Nonlinear Free Vibrations Analysis of Delaminated Composite Conical Shells

2019 ◽  
Vol 20 (01) ◽  
pp. 2050010 ◽  
Author(s):  
Abbas Kamaloo ◽  
Mohsen Jabbari ◽  
Mehdi Yarmohammad Tooski ◽  
Mehrdad Javadi
Keyword(s):  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Laminated Composite ◽  
Middle Surface ◽  
Free Vibrations ◽  
Wave Number ◽  
Vertex Angle ◽  
Conical Shells ◽  
Circumferential Wave ◽  
Delamination Length

This paper examines the nonlinear free vibration of laminated composite conical shells throughout the circumferential delamination. First, based on the energy method, the governing equation of motion for the shell was derived. To simplify the analysis, the nonlinear partial differential equations were reduced into a system of coupled ordinary differential equations using Galerkin’s method. Consequently, the results were obtained by the numerical methods. Finally, the effects of delamination, variations in the delamination length, conical shells characteristics, materials property and circumferential wave number on the nonlinear response of delaminated composite conical shells were examined. The results show that the presence of delamination leads to increase in the amplitude of oscillations for the shells. Besides, the increase in the delamination length and decrease of the circumferential wave number, number of layers, and half vertex angle of the cone and orthotropy bring about a decrease in the nonlinearity of delaminated composite conical shells. However, an increase of the middle surface radius of the shell leads to a reduction of the nonlinearity as well as an increase of the amplitude.

Nonlinear free vibration analysis of delaminated composite circular cylindrical shells

2020 ◽  
Vol 26 (19-20) ◽  
pp. 1697-1707
Author(s):  
Abbas Kamaloo ◽  
Mohsen Jabbari ◽  
Mehdi Yarmohammad Tooski ◽  
Mehrdad Javadi
Keyword(s):  
Differential Equations ◽  
Cylindrical Shells ◽  
Nonlinear Partial Differential Equations ◽  
Free Vibration Analysis ◽  
Middle Surface ◽  
Free Vibrations ◽  
Wave Number ◽  
Number Of Layers ◽  
Circular Cylindrical Shells ◽  
Delamination Length

This study aims to present an analysis of nonlinear free vibrations of simply supported laminated composite circular cylindrical shells with throughout circumference delamination. Governing equations of motion are derived by applying energy methods; using Galerkin’s method reduced the nonlinear partial differential equations to a system of coupled nonlinear ordinary differential equations, which are subsequently solved using a numerical method. This research examines the effects of delamination on the oscillatory motion of delaminated composite circular cylindrical shells and then the effects of increase in delamination length, shell middle surface radius, number of layers, and orthotropy as changes in material properties on the nonlinearity of these types of shells. The results show that delamination leads to a decrease in frequency of oscillations and displacement. An increase in delamination length, shell middle surface radius, and orthotropy of layers decreases nonlinearity and displacement, whereas an increase in the number of layers increases nonlinearity and displacement. It is also observed that an increase in the circumferential wave number can decrease the effect of delamination.

The study of the nonlinear vibration of S-S and C-C laminated composite conical shells on elastic foundations through an approximate method

2021 ◽  
pp. 095440622110214
Author(s):  
Shahin Mohammadrezazadeh ◽  
Ali Asghar Jafari
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Vibration ◽  
Approximate Method ◽  
Laminated Composite ◽  
Vertex Angle ◽  
Nonlinear Frequency ◽  
Conical Shells ◽  
Elastic Foundations ◽  
Vibration Responses ◽  
Comparison Of The Results

This paper investigates the nonlinear vibration responses of laminated composite conical shells surrounded by elastic foundations under S-S and C-C boundary conditions via an approximate approach. The laminated composite conical shells are modeled based on classical shell theory of Love employing von Karman nonlinear theory. Nonlinear vibration equation of the conical shells is extracted by handling Lagrange method. The linear and nonlinear vibration responses are obtained via an approximate method which combines Lindstedt-Poincare method with modal analysis. The validation of this study is carried out through the comparison of the results of this study with results of published literature. The effects of several parameters including the constants of elastic foundations, boundary conditions, total thickness, length, large edge radius and semi-vertex angle on the values of fundamental linear frequency and curves of amplitude parameter versus nonlinear frequency ratio for laminated composite conical shells with both S-S and C-C boundary conditions are investigated.

