An Analytical Approach for the Nonlinear Free Vibration Analysis of Thin-Walled Circular Cylindrical Shells

2021 ◽  
pp. 2150172
Author(s):  
Yacine Ben-Youssef ◽  
Youcef Kerboua ◽  
Aouni A. Lakis
Keyword(s):  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Free Vibration Analysis ◽  
Radius Ratio ◽  
Wave Number ◽  
Equilibrium Equations ◽  
Various Boundary Conditions ◽  
Linear And Nonlinear ◽  
New Formulation ◽  
The Impact

This paper presents a new formulation combining the nonlinear theory of Novozhilov with the classical finite element method for the purpose of evaluating the vibratory characteristics of thin, closed and isotropic cylindrical shells. The theory developed in this paper is able to include the shell curvature effect in the circumferential direction of the orthogonal displacements and considers the impact of initial geometric imperfections on the dynamic response of the system. The formulation first takes a general form by expressing the shell displacements as an alliance between the generalized coordinates and spatial functions. Nonlinear kinematic relationships are inferred from Novozhilov’s theory. The equations of motion as well as the expressions of the mass, linear and nonlinear stiffness matrices are derived through the Lagrange method by considering the coupling between the different modes. An application of this model is illustrated in a further step, by adopting the displacement functions derived from exact solutions of linear Sanders’ theory equilibrium equations for thin cylindrical shells. The governing equations of motion are solved with the help of a direct iterative method. Linear and nonlinear frequencies are validated by comparison with the results in the literature. The relative nonlinear frequencies are determined as a function of vibration amplitudes and then compared with published results for several cases of shells. Excellent agreement is observed between the results derived from this theory and those found in the literature. The effect of different parameters including axial and circumferential wave number, length-to-radius ratio, thickness-to-radius ratio and various boundary conditions, on the nonlinear frequencies of cylindrical shells is investigated.

Free vibration analysis and post-critical free vibrations of nanocomposite rotating beams reinforced with graphene platelet

2021 ◽  
pp. 107754632110511
Author(s):  
Arameh Eyvazian ◽  
Chunwei Zhang ◽  
Farayi Musharavati ◽  
Afrasyab Khan ◽  
Mohammad Alkhedher
Keyword(s):  
Natural Frequency ◽  
Thermal Environment ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Weight Fraction ◽  
Free Vibrations ◽  
Graphene Platelet ◽  
The Impact

Treatment of the first natural frequency of a rotating nanocomposite beam reinforced with graphene platelet is discussed here. In regard of the Timoshenko beam theory hypothesis, the motion equations are acquired. The effective elasticity modulus of the rotating nanocomposite beam is specified resorting to the Halpin–Tsai micro mechanical model. The Ritz technique is utilized for the sake of discretization of the nonlinear equations of motion. The first natural frequency of the rotating nanocomposite beam prior to the buckling instability and the associated post-critical natural frequency is computed by means of a powerful iteration scheme in reliance on the Newton–Raphson method alongside the iteration strategy. The impact of adding the graphene platelet to a rotating isotropic beam in thermal ambient is discussed in detail. The impression of support conditions, and the weight fraction and the dispersion type of the graphene platelet on the acquired outcomes are studied. It is elucidated that when a beam has not undergone a temperature increment, by reinforcing the beam with graphene platelet, the natural frequency is enhanced. However, when the beam is in a thermal environment, at low-to-medium range of rotational velocity, adding the graphene platelet diminishes the first natural frequency of a rotating O-GPL nanocomposite beam. Depending on the temperature, the post-critical natural frequency of a rotating X-GPL nanocomposite beam may be enhanced or reduced by the growth of the graphene platelet weight fraction.

Free vibration analysis of porous laminated rotating circular cylindrical shells

2019 ◽  
Vol 25 (18) ◽  
pp. 2494-2508 ◽  
Author(s):  
Ahmad Reza Ghasemi ◽  
Mohammad Meskini
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Cylindrical Shells ◽  
Free Vibration Analysis ◽  
Equilibrium Equations ◽  
Rotating Speed ◽  
Simply Supported ◽  
Numerical Result ◽  
Love’S Shell Theory ◽  
Circular Cylindrical Shells

In this research, investigations are presented of the free vibration of porous laminated rotating circular cylindrical shells based on Love’s shell theory with simply supported boundary conditions. The equilibrium equations for circular cylindrical shells are obtained using Hamilton’s principle. Also, Navier’s solution is used to solve the equations of the cylindrical shell due to the simply supported boundary conditions. The results are compared with previous results of other researchers. The numerical result of this study indicates that with increase of the porosity coefficient the nondimensional backward and forward frequency decreased. Then the results of the free vibration of rotating cylindrical shells are presented in terms of the effects of porous coefficients, porous type, length to radius ratio, rotating speed, and axial and circumferential wave numbers.

Development of beam modal function for free vibration analysis of FML circular cylindrical shells

2017 ◽  
Vol 24 (14) ◽  
pp. 3026-3035 ◽  
Author(s):  
Masood Mohandes ◽  
Ahmad Reza Ghasemi ◽  
Mohsen Irani-Rahagi ◽  
Keivan Torabi ◽  
Fathollah Taheri-Behrooz
Keyword(s):  
Free Vibration ◽  
Shell Theory ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Free Vibration Analysis ◽  
Governing Equations ◽  
Fiber Metal Laminate ◽  
Circular Cylindrical Shells ◽  
Fiber Metal

The free vibration of fiber–metal laminate (FML) thin circular cylindrical shells with different boundary conditions has been studied in this research. Strain–displacement relations have been obtained according to Love’s first approximation shell theory. To satisfy the governing equations of motion, a beam modal function model has been used. The effects of different FML parameters such as material properties lay-up, volume fraction of metal, fiber orientation, and axial and circumferential wavenumbers on the vibration of the shell have been studied. The frequencies of shells have been calculated for carbon/epoxy and glass/epoxy as composites and for aluminum as metal. The results demonstrate that the influences of FML lay-up and volume fraction of composite on the frequencies of the shell are remarkable.

