Study of vibration characteristics for orthotropic circular cylindrical shells using wave propagation approach and multivariate analysis

Free vibrations of partial fluid-filled orthotropic circular cylindrical shells are investigated using the Dynamic Stiffness Method (DSM) or Continuous Element Method (CEM) based on theFirst Order Shear Deformation Theory (FSDT) and non-viscous incompressible fluid equations. Numerical examples are given for analyzing natural frequencies and harmonic responses of cylindrical shells partially and completely filled with fluid under various boundary conditions. The vibration frequencies for different filling ratios of cylindrical shells are obtained and compared with existing experimental and theoretical results which indicate that the fluid filling can reduce significantly the natural frequencies of studiedcylindrical shells. Detailed parametric analysis is carried out to show the effects of some geometrical and material parameters on the natural frequencies of orthotropic cylindrical shells. The advantages of this current solution consist in fast convergence, low computational cost and high precision validating for all frequency ranges.

An analytical study is presented for vibration and acoustic radiation of a finite thin orthotropic composite cylindrical shell excited by a harmonic concentrated force in a hygroscopic environment. The modal analysis method is used to solve the governing equations. Theoretical results are presented in natural vibration, radial quadratic velocity, sound power and radiation efficiency, with uniform incremental moisture content. Furthermore, different stiffness, length and thickness are set respectively to research the effects of the material and structure parameters variation of the orthotropic cylindrical shell on the vibration and acoustic radiation characteristics. It is found that the natural frequencies decrease with an increase of moisture content. The modal indices associated with the lowest frequency mode reaches the modal indices corresponding to the lowest buckling mode near the critical buckling moisture content with moisture content. The radial quadratic velocity and sound radiation power decrease with the incremental moisture content in the lower frequency band. The vibration and acoustic response decrease with the enhanced stiffness. The increasing length has little impact on the sound radiation and the thickened cylindrical shell weakens the sound radiation response.

Based on the Donnell’s approximations of the thin shell theory, this paper presents solutions for the problem of free non-axisymmetric vibration of stepped circular cylindrical shells with cracks. The shell under consideration is sub-divided into multiple segments separated by the locations of thickness variations. It is assumed that at thejth step there exists a circumferential surface crack with uniform depthcj. The influence of circular cracks with constant depth on the vibration of the shell is prescribed with the aid of a matrix of local flexibility. The latter is related to the coefficient of the stress intensity known in the linear fracture mechanics. Numerical results are obtained for cylindrical shells of stepped thickness containing cracks at re-entrant corners of steps. Shells with various combinations of boundary conditions can be analyzed by the proposed method. Furthermore, the influences of the shell thicknesses, locations of step-wise variations of the thickness and other parameters on the natural frequencies are examined. The results can be used for the approximate evaluation of dynamic parameters of cylindrical shells with cracks and flaws.

SummaryAn investigation of the generic vibration of prestressed thick orthotropic cylindrical shells was carried out. A set of Flügge type equations. of motion for orthotropic shells has been reduced to an equivalent set of equations containing only non-dimensionalised geometrical parameters, loadings and generalised global constants of orthotropic materials. The influence and importance of the global constants on the vibration of cylindrical shells are studied. Based on the results, the figures shown in this paper are applicable for a large group of materials, making the understanding of the correlation between composite material properties and vibrational behaviour of the shells very easy. The results of this paper show that an increase in vibrating frequency is brought about by (1) increasing generalised rigidity ratio, (2) increasing transverse shear modular ratios, (3) decreasing generalised Poisson's ratio and (4) decreasing principal rigidity ratio. The key parameters to the problems are generalised rigidity ratio and principal rigidity ratio only.

