scholarly journals Accurate Results for Free Vibration of Doubly Curved　Shallow Shells of Rectangular Planform (Part.1)

2021 ◽  
Vol 4 (1) ◽  
pp. 29-36
Author(s):  
Daisuke Narita ◽  
Yoshihiro Narita
Keyword(s):  
Free Vibration ◽  
Shell Theory ◽  
Frequency Equation ◽  
Shell Shape ◽  
Comparison Study ◽  
Shallow Shells ◽  
Wide Range ◽  
Out Of Plane ◽  
Edge Conditions ◽  
Doubly Curved

A method is presented for determining the free vibration frequencies of doubly curved, isotropic shallow shells under general edge conditions and is used to obtain accurate natural frequencies for wide range of geometric parameters. Based on the shallow shell theory applicable to thin thickness shells, a method of Ritz is extended to derive a frequency equation wherein the displacement functions are modified to accommodate arbitrary sets of edge conditions for both in-plane and out-of-plane motions. In numerical computation, convergence is tested against series terms and comparison study is made with existing results by other authors. Twenty one sets of frequency parameters are tabulated for a wide range of shell shape and curvature ratio to serve as data for future comparison and practical design purpose.  

Free Vibration of Curvilinearly Stiffened Shallow Shells

2013 ◽  
Author(s):  
Peng Shi ◽  
Rakesh K. Kapania
Keyword(s):  
Free Vibration ◽  
Ritz Method ◽  
Beam Theory ◽  
Fe Method ◽  
Shallow Shells ◽  
First Order ◽  
Stiffened Shells ◽  
Method Base ◽  
Doubly Curved ◽  
Good Agreement

The free vibration of curvilinearly stiffened doubly curved shallow shells is investigated by the Ritz method. Base on the first order shear deformation shell theory and Timoshenko’s 3-D curved beam theory, the strain and kinetic energies of the stiffened shells are introduced. Numerical results with different geometrical shells and boundary conditions, and different stiffener locations and curvatures are analyzed to verify the feasibility of the presented Ritz method for solving the problems. The results show good agreement with those using the FE method.

Pipe Bend Analysis by Thin Shell Theory

1986 ◽  
Vol 53 (1) ◽  
pp. 173-180 ◽  
Author(s):  
J. F. Whatham
Keyword(s):  
Computer Program ◽  
Thin Shell ◽  
Shell Theory ◽  
Factor Versus ◽  
Pipe Bend ◽  
Pipe Elbow ◽  
Wide Range ◽  
Out Of Plane ◽  
Plane Bending ◽  
Thin Shell Theory

Thin shell theory is applied to pipe bends terminated by flanges or flange-ended tangent pipes and subjected to any end loading, either in-plane or out-of-plane. Graphs of flexibility factor versus pipe bend characteristic are presented for in-plane bending of a wide range of pipe elbows terminated by flanges or short flange-ended tangents. Experimental results verify the thin shell solutions for in-plane and out-of-plane bending of a flanged pipe elbow. The capabilities of a computer program BENDPAC are also described.

Free Vibration of Curvilinearly Stiffened Shallow Shells

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Peng Shi ◽  
Rakesh K. Kapania ◽  
C. Y. Dong
Keyword(s):  
Free Vibration ◽  
Shell Theory ◽  
Ritz Method ◽  
Three Dimensional ◽  
Beam Theory ◽  
Shell Element ◽  
Shallow Shells ◽  
First Order ◽  
Stiffened Shells ◽  
Good Agreement

The free vibration of curvilinearly stiffened shallow shells is investigated by the Ritz method. Based on the first-order shear deformation shell theory and three-dimensional (3D) curved beam theory, the strain and kinetic energies of the stiffened shells are introduced. The stiffener can be placed anywhere within the shell, without the need for having the stiffener and shell element nodes coincide. Numerical results with different geometrical shells and boundary conditions and different stiffener locations and curvatures are analyzed to verify the feasibility of the presented Ritz method for solving the problems. The results show good agreement with those using other methods, e.g., using a converged set of results obtained by Nastran.

Vibration Analysis of Doubly Curved Shallow Shells With Elastic Edge Restraints

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Shiliang Jiang ◽  
Tiejun Yang ◽  
W. L. Li ◽  
Jingtao Du
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Wide Spectrum ◽  
Current Method ◽  
Entire Solution ◽  
Shallow Shells ◽  
Special Cases ◽  
Out Of Plane ◽  
Expansion Coefficients ◽  
Doubly Curved

An analytical method is derived for the vibration analysis of doubly curved shallow shells with arbitrary elastic supports alone its edges, a class of problems which are rarely attempted in the literature. Under this framework, all the classical homogeneous boundary conditions for both in-plane and out-of-plane displacements can be universally treated as the special cases when the stiffness for each of restraining springs is equal to either zero or infinity. Regardless of the boundary conditions, the displacement functions are invariably expanded as an improved trigonometric series which converges uniformly and polynomially over the entire solution domain. All the unknown expansion coefficients are treated as the generalized coordinates and solved using the Rayleigh–Ritz technique. Unlike most of the existing solution techniques, the current method offers a unified solution to a wide spectrum of shell problems involving, such as different boundary conditions, varying material and geometric properties with no need of modifying or adapting the solution schemes and implementing procedures. A numerical example is presented to demonstrate the accuracy and reliability of the current method.

