Effects of Axial Imperfections on Vibrations of Anti-Symmetric Cross-Ply, Oval Cylindrical Shells

1986 ◽  
Vol 53 (3) ◽  
pp. 675-680 ◽  
Author(s):  
David Hui ◽  
I. H. Y. Du
Keyword(s):  
Vibration Mode ◽  
Cylindrical Shells ◽  
Homogeneous Material ◽  
Fundamental Vibration ◽  
Geometric Imperfections ◽  
Simply Supported ◽  
Fundamental Frequencies ◽  
Young’S Moduli ◽  
Wave Numbers ◽  
Oval Cylindrical Shells

This paper examines the effects of axial geometric imperfections on the fundamental vibration frequencies of cross-ply simply-supported oval cylindrical shells. It is found that the presence of such imperfection with small amplitudes may significantly raise or lower the fundamental frequencies, depending on the wave numbers of the imperfection and vibration mode. The effects of oval eccentricity, bending-stretching coupling of the material, the reduced-Batdorf parameter and Young’s moduli ratio are examined. It appears that the present problem has not been examined, even in the simplified case of oval cylindrical shells made of isotropic-homogeneous material.

Vibrations of rotating cylindrical shells with functionally graded material using wave propagation approach

2018 ◽  
Vol 232 (23) ◽  
pp. 4342-4356 ◽  
Author(s):  
Muzammal Hussain ◽  
M Nawaz Naeem ◽  
Aamir Shahzad ◽  
Mao-Gang He ◽  
Siddra Habib
Keyword(s):  
Wave Propagation ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Wave Number ◽  
Type I ◽  
Rotating Speed ◽  
Simply Supported ◽  
Fundamental Frequencies

Fundamental natural frequencies of rotating functionally graded cylindrical shells have been calculated through the improved wave propagation approach using three different volume fraction laws. The governing shell equations are obtained from Love’s shell approximations using improved rotating terms and the new equations are obtained in standard eigenvalue problem with wave propagation approach and volume fraction laws. The effects of circumferential wave number, rotating speed, length-to-radius, and thickness-to-radius ratios have been computed with various combinations of axial wave numbers and volume fraction law exponent on the fundamental natural frequencies of nonrotating and rotating functionally graded cylindrical shells using wave propagation approach and volume fraction laws with simply supported edge. In this work, variation of material properties of functionally graded materials is controlled by three volume fraction laws. This process creates a variation in the results of shell frequency. MATLAB programming has been used to determine shell frequencies for traveling mode (backward and forward) rotating motions. New estimations show that the rotating forward and backward simply supported fundamental natural frequencies increases with an increase in circumferential wave number, for Type I and Type II of functionally graded cylindrical shells. The presented results of backward and forward simply supported fundamental natural frequencies corresponding to Law I are higher than Laws II and III for Type I and reverse effects are found for Type II, depending on rotating speed. Our investigations show that the decreasing and increasing behaviors are noted for rotating simply supported fundamental natural frequencies with increasing length-to-radius and thickness-to-radius ratios, respectively. It is found that the fundamental frequencies of the forward waves decrease with the increase in the rotating speed, and the fundamental frequencies of the backward waves increase with the increase in the rotating speed. This investigation has been made with three different volume fraction laws of polynomial (Law I), exponential (Law II), and trigonometric (Law III). The presented numerical results of nonrotating isotropic and rotating functionally graded simply supported are in fair agreement with parts of other earlier numerical results.

ON THE FUNDAMENTAL FREQUENCIES AND MODES OF FREE VIBRATION OF CYLINDRICAL SHELLS

1991 ◽  
Vol 15 (2) ◽  
pp. 147-159
Author(s):  
J.L. Urrutia-Galicia ◽  
L.J. Arango
Keyword(s):  
Free Vibration ◽  
Elastic Material ◽  
Cylindrical Shells ◽  
Simply Supported ◽  
Fundamental Frequencies ◽  
Circular Cylindrical Shells

The fundamental frequencies and modes of free vibration of simply supported circular cylindrical shells are explored. The results include the fundamental frequencies ωmn and the modes (m,n) of steel cylindrical shells which are presented in the form of a nomogram, see Figure 6. Besides, single more general formulas are given for cylindrical shells made out of any elastic material which turn out to be very suitable for design and analysis purposes.