A comparative analysis of the dynamic stability of cylindrical and conical shells with the same geometric and mechanical characteristics under periodic uniformly distributed axial compression was presented. The study of the stability of steady periodic vibrations of thin elastic shells was based on the joint use of the method of curvilinear grids, the projection method and the parameter continuation method combined with the Newton–Kantorovich method. Geometrically nonlinear relations of the thin elastic shells theory are formulated on the basis of the vector approximation of the displacements function in the general curvilinear coordinate system in tensor form and satisfy the Kirchhoff-Love hypothesis. The discretization of the differential equations of the steady forced vibrations in the direction of the generating shells using the method of curvilinear grids was carried out. The components of the elements displacement vectors of the shells middle surface in the circular directionare approximated by trigonometric series. Reduction of the number of generalized coordinates of the discrete dynamic model of shells steady forced vibrations was performed by the Bubnov-Galerkin basis reduction method. A transition from vector ordinary differential equations to a nonlinear system of algebraic equations was made. The construction of a mathematical model of the dynamic stability of steady forced nonlinear vibrations of thin elastic shells was performed according to Floquet's theory using the projection method. The criterion for the loss of stability was the equality to zero of the determinant of the matrix of linearized equations of steady forced nonlinear vibrations of shells according to the Lyapunov theorem. A comparative analysis of frequencies and modes of natural vibrations of cylindrical and conical shells with the same geometric and mechanical characteristics and boundary conditions was performed. Nonlinear steady vibrations of the shells due to periodic axial compression were studied. The critical values of the dynamic load and the corresponding forms of loss of shell stability in the range of lower frequencies of their natural vibrations were obtained.

Free vibrations of orthotropic cylindrical shell on elastic foundation

The effect of rotary inertia of added masses on vibrations of empty and fluid-filled circular cylindrical shells

The present study aims at the investigation of free vibration analysis of thin cylindrical shells surrounded by an elastic medium, which is distributed over a particular length of the shell. The Love’s shell theory is utilized along with the Winkler foundation to obtain the governing equations of motion. An exact series expansion method of solution is employed for any arbitrary boundary conditions. The excellent accuracy of the obtained results is validated by comparing to the available literature. Moreover, several case studies are performed to provide an insight into the influence of some practically important parameters on free vibrations of circular cylindrical shells, including stiffness and length of the partial foundation. Finally, it is concluded that the proposed method can accurately determine the exact solution to the free vibration of shells partially surrounded by elastic foundations with any boundary conditions.

Stability and free vibration analyses of double-bonded micro composite sandwich cylindrical shells conveying fluid flow

Free vibration of nonlinear deformation ring-and stringer-stiffened nonuniform cylindrical shell

Magneto-electro-elastic semi-analytical models for free vibration and transient dynamic responses of composite cylindrical shell structures

Parametric resonance in cylindrical shells: a case study in the nonlinear vibration of structural shells

Stable axisymmetric vibrations of a thick-walled circular cylindrical shell made of a visco-elastic material are examined under pressure distributed in cylindrical surfaces which changes in time according to the law of harmonic. A system of four partial differential equations of the second order for defining the constituents of radial and axial displacements is written without any preliminary suppositions about the character of changes in unknown values on thickness. A spline-collocation method is used for decreasing the system dimension under an arbitrary way of fixing of sections. A corresponding boundary problem is numerically solved using a discrete Godunov method of orthogonalization.As an example the vibrations of shells with the same radius of the surface under various values of length and thickness. A comparison of results according to a strict and classic theory based on Kirchhoff−Love hypotheses is performed. Some peculiarities of changes on the radius of the radial displacement constituents which can not be detected in the frames of any approximated theory, assuming constancy of bending on the shell thickness are noted. Key words: axisymmetric vibrational bending, thick-walled cylindrical shell, visco-elastic material.

In this paper, the stability of a thin cylindrical sheel subjected to an axial leakage flow is discussed. Here, we focus on a lateral vibration of a cylindrical shell, that is the beam-like vibration of a shell. The coupled equations between a shell and a fluid are obtained by using the Donnell's shell theory and the Navier Stokes equation. The influence of the axial velocity on the unstable vibration phenomena is clarified concerning the beam-like vibration mode of a shell. The applicable range of Donnel shell theorry is confirmed for axial leakage flow-induced vibration of a thin cylindrical shell. The numerical results on the shell theory are compared with those on beam theory which have been already reported by the authors. And, the numerical parameter studies are done for several dimensions of shell and fluid.

Axially symmetric vibrations of fluid-filled poroelastic circular cylindrical shells