Free Vibrations of Thick Hollow Circular Cylinders From Three-Dimensional Analysis

1997 ◽  
Vol 119 (1) ◽  
pp. 89-95 ◽  
Author(s):  
Jinyoung So ◽  
A. W. Leissa
Keyword(s):  
Three Dimensional ◽  
Free Vibrations ◽  
Circular Cylinders ◽  
Wave Number ◽  
Algebraic Polynomials ◽  
Cylindrical Wall ◽  
Local Coordinates ◽  
Significant Figures ◽  
Circumferential Wave ◽  
Outside Diameter

A three-dimensional (3-D) method of analysis is developed for the free vibration frequencies of hollow circular cylinders of elastic material. The method is based upon local coordinates whose origin is attached to the center of cylindrical wall. It assumes for the three displacement components a Fourier series in the circumferential (θ) direction and algebraic polynomials in the radial (q) and axial (z) directions. Convergence studies for completely free cylinders show that the analysis can yield frequencies which are exact to five or six significant figures. These accurate frequencies are compared with those from other 3-D analyses available for free hollow circular cylinders having various length-to-outside diameter (L/Do) and inside-to-outside diameter (Di/Do) ratios. Extensive, accurate data are presented for the first 10 frequencies of each circumferential wave number 0 through 5 for hollow circular cylinders having Di/Do of 0.1, 0.5, and 0.9, with L/Do = 0.2, 1 and 5 and a Poisson’s ratio (v) = 0.3.

Wave Propagation Analysis in Anisotropic Plate Using Wavelet Spectral Element Approach

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
Mira Mitra ◽  
S. Gopalakrishnan
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Differential Equations ◽  
Laminated Composite ◽  
Composite Plates ◽  
Spectral Element ◽  
Wave Number ◽  
Frequency Wave ◽  
Propagation Analysis ◽  
Spectral Finite Element

In this paper, a 2D wavelet-based spectral finite element (WSFE) is developed for a anisotropic laminated composite plate to study wave propagation. Spectral element model captures the exact inertial distribution as the governing partial differential equations (PDEs) are solved exactly in the transformed frequency-wave-number domain. Thus, the method results in large computational savings compared to conventional finite element (FE) modeling, particularly for wave propagation analysis. In this approach, first, Daubechies scaling function approximation is used in both time and one spatial dimensions to reduce the coupled PDEs to a set of ordinary differential equations (ODEs). Similar to the conventional fast Fourier transform (FFT) based spectral finite element (FSFE), the frequency-dependent wave characteristics can also be extracted directly from the present formulation. However, most importantly, the use of localized basis functions in the present 2D WSFE method circumvents several limitations of the corresponding 2D FSFE technique. Here, the formulated element is used to study wave propagation in laminated composite plates with different ply orientations, both in time and frequency domains.

Asymmetric Free Vibrations of Layered Conical Shells

1982 ◽  
Vol 104 (2) ◽  
pp. 453-462 ◽  
Author(s):  
K. Chandrasekaran ◽  
V. Ramamurti
Keyword(s):  
Natural Frequencies ◽  
Middle Surface ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Orthotropic Materials ◽  
Conical Shells ◽  
Shell Models ◽  
Theoretical Predictions ◽  
Parametric Studies ◽  
Ritz Procedure

Asymmetric free vibrations of layered truncated conical shells are studied. Individual layers made of special orthotropic materials and both symmetric and asymmetric stacking with respect to the middle surface are considered. An energy-method based on the Rayleigh-Ritz procedure is employed. The influence of layer arrangements and that of the coupling between bending and stretching on the natural frequencies and mode-shapes are analyzed. Experimental results from tests on two shell models are provided for comparison with theoretical predictions. Numerical results based on extensive parametric studies are presented.