The Influence of Modal Geometrical Imperfections on the Nonlinear Vibrations of a Thin-Walled Circular Cylindrical Shell

2016 ◽  
Author(s):  
Lara Rodrigues ◽  
Paulo B. Gonçalves ◽  
Frederico M. A. Silva
Keyword(s):  
Nonlinear Vibrations ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Nonlinear Behavior ◽  
Geometric Imperfections ◽  
Modal Expansion ◽  
Simply Supported ◽  
Transversal Displacement ◽  
Geometrical Imperfections ◽  
Standard Galerkin Method

This work investigates the influence of several modal geometric imperfections on the nonlinear vibration of simply-supported transversally excited cylindrical shells. The Donnell nonlinear shallow shell theory is used to study the nonlinear vibrations of the shell. A general expression for the transversal displacement is obtained by a perturbation procedure which identifies all modes that couple with the linear modes through the quadratic and cubic nonlinearities. The imperfection shape is described by the same modal expansion. So, a particular solution is selected which ensures the convergence of the response up to very large deflections. Substituting the obtained modal expansions into the equations of motions and applying the standard Galerkin method, a discrete system in time domain is obtained. Several numerical strategies are used to study the nonlinear behavior of the imperfect shell. Special attention is given to the influence of the form of the initial geometric imperfections on the natural frequencies, frequency-amplitude relation, resonance curves and bifurcations of simply-supported transversally excited cylindrical shells.

Mechanical buckling of cylindrical shells with varying material properties

2010 ◽  
Vol 224 (8) ◽  
pp. 1551-1557 ◽  
Author(s):  
P Khazaeinejad ◽  
M M Najafizadeh
Keyword(s):  
Exponential Function ◽  
Power Law ◽  
Material Properties ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Buckling Loads ◽  
Young’S Moduli ◽  
Wave Numbers

The analytical solutions of the first-order shear deformation theory are developed to study the buckling behaviour of functionally graded (FG) cylindrical shells under three types of mechanical loads. The Poisson's ratios of the FG cylindrical shells are assumed to be constant, while the Young's moduli vary continuously throughout the thickness direction according to the volume fraction of constituents given by power-law or exponential function. The stability equations are employed to obtain the closed-form solutions for critical buckling loads of each loading case. The dependence of the critical buckling loads on the variations of the material properties with a power-law or exponential function is studied. It is observed that these effects change appreciably the critical buckling loads. Results for critical loads are tabulated for thin and moderately thick shells. Although the critical buckling load of FG cylindrical shells decreases as the circumferential wave numbers increase, it rises for axially compressed long shells as the longitudinal wave numbers increase.

Influence of Geometric Imperfections and In-Plane Constraints on Nonlinear Vibrations of Simply Supported Cylindrical Panels

1984 ◽  
Vol 51 (2) ◽  
pp. 383-390 ◽  
Author(s):  
David Hui
Keyword(s):  
Shell Thickness ◽  
Nonlinear Vibrations ◽  
Vibration Mode ◽  
Vibration Frequencies ◽  
Linear Vibration ◽  
Geometric Imperfections ◽  
Simply Supported ◽  
Cylindrical Panels ◽  
Initial Geometric Imperfections ◽  
Large Amplitude Vibrations

This papers deals with the effects of initial geometric imperfections on large-amplitude vibrations of cylindrical panels simply supported along all four edges. In-plane movable and in-plane immovable boundary conditions are considered for each pair of parallel edges. Depending on whether the number of axial and circumferential half waves are odd or even, the presence of geometric imperfections (taken to be of the same shape as the vibration mode) of the order of the shell thickness may significantly raise or lower the linear vibration frequencies. In general, an increase (decrease) in the linear vibration frequency corresponds to a more pronounced soft-spring (hard-spring) behavior in nonlinear vibration.

scholarly journals Analysis of Cylindrical Shells Using Generalized Differential Quadrature

1997 ◽  
Vol 4 (3) ◽  
pp. 193-198 ◽  
Author(s):  
C.T. Loy ◽  
K.Y. Lam ◽  
C. Shu
Keyword(s):  
Fluid Dynamics ◽  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Differential Quadrature Method ◽  
Cylindrical Shells ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Simply Supported ◽  
Fundamental Frequencies ◽  
Generalized Differential

The analysis of cylindrical shells using an improved version of the differential quadrature method is presented. The generalized differential quadrature (GDQ) method has computational advantages over the existing differential quadrature method. The GDQ method has been applied in solutions to fluid dynamics and plate problems and has shown superb accuracy, efficiency, convenience, and great potential in solving differential equations. The present article attempts to apply the method to the solutions of cylindrical shell problems. To illustrate the implementation of the GDQ method, the frequencies and fundamental frequencies for simply supported-simply supported, clamped-clamped, and clamped-simply supported boundary conditions are determined. Results obtained are validated by comparing them with those in the literature.

