On Free Vibrations of an Embedded Anisotropic Spherical Shell

1997 ◽  
Vol 119 (4) ◽  
pp. 481-487 ◽  
Author(s):  
W. Q. Chen ◽  
H. J. Ding
Keyword(s):  
Spherical Shell ◽  
Elastic Medium ◽  
Shell Theory ◽  
Three Dimensional ◽  
Homogeneous Solution ◽  
Free Vibrations ◽  
Normal Strain ◽  
Auxiliary Variables ◽  
Transverse Normal Strain ◽  
Isotropic Spherical Shell

In this paper, free vibrations of a spherically isotropic spherical shell embedded in an elastic medium of Pasternak type are studied by using a six-mode shell theory that includes effects of shear deformation, rotary inertia, and transverse normal strain. The separable homogeneous solution for displacements and stresses in a deep spherical shell is derived and two classes of vibrations are obtained by the introduction of five auxiliary variables. Numerical results are compared with those predicted by two simpler shell theories mentioned in the paper and those by three-dimensional elastic theory.

Three-Dimensional and Shell-Theory Analysis of Elastic Waves in a Hollow Sphere: Part 1—Analytical Foundation

1969 ◽  
Vol 36 (3) ◽  
pp. 431-439 ◽  
Author(s):  
A. H. Shah ◽  
C. V. Ramkrishnan ◽  
S. K. Datta
Keyword(s):  
Elastic Waves ◽  
Shell Theory ◽  
Three Dimensional ◽  
Frequency Equation ◽  
Wave Number ◽  
Normal Strain ◽  
Theory Analysis ◽  
Analytical Foundation ◽  
Transverse Normal Strain ◽  
Approximate Equations

In Part 1 of this paper an exact analysis of the nonaxisymmetric wave propagation in a hollow elastic sphere is presented. It is found that the characteristic frequency equation is independent of the longitudinal wave number. Approximate equations for thin shells and membranes are derived by way of asymptotic expansions. In general, the vibrations fall into two distinct classes, one of which is equivoluminal. Also included in the paper is a six-mode shell theory in which the effects of transverse normal strain are included. A technique due to van der Neut is used to separate the governing partial differential equations whereby two frequency equations corresponding to the two classes of vibrations are obtained.

A Refined Theory for Laminated Anisotropic, Cylindrical Shells

1974 ◽  
Vol 41 (2) ◽  
pp. 471-476 ◽  
Author(s):  
J. M. Whitney ◽  
C.-T. Sun
Keyword(s):  
Shear Deformation ◽  
Shell Theory ◽  
Theory Of Elasticity ◽  
Small Radius ◽  
Refined Theory ◽  
Normal Strain ◽  
Governing Equations ◽  
Transverse Normal Strain ◽  
Anisotropic Cylindrical Shell ◽  
Good Agreement

A set of governing equations and boundary conditions are derived which describe the static deformation of a laminated anisotropic cylindrical shell. The theory includes both transverse shear deformation and transverse normal strain, as well as expansional strains. The validity of the theory is assessed by comparing solutions obtained from the shell theory to results obtained from exact theory of elasticity. Reasonably good agreement is observed and both shear deformation and transverse normal strain are shown to be of importance for shells having a relatively small radius-to-thickness ratio.

Impulsive Deformation of Mirsky-Herrmann’s Thick Cylindrical Shells by a Numerical Method

1973 ◽  
Vol 40 (4) ◽  
pp. 1009-1016 ◽  
Author(s):  
M. Ziv ◽  
M. Perl
Keyword(s):  
Shell Theory ◽  
Pulse Velocity ◽  
Normal Strain ◽  
Finite Difference Technique ◽  
Characteristics Method ◽  
Transverse Normal Stress ◽  
Infinite Cylindrical Shell ◽  
Shell Equations ◽  
Thickness Parameter ◽  
Transverse Normal Strain

The transient response of a thick elastic semi-infinite cylindrical shell subjected to impulsive step loads is obtained. This work presents solutions to two boundary-value problems. First, the shell is exposed to an axially step pulse velocity load while second, the pulse is applied radially to the shell. The influence of the transverse normal stress and the transverse normal strain on the deformation is being studied in great detail. The shell theory employed is based on the thick-shell equations derived by Mirsky and Herrmann, which comprise these transversal effects. These equations are solved by the characteristics method, while integration is carried out by the finite-difference technique. The results also present the influence of the thickness parameter (h/R) on the solution. Comparisons are made to solutions of other shell theories which neglect the transversal effects. Major conclusions show the existence of an important influence of the transverse normal strain on the deformation.

scholarly journals Analysis of Observed Initial Stress by the Isotropic Spherical Shell Theory and Considerations.

