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1.
In this paper, the nonlinear free vibration of a stringer shell is studied. The mathematical model of the string shell, which is the most convenient for frequency analysis, is considered. Due to the geometrical properties of the vibrating shell, strong nonlinearities are evident. Approximate analytical expressions for the nonlinear vibration are provided by introducing the extended version of the Hamiltonian approach. The method suggested in the paper gives the approximate solution for the differential equation with dissipative term for which the Lagrangian exists. The aim of this study is to provide engineers and designers with an easy method for determining the shell nonlinear vibration frequency and nonlinear behavior. The effects of different parameters on the ratio of nonlinear to linear natural frequency of shells are studied. This analytical representation gives excellent approximations to the numerical solutions for the whole range of the oscillation amplitude, reducing the respective error of the angular frequency in comparison with the Hamiltonian approach. This study shows that a first-order approximation of the Hamiltonian approach leads to highly accurate solutions that are valid for a wide range of vibration amplitudes. 相似文献
2.
复杂非线性转子—轴承系统动力特性数值分析 总被引:3,自引:0,他引:3
研究非线性高维复杂转子-轴承系统的动力特性。针对系统的局部非线性特征,给出了一种降阶及配套动力积分方法。降阶系统仍保持局部非线性特征,非线性响应数值积分所需的迭代只需在局部非线性的维数上执行。对于油膜力无封闭解的实际轴承,采用变分不等方程有限元法求解Reynolds边值问题,使得油膜力及其Jacobian矩阵的计算变得非常简单明了且与具有协调一致的精度。应用上述方法计算分析了一双跨、椭圆轴承-转子系统的不平衡响应,数值结果展现了系统丰富复杂的非线性现象。 相似文献
3.
The paper presents a review of scientific studies on development, of the classical and refined models of the thermomechanical
behavior of thin-walled single- and multilayer viscoelastic elements. Allowance is made for the temperature dependence of
the properties of the material and physical and geometrical nonlinearities in the case of monoharmonic strain as one of the
most typical types of deformation. Methods of solution of nonlinear connected problems of thermoviscoelasticity and results
of solution of some specific problems on vibrations and heating-up of thin-walled rods, plates, and shells in quasistatic
and dynamic formulations are discussed. A number of thermomechanical effects are noted. They are due to the coupling of mechanical
and thermal fields and physical and geometrical nonlinearities, taken into account either separately or jointly.
S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated, from Prikladnaya Mekhanika,
Vol. 36, No. 2, pp. 39–62, February, 2000. 相似文献
4.
本文采用有限元数值方法,分析计算了大型钢筋混凝土壳的几何、物理非线性静力问题。对非线性方程组的求解,文中提出了一种将载荷增量和位移增量相结合的合理方法,保证了在临界点附近迭代法的收敛性。最后,文中通过对实际双曲冷却塔壳的分析,得到了一些对实际工程设计具有指导意义的有益结论。 相似文献
5.
H. Altenbach O. Morachkovsky K. Naumenko A. Sychov 《Archive of Applied Mechanics (Ingenieur Archiv)》1997,67(5):339-352
Summary A phenomenological constitutive model for characterization of creep and damage processes in metals is applied to the simulation
of mechanical behaviour of thin-walled shells and plates. Basic equations of the shell theory are formulated with geometrical
nonlinearities at finite time-dependent deflections of shells and plates in moderate bending. Numerical solutions of initial/boundary-value
problems have been obtained for rectangular thin plates (two-dimensional case) and axisymmetrically loaded shells of revolution
(one-dimensional case). Based on the numerical examples for the two problems, the influence of geometrical nonlinearities
on the creep deformation and damage evolution in shells and plates is discussed.
Accepted for publication 30 October 1996 相似文献
6.
Basic Equations for Viscoelastic Laminated Shells with Distributed Piezoelectric Inclusions Intended to Control Nonstationary Vibrations 总被引:2,自引:0,他引:2
The basic equations for viscoelastic laminated shells with distributed piezoelectric sensors and actuators are presented. Physical and geometrical nonlinearities are taken into account. It is shown that the asymptotic methods of nonlinear mechanics can be used in combination with the Bubnov–Galerkin method to solve nonlinear boundary value problems. 相似文献
7.