On the Natural Frequencies of a Flexible Manipulator with a Tip Payload

2005 ◽  
Vol 219 (11) ◽  
pp. 1199-1205 ◽  
Author(s):  
D C D Oguamanam ◽  
M Arshad
Keyword(s):  
Free Vibration ◽  
Parametric Study ◽  
Natural Frequencies ◽  
Frequency Equation ◽  
Flexible Manipulator ◽  
Centre Of Mass ◽  
Bernoulli Beam ◽  
Torsional Deformation ◽  
Out Of Plane ◽  
Euler Bernoulli Beam

The free vibration of a flexible manipulator that is carrying a rigid payload at the tip is examined. The centre of mass of the payload may not coincide with the point of attachment to the manipulator. The manipulator is modelled as an Euler-Bernoulli beam and it undergoes both out-of-plane and in-plane elastic flexural deformations in conjunction with torsional deformation. The explicit expression of the characteristic (or frequency) equation is presented and a parametric study is provided.

scholarly journals Free Vibration of Functionally Graded Carbon Nanotube-reinforced Doubly-curved Shells

2020 ◽  
Vol 01 ◽  
Author(s):  
Maziar Janghorban ◽  
Behrouz Karami
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Strain Gradient ◽  
Shear Deformation Theory ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Size Dependency ◽  
Wide Range ◽  
Doubly Curved

Background:: Carbon nanotubes (CNTs) reinforced structures are the main elements of structural equipment. Hence a wide range of investigations has been performed on the response of these structures. A lot of studies covered the static and dynamic phenomenon of CNTs reinforced beams, plates and shells. However, there is no study on the free vibration analysis of a doubly-curved nano-size shell made of CNTs reinforced composite materials. Methods:: This work utilized a general third-order shear deformation theory to model the nanoshell where the general strain gradient theory is used in order to capture both nonlocality and strain gradient size-dependency. The Navier solution solving procedure is adopted to solve the partial differential equations (PDEs) and get the natural frequency of the system which is obtained through the Hamilton principle. Results:: The current study shows the importance of small-scale coefficients. The natural frequency increases with rising the strain gradient-size dependency which is because of stiffness enhancement, while the natural frequency decreases by increasing the nonlocality. In addition, the numerical examples covered the CNTs distribution patterns. Conclusion:: This work also studied the importance of shell panel’s shape. It has been observed that spherical shell panel has a higher frequency compared to the hyperbolic one. Furthermore, the frequency of the system increases with growing length-to-thickness ration.

On New Analytic Free Vibration Solutions of Doubly Curved Shallow Shells by the Symplectic Superposition Method Within the Hamiltonian-System Framework

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Rui Li ◽  
Chao Zhou ◽  
Xinran Zheng
Keyword(s):  
Hamiltonian System ◽  
Free Vibration ◽  
Original Problem ◽  
Analytic Solutions ◽  
Solution Procedure ◽  
Symplectic Space ◽  
Lagrangian System ◽  
Superposition Method ◽  
Shallow Shells ◽  
Doubly Curved

Abstract This study presents a first attempt to explore new analytic free vibration solutions of doubly curved shallow shells by the symplectic superposition method, with focus on non-Lévy-type shells that are hard to tackle by classical analytic methods due to the intractable boundary-value problems of high-order partial differential equations. Compared with the conventional Lagrangian-system-based expression to be solved in the Euclidean space, the present description of the problems is within the Hamiltonian system, with the solution procedure implemented in the symplectic space, incorporating formulation of a symplectic eigenvalue problem and symplectic eigen expansion. Specifically, an original problem is first converted into two subproblems, which are solved by the above strategy to yield the symplectic solutions. The analytic frequency and mode shape solutions are then obtained by the requirement of the equivalence between the original problem and the superposition of subproblems. Comprehensive results for representative non-Lévy-type shells are tabulated or plotted, all of which are well validated by satisfactory agreement with the numerical finite element method. Due to the strictness of mathematical derivation and accuracy of solution, the developed method provides a solid approach for seeking more analytic solutions.

scholarly journals Wave Based Method for Free Vibration Analysis of Cross-Ply Composite Laminated Shallow Shells with General Boundary Conditions

Materials ◽  
2019 ◽  
Vol 12 (23) ◽  
pp. 3808 ◽  
Author(s):  
Shi ◽  
He ◽  
Wang ◽  
Ma ◽  
Shu
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Shell Theory ◽  
Free Vibration Analysis ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Theoretical Formulation ◽  
Shallow Shells ◽  
Numerical Examples ◽  
Dynamic Relationship

In this paper, a semi-analytical method is adopted to analyze the free vibration characteristics of composite laminated shallow shells under general boundary conditions. Combining two kinds of shell theory, that is, first-order shear deformation shell theory (FSDT) and classical shell theory (CST), to describe the dynamic relationship between the displacement resultants and force vectors, the theoretical formulations are established. According to the presented work, the displacement and transverse rotational variables are transformed into wave function forms to satisfy the theoretical formulation. Related to diverse boundary conditions, the total matrix of the composite shallow shell can be established. Searching the determinant of the total matrix using the dichotomy method, the natural frequency of composite laminated shallow shells is obtained. Through several classical numerical examples, it is proven that the results calculated by the presented method are more accurate and reliable. Furthermore, to discuss the effect of geometric parameters and material constants on the natural frequencies of composite laminated shallow shells, some numerical examples are calculated to analyze. Also, the influence of boundary elastic restrained stiffness is discussed.

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