Nonlinear Analysis of Transverse Shear Deformable Laminated Composite Cylindrical Shells—Part II: Buckling of Axially Compressed Cross-Ply Circular and Oval Cylinders

1992 ◽  
Vol 114 (1) ◽  
pp. 110-114 ◽  
Author(s):  
K. P. Soldatos
Keyword(s):  
Transverse Shear ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Laminated Composite ◽  
Companion Paper ◽  
Buckling Loads ◽  
Simply Supported ◽  
Laminated Composite Shells ◽  
Shear Deformable ◽  
Oval Cylindrical Shells

A linearized transverse shear deformable shell theory presented in a companion paper is confined to consideration with the buckling problem of axially compressed, cross-ply laminated noncircular cylindrical shells. Based on a solution of its governing differential equations, obtained for simply supported shells by means of Galerkin’s method, a study of the buckling problem of axially compressed circular and oval cylindrical shells, of a regular antisymmetric cross-ply laminated arrangement, is presented. Moreover, by comparing the numerical results obtained with corresponding results based on a classical Love-type shell theory, the combined influence of both the transverse shear deformation and the shell eccentricity on the buckling loads of such laminated composite shells is examined.

Dimensionless wave numbers evolution of a three spans simply supported beam when the intermediate supports are moving along the whole beam

2021 ◽  
Vol 66 (1) ◽  
pp. 17-24
Author(s):  
Zeno-Iosif Praisach ◽  
Dorel Ardeljan ◽  
Constantin-Viorel Pașcu
Keyword(s):  
Vibration Mode ◽  
Frequency Equation ◽  
Wave Number ◽  
Continuous Beam ◽  
Dimensionless Wave Number ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Continuous Beams ◽  
Maximum Value ◽  
Wave Numbers

Continuous beams simply supported with several intermediate supports are very common in engineering achievements everywhere. The paper shows the evolution of the dimensionless wave number in 3D format, respectively of the eigenfrequencies for a continuous beam with three openings when the intermediate supports take any position inside the beam. The frequency equation for calculating the dimensionless wave number is presented and the modal function is given with an example for the case where the eigenfrequency has the maximum value at fist vibration mode.

MULTI-GRID FINITE ELEMENTS IN CALCULATIONS OF MULTILAYER OVAL CYLINDRICAL SHELLS

2019 ◽  
Vol 20 (2) ◽  
pp. 174-182
Author(s):  
N. V. Pustovoi ◽  
◽  
A. N. Grishanov ◽  
А. D. Matveev ◽  
◽  
...  
Keyword(s):  
Finite Elements ◽  
Cylindrical Shells ◽  
Oval Cylindrical Shells

Limit Pressures of Cylindrical and Spherical Shells

2000 ◽  
Vol 123 (3) ◽  
pp. 288-292 ◽  
Author(s):  
Arturs Kalnins ◽  
Dean P. Updike
Keyword(s):  
Geometric Parameter ◽  
Cylindrical Shells ◽  
Length Effect ◽  
Spherical Shells ◽  
Simply Supported ◽  
Limit Pressure ◽  
Section Viii ◽  
Division 2

Tresca limit pressures for long cylindrical shells and complete spherical shells subjected to arbitrary pressure, and several approximations to the exact limit pressures for limited pressure ranges, are derived. The results are compared with those in Section III-Subsection NB and in Section VIII-Division 2 of the ASME B&PV Code. It is found that in Section VIII-Division 2 the formulas agree with the derived limit pressures and their approximations, but that in Section III-Subsection NB the formula for spherical shells is different from the derived approximation to the limit pressure. The length effect on the limit pressure is investigated for cylindrical shells with simply supported ends. A geometric parameter that expresses the length effect is determined. A formula and its limit of validity are derived for an assessment of the length effect on the limit pressures.

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