Based on Donnell shallow shell equations, the nonlinear vibrations and dynamic instability of axially loaded circular cylindrical shells under both static and harmonic forces is theoretically analyzed. First the problem is reduced to a finite degree-of-freedom one by using the Galerkin method; then the resulting set of coupled nonlinear ordinary differential equations of motion are solved by the Runge–Kutta method. To study the nonlinear behavior of the shell, several numerical strategies were used to obtain Poincaré maps, Lyapunov exponents, stable and unstable fixed points, bifurcation diagrams, and basins of attraction. Particular attention is paid to two dynamic instability phenomena that may arise under these loading conditions: parametric excitation of flexural modes and escape from the pre-buckling potential well. Calculations are carried out for the principal and secondary instability regions associated with the lowest natural frequency of the shell. Special attention is given to the determination of the instability boundaries in control space and the identification of the bifurcational events connected with these boundaries. The results clarify the importance of modal coupling in the post-buckling solution and the strong role of nonlinearities on the dynamics of cylindrical shells. 相似文献
8.
I.Intr0ducti0nThenon1inearvibrationprob1emsofshellsofrevolutionarealwaysofgreatdifficultyandofgreatvaluetostudyfortheircomplexityinmathematicsandmechanicsaswellasinwideapplications.ManyinvestigatorshavemaderesearchontheseinoneWayoranother,butfewinvolvedth… 相似文献
9.
E. N. Chumachenko 《Mechanics of Solids》2008,43(4):642-651
The necessity to develop and optimize new technological processes of gas moulding of shells under the superplasticity conditions, which ensure large elongation and complexity of the shape of end items, makes the specialists in the field of mathematical simulation to pose and solve problems of constant improvement of the imitation models. Because of a large number of “embedded” nonlinearities (the physical properties of the material, friction, and unknown boundaries), the solution of such problems requires large computer resources, high qualification of designers, and large amount of labor.In the present paper, we consider the problems of express analysis of pattern change of spatial shells on the basis of estimation of the behavior of their critical cross-sections. We solve problems of moulding of titan shells (made of VT6 alloy) in a matrix of complicated shape. We theoretically and experimentally justify the methods for predicting and constructing the optimal technological processes of shell deformation under conditions close to superplasticity by using the 2.5D designing procedures. 相似文献
10.
L. V. Kurpa E. I. Lyubitskaya I. O. Morachkovskaya 《International Applied Mechanics》2010,46(6):660-668
The paper proposes a method to solve geometrically nonlinear bending problems for thin orthotropic shallow shells and plates
interacting with a Winkler–Pasternak foundation under transverse loading. This method is based on Ritz’s variational method
and the R-function method. The developed algorithm and software are used to solve a number of test problems and to study complex-shaped
shells. The effect of the shape of shells, the boundary conditions, the stiffness of the foundation, and the load distribution
on the behavior of isotropic and orthotropic shells undergoing geometrically nonlinear bending is studied 相似文献
11.
《应用数学和力学(英文版)》2017,(5)
In this paper, Donnell's shell theory and smeared stiffeners technique are improved to analyze the postbuckling and buckling behaviors of circular cylindrical shells of stiffened thin functionally graded material(FGM) sandwich under an axial loading on elastic foundations, and the shells are considered in a thermal environment. The shells are stiffened by FGM rings and stringers. A general sigmoid law and a general power law are proposed. Thermal elements of the shells and reinforcement stiffeners are considered. Explicit expressions to find critical loads and postbuckling load-deflection curves are obtained by applying the Galerkin method and choosing the three-term approximate solution of deflection. Numerical results show various effects of temperature, elastic foundation, stiffeners, material and geometrical properties, and the ratio between face sheet thickness and total thickness on the nonlinear behavior of shells. 相似文献
12.
The nonlinear aeroelastic behavior of isotropic rectangular plates in supersonic gas flow is examined. Quadratic and cubic aerodynamic nonlinearities as well as cubic geometrical nonlinearities are considered in this study. While the aerodynamic nonlinearities are the results of the expansion of the nonlinear piston-theory aerodynamics loading up to the third-order, the geometrical nonlinearities are due to stiffening effects from the panel out-of-plane deformation consistent with the von Karman’s nonlinear plate theory. While in vacuum the typical nonlinear hardening frequency vs. oscillation amplitude, one characterized by monotonically increasing amplitudes at increasing frequencies, exists, in the presence of a high-speed flow, qualitative and quantitative changes of the nonlinear relationship are expected. This paper shows how the thin-plate behavior is influenced by the high-speed flows providing the “amplitude–frequency” dependency, which describes the nonlinear oscillations of the considered aeroelastic system. 相似文献
13.
