Nonlinear vibrations of rotating thin circular cylindrical shell

Nonlinear vibrations of thin circular cylindrical shells are investigated in this paper. Based on Love thin shell theory, the governing partial differential equations of motion for the rotating circular cylindrical shell are formulated using Hamilton principle. Taking into account the clamped-free boundary conditions, the partial differential system is truncated by using the Galerkin method. Sequentially, the effects of temperature, geometric parameters, circumferential wave number, axial half wave number and rotating speed on the nature frequency of the rotating circular cylindrical shell are studied. The dynamic responses of the rotating circular cylindrical shell are also investigated in time domain and frequency domain. Then, the effects of nonlinearity, excitation and damping on frequency responses of steady solution are investigated.     

Nonlinear vibration of a rotating laminated composite circular cylindrical shell: traveling wave vibration

In this paper, the large-amplitude (geometrically nonlinear) vibrations of rotating, laminated composite circular cylindrical shells subjected to radial harmonic excitation in the neighborhood of the lowest resonances are investigated. Nonlinearities due to large-amplitude shell motion are considered using the Donnell’s nonlinear shallow-shell theory, with account taken of the effect of viscous structure damping. The dynamic Young’s modulus which varies with vibrational frequency of the laminated composite shell is considered. An improved nonlinear model, which needs not to introduce the Airy stress function, is employed to study the nonlinear forced vibrations of the present shells. The system is discretized by Galerkin’s method while a model involving two degrees of freedom, allowing for the traveling wave response of the shell, is adopted. The method of harmonic balance is applied to study the forced vibration responses of the two-degrees-of-freedom system. The stability of analytical steady-state solutions is analyzed. Results obtained with analytical method are compared with numerical simulation. The agreement between them bespeaks the validity of the method developed in this paper. The effects of rotating speed and some other parameters on the nonlinear dynamic response of the system are also investigated.     

Flow around a flexible cylindrical shell by a plane stream of an ideal liquid

The flow by a plane stream of an ideal liquid around a cylindrical shell of zero flexural stiffness (a soft cylindrical shell), or a gas bubble on the boundary of which forces of tension act, was studied in [1–6]. The flow around an elastic plate in a linear formulation was considered in [7, 8]. We consider the flow, around a flexible cylindrical shell which possesses a flexural stiffness and at the same time admits large displacements, by a plane system of an ideal incompressible liquid. An application of methods of the theory of functions of a complex variable leads to an effective solution of the problem. The shape of the shell, the forces in it, the forces acting on the shell, and the field of velocities of the flow of the liquid are determined.     

The problem of plane flow of ideal liquid around a shell filled with gas

The plane flow of an ideal liquid around a certain volume of gas bounded by a rigid rectilinear plate perpendicular to the incident flow and by an absolutely elastic film fastened at the ends of the plate is examined. The existence of a solution is demonstrated in a certain range of variation of the parameters, and a method of finding it is indicated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 108–117, May–June, 1971.     

Penetration of an elastic circular cylindrical shell into an incompressible liquid

The plane unsteady problem of impact of a thin elastic cylindrical shell on the surface of an ideal incompressible liquid is considered. The initial stage of interaction between the body and the liquid when the stresses in the shell attain peak values is studied. The problem is treated in a linearized formulation and is solved numerically by the normal modes method within the framework of the Wagner approach. The numerical results agree with experimental data for various types of circular cylindrical shells made from mild steel. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 186–197, November–December, 1999.     

Singularities of the rotating cylindrical shell convergence process

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 110–112, May–June, 1990.     

Impact of a long thin body on a cylindrical cavity in liquid: A plane problem

An approach is developed to the investigation of the shock interaction between a long thin cylindrical body and a cylindrical cavity in an infinite compressible perfect liquid. This process accompanies the supercavitation of the body. Three typical cases of cross-sectional dimensions of the body and the cavity are examined. For each case, a mixed nonstationary boundary-value problem with an unknown moving boundary is formulated. The unknown quantities are expanded into Fourier series. An auxiliary problem is solved using the Laplace transform to establish the relationship between the pressure and the velocity on the cavity surface. As a result, the problem is reduced to an infinite system of Volterra equations of the second kind solved simultaneously with the equation of transverse motion and the equation of the contact boundary. An asymptotic solution valid at the initial stage of interaction is obtained for all the three cases, and a numerical solution is found for the most typical case __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 6, pp. 32–53, June 2006.