Vibrations Of Cylindrical Shells Research Articles

On the vibration and stability investigations of orthotropic FGMs plate and cylindrical shell: A review

On the vibration and stability investigations of orthotropic FGMs plate and cylindrical shell: A review

Wind-structure interaction mechanism of circular storage shells- a critical review

A critical review on the valuable researches about the aerodynamic load and consequent structural behavior of cylindrical storage shells, has been carried out. The wind-shell interaction mechanism has been explored through literatures to understand aerodynamic pressure characteristics, wind-induced vibration, buckling and design of cylindrical storage shell and stiffener. Important input parameters have been presented in a tabulated manner so as to correlate and compare critical output parameters (graphically) with an emphasis on circumferential wind pressure coefficient and radial deflection per unit thickness under wind-induced buckling. The scopes for future studies in this field of research have also been recommended.

Assessment of Axisymmetric Dynamic Snap-Through and Thermally Induced Vibrations in FGM Cylindrical Shells Under Instantaneous Heating

This paper addresses the investigation of axisymmetric thermally induced vibrations in Functionally Graded Material (FGM) cylindrical shells. It considers temperature-dependent (TD) properties and geometric non-linearity (the von Karman effect). The study systematically solves a transient heat conduction equation using finite differences method and the Crank–Nicolson method. During the heating stages, the evaluation of thermal forces and moments takes place. Equations of motion are derived through the application of Hamilton’s principle. Spatial dependencies are discretized using the generalized Ritz method, while temporal dependencies are approximated using the [Formula: see text]-Newmark method with Newton–Raphson linearization. A comparative analysis validates the procedure’s efficiency and precision. Parametric studies explore the influence of parameters, including the temperature-dependency material properties, geometric nonlinearity, and shell’s power-law index, providing valuable insights into FGM shell behavior under thermal shock.

Nonlinear vibrations of porous-hyperelastic cylindrical shell under harmonic force using harmonic balance and pseudo-arc length continuation methods

The resonant responses are investigated for the porous-hyperelastic Mooney–Rivlin cylindrical shell subjected to a radial harmonic excitation. Considering the higher-order shear deformation theory (HSDT), fourth-order strain-displacement relations are derived, which include the radial geometric imperfections varying along the thickness direction. Using the porous-hyperelastic Mooney–Rivlin constitution relation and Lagrange equation, the differential governing equations of motion are obtained for the porous-hyperelastic cylindrical shells. The resonant conditions are presented and the accuracy of the mathematical models is verified. The harmonic balance and pseudo-arc length continuation methods are used to obtain the amplitude-frequency and forced-amplitude curves. The stability of the solutions is analyzed by Floquet theory. The effects of the external excitation amplitudes, structure parameters and porosity infill parameters on the linear frequencies, amplitude-frequency responses and force-amplitude responses are discussed for the imperfect porous-hyperelastic cylindrical shells. The results show that the linear frequencies of the porous-hyperelastic cylindrical shells increase obviously as the uniform and sigmoid function porosity parameters reach the certain values. The increase of the structure parameters enhances the response amplitudes of the first-order mode and minified response amplitudes of the second-order mode. The decreasing porosity ratios weaken the softening nonlinear behaviors of the porous-hyperelastic cylindrical shells. With the changes of the external excitation amplitudes and structure parameters, the motion of the porous-hyperelastic cylindrical shell indicates that the synchronous vibrations occur with the period and chaotic vibrations alternately.

