Effect of Radial Thickness on the In-Plane Free Vibrations of Circular Annular Discs

1991 ◽  
Vol 113 (4) ◽  
pp. 455-460 ◽  
Author(s):  
R. K. Singal ◽  
K. Williams ◽  
H. Wang
Keyword(s):  
Energy Method ◽  
Three Dimensional ◽  
Free Vibrations ◽  
Theory Of Elasticity ◽  
Experimental Models ◽  
Frequency Equation ◽  
Modes Of Vibration ◽  
Radial Thickness ◽  
Beam Type ◽  
Experimental Values

In this paper the in-plane free vibrations of both thick and thin circular annular discs are studied. The well-known energy method, which is based on the three-dimensional theory of elasticity, is used in the derivation of the frequency equation of the disc. The frequency equation yields all the natural frequencies for all the circumferential modes of vibration, including the breathing and beam-type modes. In order to assess the validity of the analysis experimental data were acquired on several models. The paper first describes briefly the energy method analysis, this is followed by a description of the various experimental models. Finally, the calculated values of frequencies are compared with the experimental values. A very close agreement between both the theoretical and experimental values of the resonant frequencies for all the models was obtained and this validates the energy method of analysis.

A Theoretical and Experimental Study of Vibrations of Thick Circular Cylindrical Shells and Rings

1988 ◽  
Vol 110 (4) ◽  
pp. 533-537 ◽  
Author(s):  
R. K. Singal ◽  
K. Williams
Keyword(s):  
Cylindrical Shells ◽  
Three Dimensional ◽  
Free Vibrations ◽  
Theory Of Elasticity ◽  
Frequency Equation ◽  
Experimental Investigations ◽  
Resonant Frequencies ◽  
Modes Of Vibration ◽  
Circular Cylindrical Shells ◽  
Experimental Values

The free vibrations of thick circular cylindrical shells and rings are discussed in this paper. The well-known energy method, which is based on the three-dimensional theory of elasticity, is used in the derivation of the frequency equation of the shell. The frequency equation yields resonant frequencies for all the circumferential modes of vibration, including the breathing and beam-type modes. Experimental investigations were carried out on several models in order to assess the validity of the analysis. This paper first describes briefly the method of analysis. In the end, the calculated frequencies are compared with the experimental values. A very close agreement between the theoretical and experimental values of the resonant frequencies for all the models was obtained and this validates the method of analysis.

Free Vibrations of Constrained Beams

1952 ◽  
Vol 19 (4) ◽  
pp. 471-477
Author(s):  
Winston F. Z. Lee ◽  
Edward Saibel
Keyword(s):  
Natural Frequencies ◽  
Degree Of Approximation ◽  
Free Vibrations ◽  
Frequency Equation ◽  
Continuous Beam ◽  
Concentrated Mass ◽  
Simple Manner ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
Rigid Supports

Abstract A general expression is developed from which the frequency equation for the vibration of a constrained beam with any combination of intermediate elastic or rigid supports, concentrated masses, and sprung masses can be found readily. The method also is extended to the case where the constraint is a continuous elastic foundation or uniformly distributed load of any length. This method requires only the knowledge of the natural frequencies and natural modes of the beam supported at the ends in the same manner as the constrained beam but not subjected to any of the constraints between the ends. The frequency equation is obtained easily and can be solved to any desired degree of approximation for any number of modes of vibration in a quick and simple manner. Numerical examples are given for a beam with one concentrated mass, for a beam with one sprung mass, and a continuous beam with one sprung mass.

scholarly journals Flexural vibrations of the walls of thin cylindrical shells having freely supported ends

1949 ◽  
Vol 197 (1049) ◽  
pp. 238-256 ◽  
Keyword(s):  
Experimental Investigation ◽  
Natural Frequency ◽  
Energy Method ◽  
Natural Frequencies ◽  
Frequency Equation ◽  
Diameter Ratio ◽  
Frequency Range ◽  
Thin Cylinder ◽  
Nodal Pattern ◽  
Modes Of Vibration

