scholarly journals Dynamic Stiffness Formulation for Free Vibration of Truncated Conical Shell and Its Combinations with Uniform Boundary Restraints

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Chunyu Zhang ◽  
Guoyong Jin ◽  
Zhihao Wang ◽  
Xuqin Qian ◽  
Linghua Tian
Keyword(s):  
Power Series ◽  
Free Vibration ◽  
Conical Shell ◽  
Dynamic Stiffness ◽  
Recursion Formula ◽  
Geometric Dimension ◽  
Mode Shapes ◽  
Elastic Boundary ◽  
Truncated Conical Shell ◽  
Boundary Lines

This paper presents a dynamic stiffness formulation for the free vibration analysis of truncated conical shell and its combinations with uniform boundary restraints. The displacement fields are expressed as power series, and the coefficients of the series are obtained as recursion formula by substituting the power series into the governing equations. Then, the general solutions can be replaced by an algebraic sum which contains eight base functions, which can diminish the number of degrees of freedom directly. The dynamic stiffness matrix is formulated based on the relationship between the force and displacement along the boundary lines. In the formulation, arbitrary elastic boundary restraints can be realized by introducing four sets of boundary springs along the displacement directions at the boundary lines. The modeling methodology can be easily extended to the combinations of conical shells with different thickness and semivertex angles. The convergence and accuracy of the present formulation are demonstrated by comparing with the finite element method using several numerical examples. Effects of the elastic boundary condition and geometric dimension on the free vibration characteristics are investigated, and several representative mode shapes are depicted for illustrative purposes.

Free Vibration Characteristics of Sandwich Conical Shells With FGM Face Sheets: A Finite Element Approach

2019 ◽  
Author(s):  
Tripuresh Deb Singha ◽  
Apurba Das ◽  
Gopal Agarwal ◽  
Tanmoy Bandyopadhyay ◽  
Amit Karmakar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Conical Shell ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Iteration Algorithm ◽  
Operational Life ◽  
Sandwich Type ◽  
Element Method

Abstract This paper presents an analytical investigation on the free vibration characteristics of symmetric sandwich conical shell with functionally graded material (FGM) face sheets using finite element method. Sandwich-type structures offer higher stiffness to weight ratio with excellent thermal barrier in high temperature application extending the operational life of the component. The sandwich-type conical structure used in the advanced supersonic and hypersonic space vehicles. The material properties of FGM face sheets are considered to be varied in thickness direction as per simple power law distribution in terms of the volume fractions of the FGM constituents. The core layer is considered as homogeneous and made of an isotropic material (Titanium alloy-Ti–6Al–4V). A finite element method is used to reduce the governing equations of vibration problem. The QR iteration algorithm used to solve the standard eigen value problem for determine the natural frequencies. Convergence studies are performed in respect of mesh sizes to substantiate the accuracy of the proposed method. Computer codes developed to obtain the numerical results for the combined effects of twist angle and rotational speed on the free vibration characteristics of symmetric sandwich conical shell with FGM face sheets. A detailed numerical study is carried out to examine the influence of the sandwich plate type, volume fraction index on the free vibration characteristics. The typical mode shapes are also illustrated for different cases.

Free vibration response of carbon nanotube reinforced pretwisted conical shell under thermal environment

2019 ◽  
Vol 234 (3) ◽  
pp. 770-783 ◽  
Author(s):  
Pabitra Maji ◽  
Mrutyunjay Rout ◽  
Amit Karmakar
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Carbon Nanotube ◽  
Free Vibration ◽  
Conical Shell ◽  
Dynamic Equilibrium ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Mode Shapes

Finite element procedure is employed to analyze the free vibration characteristics of rotating functionally graded carbon nanotubes reinforced composite conical shell with pretwist under the thermal environment. In this paper, four types of carbon nanotube grading are considered, wherein the distribution of carbon nanotubes are made through the thickness direction of the conical shell. An eight-noded isoparametric shell element is used in the present formulation to model the panel based on the first-order shear deformation theory. For moderate rotational speeds, the generalized dynamic equilibrium equation is derived from Lagrange’s equation of motion, neglecting the Coriolis effect. The finite element code is developed to investigate the effect of twist angle, temperature, aspect ratio, and rotational speed on natural frequencies. The mode shapes of a carbon nanotube reinforced functionally graded conical shell at different twist angles and rotational speeds are also presented.

scholarly journals Free vibration analysis of 2D-FGM truncated conical shell resting on Winkler–Pasternak foundations based on FSDT