Собственные колебания композитных эллиптических цилиндрических оболочек с жидкостью

Собственные колебания композитных эллиптических цилиндрических оболочек с жидкостью

Advanced Thick FGM Plates-Cylindrical Shells in Linear Unsteady Supersonic Flow

Introduction: Thick functionally graded (FG) plates-cylindrical shells with third-order shear deformation theory (TSDT) of displacement models under thermal vibration in linear unsteady supersonic flow are investigated by using the generalized differential quadrature (GDQ) method. Method: The nonlinear coefficient term of TSDT models and the advanced nonlinear shear correction coefficient expression are used to study the thermal vibration of thick FG plates and cylindrical shells in linear unsteady supersonic flow. At the intersection of FG plates-cylindrical shells, the displacements, stress resultants, and moment resultants could be reasonably assumed in the continuity condition for the differential volume in linear unsteady supersonic flow, respectively. Result: The dynamic equilibrium differential equations of thick FG plates and cylindrical shells in linear unsteady supersonic flow, respectively in terms of partial derivatives of displacements and shear rotations subjected to partial derivatives of thermal loads, mechanical loads consist of the linear supersonic aerodynamic pressure and inertia terms can be presented. Two parametric effects including environment temperature and functionally graded material (FGM) power law index on the thermal stress and center displacement of thick FG plates-cylindrical shells in linear unsteady supersonic flow are investigated. Conclusion: The linear unsteady supersonic flow over the outer surface of thick FG platescylindrical shells provides the additional aerodynamic effect on the values of displacements and stresses.

Vibration of cylindrical shells: Design criteria for transition from shell modes to beam modes

The dynamic behavior of the cylindrical shell can be predicted by more simplified beam models for a wide range of applications. The present paper deals with finding design conditions in which the cylindrical shell performs like a beam. Employing the Hamilton’s principle, the governing equations are obtained using both Donnell-Mushtari and Flugge shell theories and the analytical solution is obtained for long cylinders with simply-supported boundary conditions at both ends. Then, by equalizing the shell and beam vibration frequencies, the shell-to-beam transition conditions are obtained for both theories. To account for the effects of shear distortion and rotatory inertia of the shell, the finite element method is applied to find the best transition conditions with less approximating assumptions. Finally, the effects of boundary conditions on the transition parameters as well as the frequency response are studied. The obtained conditions simply define that if the shell can be assumed as a beam in any specific geometrical and material conditions.

The low frequency multi-linear spectrum vibration control study of cylindrical shell through a semi-analytical method

Dynamic vibration absorber is efficient in controlling low frequency vibration of cylindrical shell, which is meaningful for engineering practice. However, the efficiency of designing dynamic vibration absorber using traditional method is low. This paper demonstrates a semi-analytical method for designing dynamic vibration absorber of cylindrical shell. The convergence analysis presented in the research proves the accuracy of the current method when handling different edge constraints through limited truncation numbers. Additionaly, forced vibration and control of multi-line spectrum vibration of cylindrical shell have also been studied. The comparison between FEM and current method shows a significant improvement when handling equivalent mass, which is a key process when designing dynamic vibration absorbers. Finally, an intriguing relationship is discovered when controlling multiple resonance peaks through a single dynamic vibration absorber. The semi-analytical method described in this paper may be beneficial when controlling the vibration of cylindrical shell structures in the further research.

Free vibration of cylindrical shells and panels with cutout via the differential transform method

Semi-numerical methods hold significant value due to their efficiency in time-consuming calculations. Accordingly, this article proposes an effective strategy to derive the vibration parameters of cylindrical shells (CSs) with cutout utilizing a semi-analytical approach entitled differential transform method (DTM). To achieve this, the governing equations of motion are first introduced based on Sander’s theory of shells. These equations give rise to a coupled system of linear ordinary differential equations, which pose a challenge in solving the eigenvalue problem. It should be emphasized that the classical version of the differential transform method could not be directly applied to solve the eigenvalue problem related to the above-mentioned coupled differential equation. An innovative technique is employed and discussed in the paper to remedy these difficulties, which could be widely used in similar problems. As a result, the natural frequencies and mode shapes of some CSs with cutouts, various internal angles, and diverse material characteristics are attained. The outcomes undergo validation through the hybrid finite element method, and the proposed method’s accuracy is rigorously proved. In conclusion, the proposed DTM provides an efficient solution to the eigenvalue problem of coupled differential equations and offers a valuable tool for obtaining accurate vibration parameters of CSs.