The paper deals with the general equations for the vibration of thin cylinders and a theoretical and experimental investigation is made of the type of vibration usually associated with bells. The cylinders are supported in such a manner that the ends remain circular without directional restraint being imposed. It is found that the complexity of the mode of vibration bears little relation to the natural frequency; for example, cylinders of very small thicknessdiameter ratio, with length about equal to or less than the diameter, may have many of their higher frequencies associated with the simpler modes of vibration. The frequency equation which is derived by the energy method is based on strain relations given by Timoshenko. In this approach, displacement equations are evolved which are comparable to those of Love and Flugge, though differences are evident due to the strain expressions used by each author. Results are given for cylinders of various lengths, each with the same thickness-diameter ratio, and also for a very thin cylinder in which the simpler modes of vibration occur in the higher frequency range. It is shown that there are three possible natural frequencies for a particular nodal pattern, two of these normally occurring beyond the aural range.

Elastic Waves in Generalized Thermo-Piezoelectric Transversely Isotropic Circular Bar Immersed in Fluid

2015 ◽  
Vol 8 (1) ◽  
pp. 82-103
Author(s):  
Palaniyandi Ponnusamy
Keyword(s):  
Classical Theory ◽  
Cross Sections ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Coupled System ◽  
Theory Of Elasticity ◽  
Inviscid Fluid ◽  
Displacement Potential ◽  
Modes Of Vibration

AbstractIn this paper, a mathematical model is developed to study the wave propagation in an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of circular cross-sections immersed in inviscid fluid. The present study is based on the use of the three-dimensional theory of elasticity. Three displacement potential functions are introduced to uncouple the equations of motion and the heat and electric conductions. The frequency equations are obtained for longitudinal and flexural modes of vibration and are studied based on Lord-Shulman, Green-Lindsay and Classical theory theories of thermo elasticity. The frequency equations of the coupled system consisting of cylinder and fluid are developed under the assumption of perfect-slip boundary conditions at the fluid-solid interfaces, which are obtained for longitudinal and flexural modes of vibration and are studied numerically for PZT-4 material bar immersed in fluid. The computed non-dimensional frequencies are compared with Lord-Shulman, Green-Lindsay and Classical theory theories of thermo elasticity for longitudinal and flexural modes of vibrations. The dispersion curves are drawn for longitudinal and flexural modes of vibrations. Moreover, the dispersion of specific loss and damping factors are also analyzed for longitudinal and flexural modes of vibrations.

scholarly journals Analytic solutions for free vibration analysis of laminated beams in three-dimensional statement

2019 ◽  
Vol 221 ◽  
pp. 01012 ◽  
Author(s):  
Sergey Golushko ◽  
Gleb Gorynin ◽  
Arseniy Gorynin
Keyword(s):  
Splitting Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Analytic Solutions ◽  
Free Vibrations ◽  
Theory Of Elasticity ◽  
Laminated Beams ◽  
Asymptotic Splitting ◽  
Euler Bernoulli Beam

In this research we consider free vibrations of laminated beams in terms of three-dimensional linear theory of elasticity. Analytic solutions for natural frequencies of laminated beams are obtained by using an asymptotic splitting method. The results were compared with classical Euler“Bernoulli beam theory and Timoshenko beam theory.

Vibration of Thick Circular Disks and Shells of Revolution

2003 ◽  
Vol 70 (2) ◽  
pp. 292-298 ◽  
Author(s):  
A. V. Singh ◽  
L. Subramaniam
Keyword(s):  
Cross Section ◽  
Three Dimensional ◽  
Free Vibrations ◽  
Theory Of Elasticity ◽  
Published Data ◽  
Axially Symmetric ◽  
Shells Of Revolution ◽  
Displacement Fields ◽  
Wide Range ◽  
Circular Disks

A fully numerical and consistent method using the three-dimensional theory of elasticity is presented in this paper to study the free vibrations of an axially symmetric solid. The solid is defined in the cylindrical coordinates r,θ,z by a quadrilateral cross section in the r-z plane bounded by four straight and/or curved edges. The cross section is then mapped using the natural coordinates (ξ,η) to simplify the mathematics of the problem. The displacement fields are expressed in terms of the product of two simple algebraic polynomials in ξ and η, respectively. Boundary conditions are enforced in the later part of the solution by simply controlling coefficients of the polynomials. The procedure setup in this paper is such that it was possible to investigate the free axisymmetric and asymmetric vibrations of a wide range of problems, namely; circular disks, cylinders, cones, and spheres with considerable success. The numerical cases include circular disks of uniform as well as varying thickness, conical/cylindrical shells and finally a spherical shell of uniform thickness. Convergence study is also done to examine the accuracy of the results rendered by the present method. The results are compared with the finite element method using the eight-node isoparametric element for the solids of revolution and published data by other researchers.

