Vibration analysis of porous metal foam shells rested on an elastic substrate

2019 ◽  
Vol 54 (3) ◽  
pp. 199-208 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Ali Dabbagh ◽  
Abbas Rastgoo
Keyword(s):  
Cylindrical Shell ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Metal Foam ◽  
Porous Metal ◽  
Elastic Substrate ◽  
Porosity Distribution ◽  
Simply Supported ◽  
First Order ◽  
Porosity Coefficient

In this article, the vibration problem of an embedded cylindrical shell consisted of porous metal foam is solved via an analytical method with respect to the influences of various porosity distributions. Three types of porosity distribution across the thickness are covered, namely, uniform, symmetric, and asymmetric. The strain–displacement relations of the shell are assumed to be derived on the basis of the first-order shear deformation shell theory. Then, the achieved relations will be incorporated with the Hamilton’s principle in order to reach the Navier equations of the cylindrical shell. Next, the well-known Galerkin’s method is utilized to calculate the natural frequencies of the system. The influences of both simply supported and clamped boundary conditions are included. In order to show the accuracy of the presented method, the results of the present research are compared with those reported by former published papers. The reported results show that an increase in the porosity coefficient can decrease the frequency of the shell. Also, the stiffness of the system can be lesser decreased while symmetric porosity distribution is chosen.

Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Central Shell Segment

2004 ◽  
Author(s):  
U. Yuceoglu ◽  
V. O¨zerciyes
Keyword(s):  
Cylindrical Shell ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Adhesive Layer ◽  
Shear Stresses ◽  
First Order ◽  
Stress Resultant ◽  
Circular Cylindrical Shells

This study is concerned with the “Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Central Shell Segment.” The base shell is made of an orthotropic “full” circular cylindrical shell reinforced and/or stiffened by an adhesively bonded dissimilar, orthotropic “full” circular cylindrical shell segment. The stiffening shell segment is located at the mid-center of the composite system. The theoretical analysis is based on the “Timoshenko-Mindlin-(and Reissner) Shell Theory” which is a “First Order Shear Deformation Shell Theory (FSDST).” Thus, in both “base (or lower) shell” and in the “upper shell” segment, the transverse shear deformations and the extensional, translational and the rotary moments of inertia are taken into account in the formulation. In the very thin and linearly elastic adhesive layer, the transverse normal and shear stresses are accounted for. The sets of the dynamic equations, stress-resultant-displacement equations for both shells and the in-between adhesive layer are combined and manipulated and are finally reduced into a ”Governing System of the First Order Ordinary Differential Equations” in the “state-vector” form. This system is integrated by the “Modified Transfer Matrix Method (with Chebyshev Polynomials).” Some asymmetric mode shapes and the corresponding natural frequencies showing the effect of the “hard” and the “soft” adhesive cases are presented. Also, the parametric study of the “overlap length” (or the bonded joint length) on the natural frequencies in several modes is considered and plotted.

Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells With a Bonded Central Lap Joint

2003 ◽  
Author(s):  
V. O¨zerciyes ◽  
U. Yuceoglu
Keyword(s):  
Cylindrical Shell ◽  
Differential Equations ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Adhesive Layer ◽  
Lap Joint ◽  
First Order ◽  
Single Lap Joint ◽  
Circular Cylindrical Shells

In this study, the problem of the free asymmetric vibrations of composite “full” circular cylindrical shells with a bonded single lap joint is considered. The “full” circular cylindrical shell adherends to be made of dissimilar and orthotropic materials are connected by relatively very thin, yet flexible and linearly elastic adhesive layer. The bonded single lap joint is a centrally located in the composite shell system. The analysis is based on a “Timoshenko-Mindlin (and Reissner) Type Shell Theory” which is a “First Order Shear Deformation Shell Theory (FSDST)”. In the formulation, the set of governing differential equations is reduced to a system of first order ordinary differential equations in the “state vector” form. Then, they are integrated by means of a numerical procedure, that is, the “Modified Transfer Matrix Method (with Chebyshev Polynomials)”. The mode shapes and the natural frequencies of the “full” cylindrical shell lap joint system are investigated for various boundary conditions. Also, the effects, on the modes and natural frequencies, of the “hard” (or rather relatively stiff) and the “soft” (or relatively very flexible) adhesive layer cases are considered and presented. Some of the numerical results of the important parametric studies are computed and plotted.

Local loads on a toroidal shell

1992 ◽  
Vol 27 (2) ◽  
pp. 59-66 ◽  
Author(s):  
D Redekop ◽  
F Zhang
Keyword(s):  
Cylindrical Shell ◽  
Shell Theory ◽  
Elastic Shell ◽  
Toroidal Shell ◽  
Pipe Bend ◽  
Local Loads ◽  
Simply Supported ◽  
Linear Elastic ◽  
Wide Range ◽  
Theory Solution

In this study the effect of local loads applied on a sectorial toroidal shell (pipe bend) is considered. A linear elastic shell theory solution for local loads is first outlined. The solution corresponds to the case of a shell simply supported at the two ends. Detailed displacement and stress results are then given for a specific shell with loadings centred at three positions; the crown circles, the extrados, and the intrados. These results are compared with results for a corresponding cylindrical shell. The paper concludes with a table summarizing results for characteristic displacements and stresses in a number of shells, covering a wide range of geometric parameters.

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.

