Vibration Of Orthotropic Cylindrical Shells Research Articles

A symplectic analytical approach for free vibration of orthotropic cylindrical shells with stepped thickness under arbitrary boundary conditions

Exact analytical solutions for free vibration of isotropic and orthotropic cylindrical shells with uniform and stepped thickness subject to general boundary conditions are presented by means of a symplectic analytical approach. The Reissner shell theory is adopted to formulate a theoretical model. By introducing a Hamiltonian system, the governing higher order partial differential equation is reduced to a set of ordinary differential equations which can be analytically solved by separating the variables. Applying the end boundary and interface continuous conditions, a set of analytical characteristic frequency equations are obtained, and exact solutions can be determined. To ensure accuracy and validity of the symplectic method, the analytical solutions for uniform and stepped cylindrical shells with isotropic or orthotropic material properties and with arbitrary boundary conditions are compared with available published data and FEM solution. A set of comprehensive new result for orthotropic stepped cylindrical shells under classical and elastic restraints are presented. Some typical mode shapes for various examples are illustrated. In addition, the effects of boundary conditions and orthotropic properties on vibration frequency are analyzed. The result shows that the fundamental frequency is higher for a boundary with more constraints.

Коливання ортотропної циліндричної оболонки з множиною отворів довільної конфігурації та мішаними крайовими умовами

Коливання ортотропної циліндричної оболонки з множиною отворів довільної конфігурації та мішаними крайовими умовами

Vibration of orthotropic cylindrical shell with a set of inclusions of arbitrary configuration

In the framework of the refined theory, which takes into account transverse shear deformation and all inertial components, the solution of the problem on the steady state vibrations of the orthotropic closed cylindrical shell with the arbitrary number of rigid inclusions of the arbitrary geometrical form, orientation, and location is constructed. External boundaries of the shell are of the arbitrary geometrical configuration. Arbitrary harmonic in time boundary conditions are considered on the external boundaries of the shell. The inclusions have different types of connections with the shell. The solution is built on the basis of the indirect boundary elements method and the sequential approach to the representation of the Green's function. The boundary value problem is reduced to the system of algebraic equations.

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

A study of free vibration of orthotropic circular cylindrical shells is presented. The vibration control equations of shells are based on Flugge classical thin shell theory. Wave approach is used in the analysis, in which the boundary conditions of shells can be simplified according to the associated beam. The free vibration frequencies of shells can be obtained from a frequency polynomial equation of order 6. The parametric analysis of the free vibration of orthotropic cylindrical shells is investigated using a statistical method. The effects of geometrical parameters and material characteristics upon frequencies are investigated here. Multivariate analysis (MVA) can be a useful tool for this parametric study. Some statistical characteristics, including correlation analysis and ANOVA are applied. ANOVA has been conducted to predict the statistical significance of the various factors. Calculations are performed in the Minitab statistical software. The results show that the L/R, h/R and m have larger effects on the lowest frequency. The importance of input parameters is ranked according to their contributions to the total variance. A knowledge and data visualization approach, Self-organizing mapping (SOM) is also adopted here for mining some intrinsic characteristics of shells.

Non-linear vibration of composite orthotropic cylindrical shells on the non-linear elastic foundations within the shear deformation theory

Present study deals with the non-linear vibration of orthotropic cylindrical shells on the nonlinear elastic foundations. To account for the large deformations of the orthotropic cylindrical shell, von-Karman type of geometrical nonlinearity is included into the formulation. The shear deformation theory (SDT) is used to obtain the basic equations of orthotropic cylindrical shells on the nonlinear elastic foundations within the Donnell’s shell theory. The superposition and Galerkin methods are adopted to convert the above equations into a nonlinear ordinary differential equation. The frequency-amplitude relationships for orthotropic cylindrical shells on the nonlinear elastic foundations in the framework of the SDT are obtained in the form of Jacobi elliptic function. The validity of the present method is demonstrated by comparing the present results with those available in the literature. Moreover, some new results are also presented for the nonlinear frequency parameters of the cylindrical shells to study effects of non-linear elastic foundations, vibration amplitude, shear stresses, orthotropy and shell characteristics.

Nonlinear parametric vibrations of orthotropic cylindrical shells interacting with a pulsating fluid flow

The paper addresses the dynamic interaction of an orthotropic cylindrical shell with the fluid flowing inside. Its velocity has a constant component and low-amplitude pulsations. A method to calculate the characteristics of the parametric vibrations of the shell when the velocity of the fluid is close to critical is proposed. The amplitude–frequency characteristics of the shell–fluid system at fundamental parametric resonance are determined

Free Vibrations of Orthotropic Cylindrical Shell on Elastic Foundation

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Free vibrations of orthotropic cylindrical shell on elastic foundation

Free vibrations of orthotropic cylindrical shell on elastic foundation

Influence of transverse-shear deformation on intrinsic vibrations of orthotropic cylindrical shells reinforced by longitudinal struts

Influence of transverse-shear deformation on intrinsic vibrations of orthotropic cylindrical shells reinforced by longitudinal struts

Simplified equations and solutions for the vibration of orthotropic cylindrical shells

Starting with Love type equations of motion for orthotropic circular cylindrical shells, the theory is simplified by assumptions similar to those in the Donnell-Mushtari-Vlasov development for isotropic shells. Closed form solutions for simply supported cases are then obtained. Results of two example cases are compared with finite element results and are shown to agree well. It is argued that this simplified approach allows easy assessment of the influence of design parameter changes.

Flexural Vibration of Orthotropic Cylindrical Shells in a Fluid Medium

Flexural Vibration of Orthotropic Cylindrical Shells in a Fluid Medium