Yokoo Yoshitsura Matsunaga Hiroyuki 《International Journal of Solids and Structures》1974,10(2):261-274
This paper presents a general nonlinear theory of elastic shells for large deflections and finite strains in reference to a certain natural state. By expanding the displacement components into power series in the coordinate θ3 normal to the undeformed middle surface of shells, the expansions of the Cauchy-Green strain tensors are expressed in terms of these expanded displacement components. Through the modified Hellinger-Reissner variational principle for a three-dimensional elastic continuum, a set of the fundamental shell equations is derived in terms of the expanded Cauchy-Green strain tensors and Kirchhoff stress resultants. The Love-Kirchhoff hypothesis is not assumed and higher order stretching and bending are taken into consideration. For elastic shells of isotropic materials, assuming the strain-energy to be an analytic function of the strain measures, general nonlinear constitutive equations are then derived. Thus, a complete and consistent two-dimensional shell theory incorporating the geometrical and physical nonlinearities is established. The classical theories of shells are directly derivable from the present results by proper truncations of the series. 相似文献
14.
The paper outlines the fundamentals of the method of solving static problems of geometrically nonlinear deformation, buckling,
and postbuckling behavior of thin thermoelastic inhomogeneous shells with complex-shaped midsurface, geometrical features
throughout the thickness, or multilayer structure under complex thermomechanical loading. The method is based on the geometrically
nonlinear equations of three-dimensional thermoelasticity and the moment finite-element scheme. The method is justified numerically.
Results of practical importance are obtained in analyzing poorely studied classes of inhomogeneous shells. These results provide
an insight into the nonlinear deformation and buckling of shells under various combinations of thermomechanical loads 相似文献
15.
Elastic ribbons subjected to twist and stretch handle multiple morphological instabilities, amongst others, the longitudinally wrinkled and creased helicoids are investigated in the present paper as promising periodic nonlinear waveguides. Modeling the ribbon by isogeometric Kirchhoff–Love shells, the first longitudinal buckling mode is recovered numerically and used into the Bloch–Floquet method to obtain dispersion curves. After analyzing the effects of the buckling pattern on the different wavemodes, it is shown that classical linear axial waves interact with bending ones and become dispersive. Additionally, as buckling involves geometrical nonlinearities, the structure is expected to host stable nonlinear waves. Indeed, clear supersonic rarefaction trains are observed experimentally and their characteristics are found in agreement with the weakly nonlinear Boussinesq model. 相似文献
16.
《International Journal of Solids and Structures》2007,44(10):3136-3155
A study of the collapse behaviour of hemi spherical and shallow spherical shells and their modes of deformation under impact loading are presented in this paper. Aluminium spherical shells of various radii and thicknesses were made by spinning. These were subjected to impact loading under a drop hammer and the load histories were obtained in all the cases. Three-dimensional numerical simulations were carried out for all the tested specimen geometries using LS-DYNA®. Material, geometric and contact nonlinearities were incorporated in the analysis. The uni-axial stress–strain curve for the material was obtained experimentally and was assumed to be piecewise linear in the plastic region. The results from impact experiments are used for the validation of the numerical simulations. Three distinct modes of deformation, namely local flattening, inward dimpling and formation of multiple numbers of lobes were analysed and influence of various parameters on these modes is discussed. 相似文献
17.
18.
V. A. Maksimuuk V. S. Tarasyuk I. S. Chernyshenko 《International Applied Mechanics》1999,35(6):614-620
A study is made of geometrically and physically nonlinear inverse problems concerning the axisymmetric deformation of cylindrical
shells into conical shells. Results obtained from the numerical solution of the problems are used to determine the laws of
distribution of the surface loads, stresses, strains, and displacements in relation to the initial parameters and nonlinearities
of the shells.
S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya
Mekhanika, Vol. 35, No. 6, pp. 86–91, June, 1999. 相似文献
19.
Physically and geometrically nonlinear deformation of conical shells with an elliptic hole 总被引:1,自引:1,他引:0
I. S. Chernyshenko E. A. Storozhuk S. B. Kharenko 《International Applied Mechanics》2008,44(2):174-181
The elastoplastic state of conical shells weakened by an elliptic hole and subjected to finite deflections is studied. The
material of the shells is assumed to be isotropic and homogeneous; the load is constant internal pressure. The problem is
formulated and a technique for numerical solution with allowance for physical and geometrical nonlinearities is proposed.
The distribution of stresses, strains, and displacements along the hole boundary and in the zones of their concentration is
studied. The solution obtained is compared with the solutions of the physically and geometrically nonlinear problems and a
numerical solution of the linear elastic problem. The stress-strain state around an elliptic hole in a conical shell is analyzed
considering both nonlinearities
__________
Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 69–77, February 2008. 相似文献