Passive damping of vibrations of plates and cylindrical shells interacting with a flowing fluid using piezoelectric elements

The paper presents a mathematical formulation of the problem of natural and forced harmonic vibrations of electro-elastic thin-walled structures interacting with a flowing fluid. The numerical algorithm based on the finite element method is used to choose optimal parameters of a shunt electric circuit for problems of passive vibration damping. The key idea behind the proposed approach is a solution of eigenvalue problem. It allows us to obtain higher damping rate of free vibrations compared to those evaluated by the commonly used analytical expressions and leads to the smallest difference in the natural frequencies of the structure and the electric circuit.

Natural Vibrations of Composite Cylindrical Shells Partially Filled with Fluid

Natural Vibrations of Composite Cylindrical Shells Partially Filled with Fluid

Magneto-thermo-elastic coupled free vibration and nonlinear frequency analytical solutions of FGM cylindrical shell

The magneto-thermo-elastic coupled free vibration of functionally graded materials (FGM) cylindrical shell is investigated. Based on the physical neutral surface theory and Kirchhoff-Love theory, the expressions of internal force and internal torque are obtained by considering the constitutive relationship that includes thermal stress. According to the electromagnetic elasticity theory, the model of Lorentz forces of the shell in magnetic field are derived. The expressions of potential energy, kinetic energy and its variational operators are given by introducing geometric nonlinearity, respectively. Based on Hamilton principle, the magneto-thermal-elastic coupled vibration equation of FGM cylindrical shell in multi-physical field is established. The displacement functions under simply supported boundary conditions are solved, which are combined with Galerkin method for derivation of nonlinear ordinary differential equations. The second-order approximate analytical solution of natural frequency is obtained by applying the multi-scale method. The characteristic curves of natural frequency with different parameters are drawn through numerical examples. The results show that reducing the volume fraction index and increasing the initial amplitude can lead to the increase of the natural frequency under transient conditions. With the increase of temperature and magnetic induction intensity, the natural frequency decreases. In addition, the natural frequency is also influenced by the shell size and volume fraction index.

Nonlinear coupled multi-mode vibrations of simply-supported cylindrical shells: Comparison studies

In spite of extensive studies on the nonlinear vibrations of cylindrical shells, the significant influences of some effective modes and the in-plane nonlinearity on the nonlinear coupled multi-mode vibrations are not clear. In this work, which is based on Donnell’s nonlinear shell theory and Amabili–Reddy’s third-order shear deformation theory, the nonlinear differential equations of motion of both the thin-walled and moderately thick cylindrical shells under the simply-supported boundary condition are established via Lagrange equations. These high-dimensional differential equations with the quadratic and cubic nonlinearities are solved by using an iteration procedure that is a combination of incremental harmonic balance method, pseudo-arclength method and extrapolation techniques. Turning and bifurcation points of the system are determined with the help of the direct method, the stability of solution of the frequency–response is examined by using the multi-variable Floquet theory. The numerical responses obtained by adopting two present shell theories are compared to investigate the influence of ignoring the in-plane nonlinearity on nonlinear vibrations. In the coupled multi-mode vibrations with respect to the fundamental mode m,n, apart from the regular modes i×m,j×ni=1,3,5,…,andj=0,1,2,3,… that include the axisymmetric and asymmetric modes, some irregular modes are taken into account to study the frequency–responses. Results show that present iteration procedure is efficient and successful to get the frequency–responses of the coupled multi-mode vibrations, and the influence of the irregular mode on the coupled multi-mode vibration is dependent on the relationship between the natural frequency of the irregular mode and that of the fundamental mode.

A Dynamic Matrix for the Study of Free Vibrations of Thin Circular Cylindrical Shells under Different Boundary Conditions

Although free vibrations of thin-walled cylinders have been extensively addressed in the relevant literature, finding a good balance between accuracy and simplicity of the procedures used for natural frequency assessment is still an open issue. This paper proposes a novel approach with a high potential for practical application for rapid esteem of natural frequencies of thin-walled cylinders under different boundary conditions. Starting from Donnell–Mushtari’s shell theory, the differential problem is simplified by using the principle of virtual work and introducing the flexural waveforms of a beam as constrained as the cylinder. Hence, the formulation is reduced to the eigenvalue problem of an equivalent 3 × 3 dynamic matrix, which depends on the cylinder geometry, material, and boundary conditions. Several comparisons with experimental, numerical, and analytical approaches are presented to prove model reliability and practical interest. An excellent balance between fast usability and accuracy is achieved. The user-friendliness of the model makes it suitable to be implemented during the design stage without requiring any deep knowledge of the topic.