Investigation of the Free Vibrations of Composite Anisogrid Lattice Conical Shells Formed by Geodesically Spiral and Circumferential Ribs

2017 ◽  
Vol 09 (04) ◽  
pp. 1750047 ◽  
Author(s):  
Siamak E. Khadem ◽  
Reza Nezamoleslami
Keyword(s):  
Conical Shell ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Wave Number ◽  
Vertex Angle ◽  
Conical Shells ◽  
Outer Skin ◽  
Special Cases ◽  
Composite Lattice ◽  
Lattice Part

This paper focuses on the dynamic behavior of composite anisogrid lattice conical shells. Lattice composite conical shell consists of composite helical and circumferential ribs and thin outer skin. The free vibration analysis of anisogrid composite lattice conical shell is presented. A smeared method is employed to calculate the variable coefficients of stiffness of conical shell and more close to the realistic applications. The lattice part of conical shell is modeled as a beam, so in addition to the axial loads, ribs endure shear loads and bending moments. The first-order shear deformation shell theory is used to account for the effects of transverse shear deformations and rotary inertia. The current results are verified with 3D finite element model of conical shell by ANSYS Software and those reported in the literature. Some special cases as influences of geometric parameters of lattice part of shell, effects of boundary conditions and circumferential wave number on natural frequencies of the shell are discussed. It was concluded that employment of the smear method could be recommended for determining the coefficients of stiffness of the composite lattice conical shells with outer skin. Also increasing the vertex angle of cone increases the natural frequencies of conical shell.

Dynamic Stability of Truncated Conical Shells Under Pulsating Torsion

1981 ◽  
Vol 48 (2) ◽  
pp. 391-398 ◽  
Author(s):  
J. Tani
Keyword(s):  
Dynamic Stability ◽  
Practical Importance ◽  
Low Frequency ◽  
Instability Region ◽  
Wave Number ◽  
Vibration Modes ◽  
Conical Shells ◽  
Instability Regions ◽  
The Galerkin Method ◽  
Circumferential Wave

The dynamic stability of clamped, truncated conical shells under periodic torsion is analyzed by the Galerkin method in conjunction with Hsu’s results. The instability regions of practical importance are clarified for relatively low frequency ranges. Numerical results indicate that under the purely periodic torsion only the combination instability region exists but that with an increase in the static torsion the principal instability region becomes most significant. The relative openness of the instability regions is found to depend sensitively on the circumferential phase difference of two vibration modes excited simultaneously at the resonance with the same circumferential wave number.

On Vibrations of Elastic Spherical Shells

1962 ◽  
Vol 29 (1) ◽  
pp. 65-72 ◽  
Author(s):  
P. M. Naghdi ◽  
A. Kalnins
Keyword(s):  
Middle Surface ◽  
Free Edge ◽  
Free Vibrations ◽  
Numerical Results ◽  
Mode Shapes ◽  
Normal Displacement ◽  
Spherical Shells ◽  
Hemispherical Shell ◽  
Basic Equations ◽  
Circumferential Wave

This investigation is concerned with axisymmetric as well as asymmetric vibrations of thin elastic spherical shells. First, with the limitation to torsionless axisymmetric motion, the basic equations for spherical shells of the classical bending theory of Love’s first approximation are reduced to a system of two coupled differential equations in normal displacement of the middle surface and a stress function; this system of equations is applied to free vibrations of a hemispherical shell with a free edge and numerical results are obtained for the lowest natural frequency as a function of the thickness of the shell. The remainder of the paper is, in the main, devoted to a study of asymmetric vibrations of a hemispherical shell with a free edge according to the extensional theory. Numerical results for natural frequencies (of the four lowest circumferential wave numbers) and mode shapes are given and the results are compared with the prediction of Rayleigh’s inextensional theory.

Effect of Axial Load on Free Vibration of Orthotropic Truncated Conical Shells

1996 ◽  
Vol 118 (2) ◽  
pp. 164-168 ◽  
Author(s):  
L. Tong
Keyword(s):  
Axial Load ◽  
Compressive Load ◽  
Free Vibrations ◽  
Governing Equations ◽  
Conical Shells ◽  
Material Parameters ◽  
Axial Tension ◽  
Wave Numbers ◽  
Axially Loaded ◽  
Circumferential Wave

An analytical solution in the form of a power series is obtained for the three governing equations of free vibrations of axially loaded orthotropic conical shells. Numerical results are presented for the frequency parameters and the associated circumferential wave numbers of the axially loaded shells with different geometric and material parameters and under two types of boundary conditions. It is noted that the axially compressive load decreases the frequency parameters while the axial tension load increases the frequency parameters.

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