Stability and Natural Vibrations of Shells with Variable Geometric and Mechanical Parameters

The bifurcation stability and natural vibrations of shells of revolution with variable geometric and mechanical parameters are studied by using refined models and the variational–difference method. The qualitative and quantitative effects of the external geometry, material properties, and design features on the critical load and natural frequency are evaluated     

Natural Vibrations Of Corrugated Cylindrical Shells

A method for determining the natural frequencies and modes of corrugated noncircular cylindrical shells is presented. The influence of the length and amplitude of corrugations on the fundamental frequency of unloaded and axially compressed shells is examined. The difference between the dependences of frequencies and critical loads on shell geometry is shown. The possibility of optimizing shells in frequencies and critical loads is established__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 5, pp. 58–67, May 2005     

Natural Vibrations of Truncated Conical Shells of Variable Thickness

Journal of Applied Mechanics and Technical Physics - The paper presents the results of studying the natural frequencies of circular truncated conical shells, the thickness of which varies according...     

Influence of Initial Geometric Imperfections on the Vibrations and Dynamic Stability of Elastic Shells

The results from studies into the vibrations and dynamic stability of thin elastic shells with initial geometric imperfections are analyzed. The corresponding dynamic problems are solved in both linear and nonlinear formulations. The influence of initial axisymmetric and nonaxisymmetric deflections on natural, forced, parametrically excited, and self-excited vibrations (flutter) is studied. The dynamic buckling of imperfect shells under short-term impulsive loading is examined. Some aspects of experimental investigation into the vibrations of shells with small geometric imperfections (deviations from the design shape) are considered     

Natural Vibrations of Ribbed Cylindrical Shells with Low Shear Stiffness

A technique is proposed to determine the natural frequencies of rib-reinforced cylindrical shells with low shear stiffness. The equations of motion based on the Timoshenko model are used. The influence of the transverse shear moduli of the shell and ribs on the minimum natural frequencies and corresponding modes is studied by way of numerical examples. It is shown that the effect of the discrete ribs is different from that predicted by the classical theory of ribbed shells__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 4, pp. 66–74, April 2005.     

Vibrations and Stability of Shallow Ribbed Shells with a Rectangular Planform

A technique is developed to determine the critical stresses and natural frequencies of shallow ribbed shells with a rectangular planform and the corresponding buckling wave and natural modes. The effect of discrete rib arrangement on these characteristics is studied by numerical examples.     

A Note on Analysis of the Natural Vibrations of Shallow Shells with Cuts on the Surface

A new approach is proposed to study the dynamic behavior of shells with an arbitrary planform weakened by surface cuts (cracks.) The approach is based on the method of R-functions. The computer simulation is carried out using the POLE-SHELL problem-oriented system, which implements the method of R-functions and variational methods. Numerical results are presented     

On Free Nonlinear Vibrations of Fluid-Filled Cylindrical Shells with Multiple Natural Frequencies

Nonlinear free vibrations of a cylindrical shell fully filled with a perfect incompressible fluid are studied. The case is examined where two natural frequencies of the shell are close __________ Published in Prikladnaya Mekhanika, Vol. 41, No. 10, pp. 127–138, October 2005     

The Nonlinear Vibrations and Stability of Orthotropic Cylindrical Liquid-Carrying Shells Under Periodic Actions

The nonlinear resonance vibrations and stability of nonlinear orthotropic shells partially filled with a liquid and subjected to longitudinal and transverse periodic loading are studied. The equations of motion are derived with regard for the existence and nonlinear interaction of conjugate flexural modes of the shell. Stationary regimes for forced and parametric vibrations are found and analyzed for stability under the conditions of fundamental and subharmonic resonances. The amplitude–frequency characteristics of these regimes are constructed for various parameters of the system     

Experimental Investigation of the Natural Vibrations of Shells of Revolution with a Liquid and Added Masses

It is established that the effect of rigidly attached masses on the natural frequencies is considerably greater than that of the liquid filling the shell. It is shown that the resonant vibrations of the shell can be excited by a wind load on a thin plate rigidly attached to the shell with an added mass     

On Multimode Nonlinear Vibrations of Filled Cylindrical Shells

A technique is proposed to study the multimode nonlinear vibrations of circular shells fully filled with a perfect incompressible liquid. This technique is used to study the basic laws of modal interaction at nonlinear, including sub-harmonic resonances     

Vibrations of Cylindrical Shells Filled with a Liquid

The paper reports on experimental results for a dynamic system of two identical shells filled with a liquid and placed on a common elastic foundation. It is established that vibrations excited in one of the shells synchronize the vibrations of the whole system     

Numerical Solution of Spectral Problems in Studying the Stability and Natural Vibrations of Compound Rods

Equivalent generalized problems are obtained for new spectral problems described by ordinary differential equation of the fourth order with conjugation conditions. High-accuracy discretization algorithms are developed based on classes of piecewise-polynomial functions that may have a discontinuous first derivative at the point where the conjugation conditions are specified     

Forced Axisymmetric Nonlinear Vibrations of Reinforced Conical Shells

A numerical method for analysis of the axisymmetric nonlinear vibrations of conical shells is developed based on the integro-differential method of constructing difference schemes. A prediction analysis is conducted of the response of shells with various taper angles to an impulsive load     

Vibrations of Thin Piezoelectric Flexural Shells: Two-Dimensional Approximation

We consider the eigenvalue problem for a thin piezoelectric shell, of thickness 2∈, clamped along a portion of its lateral surface under the geometrical assumption that the space of inextensional displacements is infinite-dimensional. We then show that the eigensolutions converge, as ∈→0, to the eigensolutions of the two-dimensional piezoelectric flexural shell. This revised version was published online in June 2006 with corrections to the Cover Date.     

圆柱壳非线性振动的多重模式分析

分析了各向同性圆柱壳的非线性自由振动，文中采用经典的非线性弹性力学方法推导了圆柱壳的大振幅运动方程，这些方程静态形式与冯．卡门的板理论方程其有同样的精度。文中采用双重富氏级主伽辽金方法近似地求解运行方程，利用谐波地和牛顿－莱福逊法妥高度耦合的非线性微分方程组，分析了模式的耦合对非线性频率的影响。     

圆柱壳的非线性自由振动分析

本文分析了各向同性封闭圆柱壳的非线性自由振动。文中采用经典的非线性弹性力学方法推导了圆柱壳的大振幅运动方程,这些方程的静态形式与冯·卡门的板理论方程具有同样的精度。文中讨论了四种基本振动模态,并且还以数学公式的形式给出了一般的最终结果,一些例子以曲线给出结果,并进行了比较。结果还表明线性振动可以作为非线性振动的一种特例。