NUMERICAL MODELING OF DYNAMIC DEFORMATION OF A THREE-LAYER RIBBED CYLINDRICAL SHELL UNDER AXISYMMETRIC IMPULSE LOADS

The non-stationary vibrations of three-layer composite cylindrical shell under axisymmetric impulse loads have been researched. The mathematical model and method for calculating the dynamic deformation of the shell system under consideration is based on the geometrically nonlinear theory of Timoshenko’s type shells and ribs. The results of numerical analysis of the problem are presented.

Effect of anisotropic stiffness degradation on the forced vibration of cylindrical shells

Structural defects are commonly encountered in engineering applications. They can significantly affect not only the structural integrity but also the natural frequencies and vibration responses of cylindrical shells subject to external loading. This study proposes a novel concept of stiffness degradation to analyze the effect of defects on the vibration of shell structures. Specifically, stiffness degradation factors (SDFs) are introduced into the model of a cylindrical shell based on Sanders shell theory, and their influences on the dynamic response of an infinite-length cylindrical shell are evaluated by analyzing vibrations at multiple locations. The results show that vertical vibrations at receiver points located away from the driving point are more susceptible to the stiffness degradation, particularly at higher frequencies. The degradation of flexural stiffness has a greater effect on the vibration of cylindrical shells than the degradation of membrane stiffness, particularly in terms of the resonant frequency decrease. Furthermore, stiffness degradation in the circumferential direction has a greater effect on shell vibration than in the longitudinal direction. By examining the effects of eight SDFs separately, it is revealed that the vibration response of a cylindrical shell is affected by the directions and types of stiffness degradation, the frequency range, and the observation point. Overall, this study provides a general analytical framework for analyzing the vibration response of cylindrical shells including the effect of anisotropic stiffness degradation, which could be applied to composite shell structures with directional fiber orientations and shell structures with various defect modes.

Non-linear dynamics of cantilevered circular cylindrical shells with thickness stretch, containing quiescent fluid with small-amplitude sloshing

Studies on nonlinear vibrations of circular cylindrical shells containing fluid are mostly limited to thin simply supported shells, such that no results regarding the behavior of thick cantilevered shells with shear and thickness deformations can be found in the literature. In this article, for the first time, thin and thick circular cylindrical shells with clamped-free boundary conditions are modeled according to the third-order shear deformation theory with thickness stretch. The contained liquid satisfies the Laplace equation and linearized boundary conditions are imposed at the free surface and at the contact with the shell. Using Lagrange equations, the governing differential equations of the system in terms of shell-fluid interaction are derived. In linear free vibration analysis, it was found that increasing the fluid level inside the shell and decreasing the shell thickness, cause a significant rise in the fluid free-surface wave elevation. This increase is such that limits the application of linear sloshing theory. It was observed that the fluid presence can change the nonlinear behavior from softening to hardening type and intensifies the shell thickness deformation. In addition, the presence of contained liquid reduces the circumferential dynamic contraction of the shell caused by large amplitude vibrations.

Comparative analysis of dynamic stability of cylindrical and conical shells under periodic axial compression

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.

Numerical analysis of thin cylindrical shell vibrations with a weak nonlinearity

Numerical analysis of thin cylindrical shell vibrations with a weak nonlinearity

Vibrations of Cylindrical Sandwich Shell with Fused Deposition Processed Honeycomb Core and Carbon Nanotubes Reinforced Composite Faces Sheets

Vibrations of Cylindrical Sandwich Shell with Fused Deposition Processed Honeycomb Core and Carbon Nanotubes Reinforced Composite Faces Sheets