the variational equation of the nonlinear bending theory of doubledeck reticulated shallow shells, equations of large deflection and boundary conditions for a double-deck reticulated circular shallow spherical shell under a uniformly distributed pressure are derived by using coordinate transformation means and the principle of stationary complementary energy. The characteristic relationship and critical buckling pressure for the shell with two types of boundary conditions are obtained by taking the modified iteration method. Effects of geometrical parameters on the buckling behavior are also discussed. 相似文献