2014 ◽  
Vol 229 (5) ◽  
pp. 818-839 ◽  
Author(s):  
A Asanjarani ◽  
S Satouri ◽  
A Alizadeh ◽  
MH Kargarnovin
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Conical Shell ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Two Dimensional ◽  
Graded Material ◽  
Truncated Conical Shell

Based on the first-order shear deformation theory, this paper focuses on the free vibration behavior of two-dimensional functionally graded material truncated conical shells resting on Winkler–Pasternak foundations. The materials are assumed to be isotropic and inhomogeneous in the length and thickness directions of truncated conical shell. The material properties of the truncated conical shell are varied in these directions according to power law functions. The derived governing equations are solved using differential quadrature method. Convergence of this method is checked and the fast rate of convergence is observed. The primary results of this study are obtained for ( SS− SL), ( CS− CL), and ( CS− SL) boundary conditions and compared with those available in the literatures. Furthermore, effects of geometrical parameters, material power indexes, mechanical boundary conditions, Winkler and Pasternak foundation moduli on the nondimensional frequency parameters of the two-dimensional functionally graded material truncated conical shell are studied.

Thermal effect on free vibration of functionally graded truncated conical shell panels

2016 ◽  
Vol 103 ◽  
pp. 45-61 ◽  
Author(s):  
Najmeh Jooybar ◽  
Parviz Malekzadeh ◽  
Alireza Fiouz ◽  
Mohammad Vaghefi
Keyword(s):  
Free Vibration ◽  
Thermal Effect ◽  
Conical Shell ◽  
Functionally Graded ◽  
Truncated Conical Shell

Free Vibration of Polar-Orthotropic Sector Plates Resting on Point Supports

1985 ◽  
Vol 107 (3) ◽  
pp. 334-338 ◽  
Author(s):  
Y. Narita
Keyword(s):  
Power Series ◽  
Free Vibration ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Opening Angle ◽  
Simply Supported ◽  
Annular Sector ◽  
Sector Plate ◽  
Polar Orthotropic ◽  
Double Power Series

An accurate Ritz solution for the free vibration of point-supported annular sector plates of polar orthotropy is presented. A double power series function is used to represent deflection of the plate, with Lagrange multipliers to impose the constraint conditions. To establish accuracy of the approach, the frequency parameters of a sector plate with some supporting points distributed along the boundary are compared to those of a uniformly simply supported plate. The natural frequencies and mode shapes are presented for wide ranges of the opening angle, radius ratio, and orthotropic parameters.

Free Vibrations of Noncircular Cylindrical Shells Having Circumferentially Varying Thickness

1985 ◽  
Vol 52 (1) ◽  
pp. 149-154 ◽  
Author(s):  
K. Suzuki ◽  
A. W. Leissa
Keyword(s):  
Power Series ◽  
Free Vibration ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Thickness Variation ◽  
Series Expansions ◽  
Varying Thickness ◽  
Power Series Expansions ◽  
Vibration Problems

An exact method using power series expansions is presented for solving free vibration problems for noncircular cylindrical shells having circumferential thickness variation. The method is used to obtain the first known results for this class of problems. Frequencies and mode shapes are presented for a set of elliptical cylindrical shells having second degree thickness variation in each quadrant.

scholarly journals Free vibration of a spinning truncated conical shell.

1988 ◽  
Vol 54 (497) ◽  
pp. 22-30
Author(s):  
Gen YAMADA ◽  
Yukinori KOBAYASHI ◽  
Tetsuo OTAGIRI ◽  
Toshihiro Irie
Keyword(s):  
Free Vibration ◽  
Conical Shell ◽  
Truncated Conical Shell

The effects of shear deformation on the free vibration of elastic beams with general boundary conditions

2009 ◽  
Vol 224 (1) ◽  
pp. 71-84 ◽  
Author(s):  
J Li ◽  
H Hua
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Shear Deformation ◽  
Dynamic Stiffness ◽  
Beam Theory ◽  
Mode Shapes ◽  
Governing Equations ◽  
One Dimensional ◽  
Elastic Beams ◽  
Shear Deformable

Free vibration characteristics of shear deformable elastic beams subjected to different sets of boundary conditions are investigated. The analysis is based on a unified one-dimensional shear deformation beam theory. The governing equations of the elastic beams are obtained by means of Hamilton's principle. Four different boundary conditions are considered. The natural frequencies and mode shapes are obtained by applying the dynamic stiffness method, where the elements of the exact dynamic stiffness matrix are derived by using the analytical solutions of the governing equations of the beam in free vibration. The numerical results for the particular beams with different slenderness ratios are presented and compared with those available in the literature.

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