Effect of Winkler and Pasternak elastic foundation on the vibration of rotating functionally graded material cylindrical shell

2018 ◽  
Vol 232 (24) ◽  
pp. 4564-4577 ◽  
Author(s):  
Muzamal Hussain ◽  
Muhammad Nawaz Naeem ◽  
Mohammad Reza Isvandzibaei
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Radius Ratio ◽  
Wave Number ◽  
Simply Supported ◽  
Elastic Foundations

In this paper, vibration characteristics of rotating functionally graded cylindrical shell resting on Winkler and Pasternak elastic foundations have been investigated. These shells are fabricated from functionally graded materials. Shell dynamical equations are derived by using the Hamilton variational principle and the Langrangian functional framed from the shell strain and kinetic energy expressions. Elastic foundations, namely Winkler and Pasternak moduli are inducted in the tangential direction of the shell. The rotational motions of the shells are due to the Coriolis and centrifugal acceleration as well as the hoop tension produced in the rotating case. The wave propagation approach in standard eigenvalue form has been employed in order to derive the characteristic frequency equation describing the natural frequencies of vibration in rotating functionally graded cylindrical shell. The complex exponential functions, with the axial modal numbers that depend on the boundary conditions stated at edges of a cylindrical shell, have been used to compute the axial modal dependence. In our new investigation, frequency spectra are obtained for circumferential wave number, length-to-radius ratio, height-to-radius ratio with simply supported–simply supported and clamped–clamped boundary conditions without elastic foundation. Also, the effect of elastic foundation on the rotating cylindrical shells is examined with the simply supported–simply supported edge. To check the validity of the present method, the fundamental natural frequencies of non-rotating isotropic and functionally graded cylindrical shells are compared with the open literature. Also, a comparison is made for infinitely long rotating with the earlier published paper.

scholarly journals Natural Frequencies of FG Plates with Two New Distribution of Porosity

2021 ◽  
Vol 26 (2) ◽  
pp. 128-142
Author(s):  
Slimane Merdaci ◽  
Adda Hadj Mostefa ◽  
Osama M.E.S. Khayal
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Simply Supported ◽  
Fg Plates ◽  
Porosity Coefficient ◽  
The Impact ◽  
New Distribution

Abstract The functionally graded plates (FGP) with two new porosity distributions are examined in this paper. In this work the plate is modeled using the higher-order shear deformation plate principle. The shear correction variables are neglected. To evaluate the equations of motion, the Hamilton method will be used herein. Therefore, the free vibration analysis of FG plate is developed in this work. For porous smart plates with simply-supported sides, natural frequencies are obtained and verified with the established findings in the literature. The impact of the porosity coefficient on the normal frequencies of the plate for various thickness ratios, geometric ratios, and material properties was investigated in a thorough numerical analysis.

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.

scholarly journals Nonlinear Vibration of Truncated Conical Shells: Donnell, Sanders and Nemeth Theories

2020 ◽  
Vol 21 (1) ◽  
pp. 83-97 ◽  
Author(s):  
Mehrdad Bakhtiari ◽  
Aouni A. Lakis ◽  
Youcef Kerboua
Keyword(s):  
Free Vibration ◽  
Nonlinear Vibration ◽  
Equations Of Motion ◽  
Element Model ◽  
Amplitude Equation ◽  
Radius Ratio ◽  
Equilibrium Equations ◽  
Nonlinear Free Vibration ◽  
Conical Shells ◽  
Simplifying Assumptions

AbstractNonlinear free vibration of truncated conical shells has been investigated for three different shell theories; Donnell, Sanders and Nemeth to investigate the effect of their simplifying assumptions. The displacement field of a finite element model that was obtained from the exact solution of equilibrium equations of Sander’s improved first-approximation theory is used to define the nonlinear strain energy of conical shells. Employing generalized coordinates method the equations of motion are derived and subsequently the amplitude equation of nonlinear vibration of conical shells was developed. The amplitude equation is solved for multiple cases of isotropic materials. Linear and nonlinear free vibration results are validated against the existing studies in scientific literature and demonstrate good accordance. The validated model is used to investigate effects of different parameters including circumferential mode number, cone-half angle, length to radius ratio, thickness to radius ratio and boundary conditions for the nonlinear vibration of conical shells.

Chebyshev Collocation Solutions for Vibration Analysis of Circular Cylindrical Shells with Arbitrary Boundary Conditions

2017 ◽  
Vol 17 (02) ◽  
pp. 1750020 ◽  
Author(s):  
Nuttawit Wattanasakulpong ◽  
Sacharuck Pornpeerakeat ◽  
Arisara Chaikittiratana
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Chebyshev Collocation Method ◽  
Arbitrary Boundary ◽  
Chebyshev Collocation ◽  
Various Boundary Conditions ◽  
Circular Cylindrical Shells

This paper applies the Chebyshev collocation method to finding accurate solutions of natural frequencies for circular cylindrical shells. The shells with different boundary conditions are considered in the parametric study. By using the method to solve the coupled differential equations of motion governing the vibration of the shell, numerical results are obtained from the algebraic eigenvalue equation using the Chebyshev differentiation matrices. And the results satisfy both the geometric and force boundary conditions. Based on the numerical examples, the proposed method shows its capacity and reliability in predicting accurate frequency results for circular cylindrical shells with various boundary conditions as compared to some exact solutions available in the literature.

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