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991.
In this paper, we analyze the nonlinear dynamic response of an orthotropic laminate in a simply supported boundary condition subject to thermal and mechanical loading. The equation of motion for the laminate’s deflection is obtained in a decoupled Duffing equation by means of a Galerkin-type method without Berger’s approximations. The Duffing equation incorporates an arbitrary thermal field, with both the in-plane and transverse temperature variations in a steady-state and a transient state. The formulation indicates that the transverse temperature variation produces an additional pressure load, while the in-plane temperature variation affects the system frequency. The equation allows for characterization of the laminate behaviors in nonlinear thermal buckling, thermal vibration and thermal mechanical response. 相似文献
992.
T. A. Bodnar’ 《Journal of Applied Mechanics and Technical Physics》2007,48(6):818-823
An approximate solution ω = A[ω, μ] of the nonlinear integral Nekrasov equation is obtained by successive replacement of the
kernel of the integral operator by a close one. The solution is sought not directly at the bifurcation point μ1 = 3 of the linearized equation ω = μL[ω] but at the point μ = 1 at which operator A[ω, μ], remaining nonlinear in ω, is linear
in μ.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 50–56, November–December, 2007. 相似文献
993.
Wave processes are studied within the framework of a turbulence model that describes the reaction-diffusion processes in physicochemical hydrodynamics [{xc1}–{xc5}]. For certain parameters of the equation, exact analytical traveling-wave solutions in the form of kinks are obtained. In the general case, the wave processes can be analyzed using numerical simulation. It is confirmed that for a zero dispersion coefficient the nonlinear wave processes are disordered. It is established that when the dispersion terms are taken into account, as for the Kuramoto-Sivashinsky equation, periodic structures develop in the system starting from a certain threshold dispersion-coefficient value. 相似文献
994.
An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones. 相似文献
995.
D. N. Sheidakov 《Journal of Applied Mechanics and Technical Physics》2007,48(4):547-555
The stability problem of a rectangular plate undergoing uniform biaxial in-plane tensile strain is solved using the three-dimensional
equations of nonlinear elasticity. The surfaces of the plate are stress-free, and special boundary conditions that allow one
to separate variables in the linearized equilibrium equations are specified on the lateral surfaces. For three particular
models of incompressible materials, the critical curves are constructed and the instability region is determined in the plane
of the loading parameters (the multiplicities of elongations of the plate material in the unperturbed equilibrium state).
The numerical results show that for thin plates loaded by tensile stresses, the size and shape of the instability region depend
only slightly on the relation among the length, width, and thickness of the plate. Based on the results obtained, a simple
approximate stability criterion is proposed for an elastic plate under tensile loads.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 94–103, July–August, 2007. 相似文献
996.
Yu. Ya. Trifonov 《Journal of Applied Mechanics and Technical Physics》2007,48(1):91-100
The linear and nonlinear stability of downward viscous film flows on a corrugated surface to freesurface perturbations is
analyzed theoretically. The study is performed with the use of an integral approach in ranges of parameters where the calculated
results and the corresponding solutions of Navier-Stokes equations (downward wavy flow on a smooth wall and waveless flow
along a corrugated surface) are in good agreement. It is demonstrated that, for moderate Reynolds numbers, there is a range
of corrugation parameters (amplitude and period) where all linear perturbations of the free surface decay. For high Reynolds
numbers, the waveless downward flow is unstable. Various nonlinear wavy regimes induced by varying the corrugation amplitude
are determined.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 110–120, January–February, 2007. 相似文献
997.
In literature, nonlinear traveling waves in elastic circular rods have only been studied based on single partial differential
equation (pde) models, and here we consider such a problem by using a more accurate coupled-pde model. We derive the Hamiltonian
from the model equations for the long finite-amplitude wave approximation, analyze how the number of singular points of the
system changes with the parameters, and study the features of these singular points qualitatively. Various physically acceptable
nonlinear traveling waves are also discussed, and corresponding examples are given. In particular, we find that certain waves,
which cannot be counted by the single-equation model, can arise.
The project supported by the Research Grants Council of the HKSAR, China (City U 1107/99P) and the National Natural Science
Foundation of China (10372054 and 10171061) 相似文献
998.
给出两水平固壁间两层不可压缩理想流体中二维非线性界面波的演化方程,首先建立出这个演化方程,并由此方程在一定条件下得到二维非线性界面长波满足的近似方程,然后从理论上证明这个长波近似方程包含了以下两个描述一阶界面升高的著名的浅水孤立波方程;Korteweg-de Vries(KdV)方程和Kadomtsev-Petvishvili(KP)方程,所得特殊结果与前人的一致,表明所建立的二维非线性界面波演化方程正确且具有一般性。 相似文献
999.
以线性系统的非线性修改方法为基础,导出了局部非线性振动的灵敏度分析方法;提出了灵敏度为指导的优化设计思想,并将其应用于大型结构上的局部非线性因素的优化设计。文中介绍一些典型非线性特征的数学描述。最后,本文以火炮结构中的炮口振动为例,提出在炮口处增设炮口减振器的设计思想,并用本文方法对炮口减振器的参数进行优化设计,得到满意的结果。 相似文献
1000.
In this paper chaotic behavior of nonlinear viscoelastic panels in asupersonic flow is investigated. The governing equations, based on vonKàarmàn's large deflection theory of isotropic flat plates, areconsidered with viscoelastic structural damping of Kelvin's modelincluded. Quasi-steady aerodynamic panel loadings are determined usingpiston theory. The effect of constant axial loading in the panel middlesurface and static pressure differential have also been included in thegoverning equation. The panel nonlinear partial differential equation istransformed into a set of nonlinear ordinary differential equationsthrough a Galerkin approach. The resulting system of equations is solvedthrough the fourth and fifth-order Runge–Kutta–Fehlberg (RKF-45)integration method. Static (divergence) and Hopf (flutter) bifurcationboundaries are presented for various levels of viscoelastic structuraldamping. Despite the deterministic nature of the system of equations,the dynamic panel response can become random-like. Chaotic analysis isperformed using several conventional criteria. Results are indicative ofthe important influence of structural damping on the domain of chaoticregion. 相似文献