Free vibration analysis of cylindrical shells using the Haar wavelet method

A numerical solution for vibration analysis of composite laminated conical, cylindrical shell and annular plate structures

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.

Free vibration characteristics of cylindrical shells partially buried in elastic foundations

Free vibrations of cylindrical shells with arbitrary boundary conditions: A comparison study

Frequency analysis of rotating truncated conical shells using the Haar wavelet method

Analysis of nonlinear vibrations of thin cylindrical shells subjected to supersonic flow

A dynamic analysis method has been developed to investigate and characterize embedded delamination on the dynamic response of composite laminated structures. A nonlinear finite element model for geometrically large amplitude free vibration intact shallow cylindrical and delamination shell analysis is presented using higher order shear deformation theory where the nonlinearity was introduced in the Green-Lagrange sense. The governing equation of the vibrated shell were derived using the Variational approach. The effect of different orthotropicity ratio, and delamination size on the non-dimenational fundamental frequency and frequency ratios of plate for different stacking sequences. Finally the results were compared with those available in literatures where the discrepancy of the results was (15.8022 % with considering the nonlinearity).

This article presents an innovative approach using the Differential Transform Method (DTM) to analyze the vibration characteristics of cylindrical shells, integrating Taylor's series with Sander's classical theory. It demonstrates DTM's efficiency, accuracy, and potential as an alternative method. The study introduces a novel application of the DTM in exploring the free vibration of cylindrical shells, detailing a technique to address challenges such as normalization, linear solution methodologies, and parameter derivative modifications. A dimensionless parameter analysis evaluates the impact of length, radius, thickness, and modulus of elasticity. Comparative analysis with Hybrid Finite Element Method (FEM) data and validation against existing literature highlights DTM's precision and reliability. In conclusion, DTM offers a robust solution for the eigenvalue problem in coupled differential equations, providing accurate vibration parameters. Additionally, an important relationship between the modulus of elasticity and frequency in the dimensionless state was obtained.

In this paper, the nodal line finite difference method (NLFDM) is extended to the analysis of a thin circular cylindrical shell, as shown in Fig. 1, undergoing free vibrations [1]. The material of the circular cylindrical shell is assumed to be linear elastic isotropic. The complexity of a theoretical analysis of a vibration problem depends largely on the number of degrees of freedom of the structural system in question. Since a thin circular cylindrical shell is a continuous system it has an infinite number of degrees of freedom. The NLFDM [10] transforms this continuous system into a system having a finite number of degrees of freedom. While carrying out the dynamic (or static) analysis by the NLFDM, the number of degrees of freedom depends on the number of the used nodal lines. The natural frequencies and modes are treated in more detail because they are basic to understanding the dynamic response under any kind of excitation. It will be shown that the number of natural frequencies and that of normal modes, for axial wave number different from zero, are each equal to three times the number of nodal lines used. The orthogonality relationships of the normal modes obtained by the nodal line finite difference method are also included. It should be remarked that these relationships are slightly different from those obtained by the finite element method; in fact the overall matrix of coefficients replaces the stiffness matrix, and any two different modes are orthogonal with resp ect to the unit matrix instead of the mass matrix.

Purely axial vibration of thin cylindrical shells with shear-diaphragm boundary conditions

This paper investigates the free vibration characteristics of truncated conical shells with variable thickness using the Haar wavelet method. Based on the Love first-approximation theory, the governing partial differential equations are formulated, which are transformed into ordinary differential equations using the separation of variables. The Haar wavelet discretization method is introduced to predict the dynamic characteristics of truncated circular conical shells with linearly and parabolically varying thickness. The present analysis is validated by comparing the numerical results with those available in the literature and very good agreement is achieved. The effects of geometrical parameters and boundary conditions on the vibration characteristics of conical shells with variable thickness are presented. The advantages of this method consist in its simplicity, fast convergence and high precision.

This paper focuses on an analysis of free vibration of thick rotating stiffened composite cylindrical shells with different boundary conditions. The analysis is performed on the basis of a three-dimensional theory by using the layerwise-differential quadrature method (LW-DQM). The equations of motion are derived employing Hamilton’s principle. In order to accurately allow for the thickness effects, a layerwise theory is used to discretize the equations of motion and related boundary conditions through the thickness of the shells. Then, the equations of motion and the boundary conditions are transformed into a set of algebraic equations by using the DQM in the longitudinal direction. This study demonstrates the applicability, accuracy, stability, and fast rate of convergence of the present method in free vibration analyses of rotating stiffened cylindrical shells. The presented results are compared with those of other shell theories obtained by conventional methods and with a special case where the number of stiffeners approaches zero, i.e., an nonstiffened cylindrical shell, and excellent agreements are achieved. Finally, some new results are presented, which can be used as benchmark solutions for future investigations.

This paper aims to provide an insight on the mechanism for the fast convergence of multigrid (MG) V-cycle algorithms. With this goal, the Fourier transform analysis is implemented to compute quantitatively the frequency spectrum of components of the residual resulted from the MG iterations. MG method has been extensively employed to solve large-scale systems of algebraic equations. Hence, one needs to understand its fast convergence property and scalability mechanism before applying MG method to a system equation, which affects the computational efficiency directly. In a first step, a number of novel features of the MG algorithm are studied, including the relationships among the iteration numbers needed for converged solutions, condition number of the system matrix and the grid-spacing in this paper. In a second step, the complexity of the MG method is researched, and various numerical experiments have been conducted in solving algebraic equations of models in finite element method for both heat transfer problems and solid mechanics problems. It is found that if the number of iterations in different grids is fixed, the optimal iteration mode is determined according to the attenuation of the high-frequency and low-frequency components of the residual. Our results also show that the complexity of the MG method is close to [Formula: see text], meaning that it is a close-to-linear scalable solver, which echoes the findings given by other literature. This study has revealed an important insight that the linear scalability is achieved by mitigating the negative effects (stagnation in convergence) of the large condition number of the system matrix created on the finest grid, using a sequence of coarser grids with smaller and smaller condition numbers.

appear to be relatively independent of the nominal radius of the shell. Based on the local curvature of the flat spot' rather than on the nominal curvature which is commonly used, a new upper bound may be determined for the collapse strength of an initially imperfect spherical shell. This observation is the basis of an analysis developed in Ref. 14 which adequately predicts both the elastic and inelastic strength of 36 machined models with local flat spots covering a relatively wide range of 6,

A comparison between the vibration of fiber-metal laminate (FML) and composite cylindrical shells has been studied in this manuscript. Love’s first approximation shell theory has been applied to obtain Strain-displacement relations. In addition, beam modal function model has been used to analyze the cylindrical shell with different boundary conditions. In this manuscript, the frequencies of FML and composite cylindrical shells have been compared to each other for different materials, lay-ups, boundary conditions, axial and circumferential wave numbers. The most commercially available FMLs are CARALL (carbon reinforced aluminium laminate), and GLARE (glass reinforced aluminium laminate), which are studied in this research. The results showed although the frequencies of carbon/epoxy are greater than glass/epoxy for all of the n, this process is not constant for FML. Also, with increasing the n, the frequencies of FML cylindrical shells are converged more faster than the composite one. Moreover, the frequencies of both boundary conditions are converged with increasing n for both FML and composite cylindrical shells.