Effect of Ring Support Position and Geometrical Dimension on the Free Vibration of Ring-Stiffened Cylindrical Shells

2014 ◽  
Vol 580-583 ◽  
pp. 2879-2882
Author(s):  
Xiao Wan Liu ◽  
Bin Liang
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Ritz Method ◽  
Geometrical Dimension ◽  
Stiffened Cylindrical Shell ◽  
Simply Supported ◽  
Ring Support ◽  
Stiffened Cylindrical Shells

Effect of ring support position and geometrical dimension on the free vibration of ring-stiffened cylindrical shells is studied in this paper. The study is carried out by using Sanders shell theory. Based on the Rayleigh-Ritz method, the shell eigenvalue governing equation is derived. The present analysis is validated by comparing results with those in the literature. The vibration characteristics are obtained investigating two different boundary conditions with simply supported-simply supported and clamped-free as the examples. Key Words: Ring-stiffened cylindrical shell; Free vibration; Rayleigh-Ritz method.

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.

Vibration Analysis of a Railway Carbody Model as a Non-Circular Cylindrical Shell

2007 ◽  
Author(s):  
Yukinori Kobayashi ◽  
Kotaro Ishiguri ◽  
Takahiro Tomioka ◽  
Yohei Hoshino
Keyword(s):  
Cylindrical Shell ◽  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Elastic Vibration ◽  
Mode Shapes ◽  
Simply Supported ◽  
Vibration Problems ◽  
Good Agreement

Railway carbody is modeled as a non-circular cylindrical shell with simply-supported ends in this paper. The shell model doesn’t have end plates of the carbody and other equipments attached to actual carbody are neglected. We have applied the transfer matrix method (TMM) to the analysis of three-dimensional elastic vibration problems on the carbody. We also made a 1/12 size carbody model for experimental studies to verify the validity of the numerical simulation. The model has end plates and was placed on soft sponge at both ends of the model to emulate the freely-support. The modal analysis was applied to the experimental model, and natural frequencies and mode shapes of vibration were measured. Comparing the results by TMM and the experiment, natural frequencies and mode shapes of vibration for lower modes show good agreement each other in spite of differences of boundary conditions.

A Study on the Free Vibration of the Prestressed Joined Cylindricalspherical Shell Structures

2013 ◽  
Vol 390 ◽  
pp. 207-214 ◽  
Author(s):  
Mahdi Yusefzad ◽  
Firouz Bakhtiari Nejad
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Shell Structure ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Shell Structures ◽  
Mode Shapes ◽  
Free Boundary Conditions ◽  
Modal Test

The free vibration characteristics of the prestressed joined spherical–cylindrical shell with free-free boundary conditions are investigated. The Flügge shell theory and Rayleigh-Ritz energy method are applied in order to analyze the free vibration characteristics of the joined shell. In the modal test, the LMS software is used to calculate mode shapes and natural frequencies of the joined shell structure. The natural frequencies and mode shapes are calculated numerically and they are compared with those of the FEM and modal test to confirm the reliability of the analytical solution. The effects of the shallowness and length of the cylindrical shell to the free vibrational behavior of joined shell structure and the effect of internal pressure on the modal charactristics are investigated.

Vibrations of Composite Noncircular Cylindrical Shells

1995 ◽  
Vol 117 (4) ◽  
pp. 470-476 ◽  
Author(s):  
V. Kumar ◽  
A. V. Singh
Keyword(s):  
Shell Theory ◽  
Natural Frequencies ◽  
Composite Shell ◽  
Cylindrical Shells ◽  
Middle Layer ◽  
Displacement Fields ◽  
Shell Surface ◽  
First Order ◽  
Cylindrical Panels ◽  
Vibrational Characteristics

The free vibrational characteristics of composite noncircular cylindrical shells are investigated in this paper. The shells are composed of layered media of different material properties. The thickness of each layer is considered to be constant. First order composite shell theory, which includes the effects of shear deformation and rotary inertia, is used in the formulation. A combination of Bezier functions and beam functions is used to describe the displacement fields along the circumference and longitudinal directions, respectively, of the shell surface. The shell is modelled using a number of curved cylindrical panels. Displacement (C0), slope (C1) and curvature (C2) continuities between the panels are enforced by proper blending of the Bezier curves. Numerical results are included for a circular sandwich shell and a two-layer cross-ply oval cylinder that provide excellent agreement with those from the literature. The natural frequencies of clamped oval sandwich cylinders made of stiff outer layers and light middle layer are also presented.

A Porous Microbeam Model for Bending and Vibration Analysis Based on the Sinusoidal Beam Theory and Modified Strain Gradient Theory

2018 ◽  
Vol 10 (05) ◽  
pp. 1850059 ◽  
Author(s):  
Yan Qing Wang ◽  
Hu Long Zhao ◽  
Chao Ye ◽  
Jean W. Zu
Keyword(s):  
Strain Gradient ◽  
Metal Foam ◽  
Slenderness Ratio ◽  
Beam Theory ◽  
Porous Metal ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Modified Strain Gradient Theory ◽  
Size Dependent ◽  
Porosity Coefficient

In this research, we analyze size-dependent bending and vibration of microbeams made of porous metal foams. The porous microbeam model is developed based on the sinusoidal beam theory and the modified strain gradient theory. Hamilton’s principle is employed to obtain the governing equations and boundary conditions of the porous microbeam. Analytical solutions are presented for deflections and natural frequencies of the porous microbeam by using Navier’s method. The influences of the porosity distribution, the porosity coefficient, the slenderness ratio, and the microbeam thickness are clarified on the static bending and free vibration of porous microbeams. These findings can be applied to the design of metal foam microstructures in engineering.

Sign in / Sign up

Export Citation Format

Share Document