1995 ◽  
Vol 111 (13) ◽  
pp. 913-918 ◽  
Author(s):  
Katsuhiko SUGAWARA ◽  
Hyun Kuk JANG ◽  
Xingchun HUANG
Keyword(s):  
Spherical Shell ◽  
Initial Stress ◽  
Shell Theory ◽  
Isotropic Spherical Shell

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

scholarly journals Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Mircea Bîrsan
Keyword(s):  
Energy Density ◽  
Constitutive Model ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Shell Theory ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Classical Shell Theory ◽  
Three Dimensional Elasticity ◽  
General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

Free Vibrations of Thick, Complete Conical Shells of Revolution From a Three-Dimensional Theory

2005 ◽  
Vol 72 (5) ◽  
pp. 797-800 ◽  
Author(s):  
Jae-Hoon Kang ◽  
Arthur W. Leissa
Keyword(s):  
Ritz Method ◽  
Three Dimensional ◽  
Axial Direction ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Shells Of Revolution ◽  
Dimensional Theory ◽  
Conical Shells ◽  
Cylindrical Coordinate

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution in which the bottom edges are normal to the midsurface of the shells based upon the circular cylindrical coordinate system using the Ritz method. Comparisons are made between the frequencies and the corresponding mode shapes of the conical shells from the authors' former analysis with bottom edges parallel to the axial direction and the present analysis with the edges normal to shell midsurfaces.

scholarly journals Analysis of high-rise constructions with the using of three-dimensional models of rods in the finite element program PRINS

2018 ◽  
Vol 33 ◽  
pp. 02033
Author(s):  
Vladimir Agapov
Keyword(s):  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Free Vibrations ◽  
Finite Element Program ◽  
One Dimensional ◽  
Static And Dynamic Analysis ◽  
High Rise ◽  
Element Program ◽  
Dimensional Models ◽  
Three Dimensional Models

The necessity of new approaches to the modeling of rods in the analysis of high-rise constructions is justified. The possibility of the application of the three-dimensional superelements of rods with rectangular cross section for the static and dynamic calculation of the bar and combined structures is considered. The results of the eighteen-story spatial frame free vibrations analysis using both one-dimensional and three-dimensional models of rods are presented. A comparative analysis of the obtained results is carried out and the conclusions on the possibility of three-dimensional superelements application in static and dynamic analysis of high-rise constructions are given on its basis.

A refined sinusoidal model for functionally graded plates subjected to thermomechanical loading

2018 ◽  
Vol 53 (14) ◽  
pp. 1883-1896
Author(s):  
Ren Xiaohui ◽  
Wu Zhen
Keyword(s):  
Functionally Graded Material ◽  
Thermal Loading ◽  
Functionally Graded ◽  
Normal Strain ◽  
Sinusoidal Model ◽  
Proposed Model ◽  
Graded Material ◽  
Plane Displacement ◽  
Stress Free Boundary ◽  
Transverse Normal Strain

A refined sinusoidal model considering transverse normal strain has been developed for thermoelastic analysis of functionally graded material plate. Although transverse normal strain has been considered, the additional displacement parameters are not increased as transverse normal strain only includes the thermal expansion coefficient and thermal loading. Moreover, the merit of the previous sinusoidal model satisfying tangential stress-free boundary conditions on the surfaces can be maintained. It is important that the effects of transverse normal thermal deformation are incorporated in the in-plane displacement field, which can actively influence the accuracy of in-plane stresses. To assess the performance of the proposed model, the thermoelastic behaviors of functionally graded material plates with various configurations have been analyzed. Without increase of displacement variables, accuracy of the proposed model can be significantly improved by comparing to the previous sinusoidal model. Agreement between the present results and quasi-dimensional solutions are very good, and the proposed model only includes the five displacement variables which can illustrate the accuracy and effectiveness of the present model. In addition, new results using several models considered in this paper have been presented, which can serve as a reference for future investigations.

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