Propagation of Harmonic Waves in Orthotropic Circular Cylindrical Shells

1973 ◽  
Vol 40 (1) ◽  
pp. 168-174 ◽  
Author(s):  
A. E. Armena`kas ◽  
E. S. Reitz
Keyword(s):  
Shell Theory ◽  
Cylindrical Shells ◽  
Three Dimensional ◽  
Longitudinal Shear ◽  
Theory Of Elasticity ◽  
Frequency Equation ◽  
Radial Coordinate ◽  
Harmonic Waves ◽  
Circular Cylindrical Shells ◽  
General Frequency

In this investigation, the general frequency equation for trains of harmonic waves having an arbitrary number of circumferential nodes, traveling in orthotropic, circular, cylindrical shells is established on the basis of the three-dimensional linear theory of elasticity, by expanding the displacement components in power series of the radial coordinate. Simpler forms of the frequency equation for axisymmetric nontorsional and torsional motion and for longitudinal-shear and plane-strain motion are established and discussed. The frequency equation has been evaluated numerically on an IBM 360/50 digital computer system and the numerical results are compared with those obtained on the basis of an approximate shell theory.

Epithelial Organotypic Cultures: A Viable Model to Address Mechanisms of Carcinogenesis by Epitheliotropic Viruses

2018 ◽  
Vol 18 (4) ◽  
pp. 246-255 ◽  
Author(s):  
Lara Termini ◽  
Enrique Boccardo
Keyword(s):  
Three Dimensional ◽  
Cell Types ◽  
Experimental Models ◽  
Biological Research ◽  
Specific Gene ◽  
Specific Cell ◽  
Organotypic Cultures ◽  
Skin Physiology

In vitro culture of primary or established cell lines is one of the leading techniques in many areas of basic biological research. The use of pure or highly enriched cultures of specific cell types obtained from different tissues and genetics backgrounds has greatly contributed to our current understanding of normal and pathological cellular processes. Cells in culture are easily propagated generating an almost endless source of material for experimentation. Besides, they can be manipulated to achieve gene silencing, gene overexpression and genome editing turning possible the dissection of specific gene functions and signaling pathways. However, monolayer and suspension cultures of cells do not reproduce the cell type diversity, cell-cell contacts, cell-matrix interactions and differentiation pathways typical of the three-dimensional environment of tissues and organs from where they were originated. Therefore, different experimental animal models have been developed and applied to address these and other complex issues in vivo. However, these systems are costly and time consuming. Most importantly the use of animals in scientific research poses moral and ethical concerns facing a steadily increasing opposition from different sectors of the society. Therefore, there is an urgent need for the development of alternative in vitro experimental models that accurately reproduce the events observed in vivo to reduce the use of animals. Organotypic cultures combine the flexibility of traditional culture systems with the possibility of culturing different cell types in a 3D environment that reproduces both the structure and the physiology of the parental organ. Here we present a summarized description of the use of epithelial organotypic for the study of skin physiology, human papillomavirus biology and associated tumorigenesis.

scholarly journals Organoids of the female reproductive tract

2021 ◽  
Vol 99 (4) ◽  
pp. 531-553 ◽  
Author(s):  
Cindrilla Chumduri ◽  
Margherita Y. Turco
Keyword(s):  
Reproductive Tract ◽  
Personalised Medicine ◽  
Three Dimensional ◽  
In Vitro Models ◽  
Experimental Models ◽  
Female Reproductive Tract ◽  
Cellular Heterogeneity ◽  
Dynamic Regulation ◽  
Pregnancy And Childbirth

AbstractHealthy functioning of the female reproductive tract (FRT) depends on balanced and dynamic regulation by hormones during the menstrual cycle, pregnancy and childbirth. The mucosal epithelial lining of different regions of the FRT—ovaries, fallopian tubes, uterus, cervix and vagina—facilitates the selective transport of gametes and successful transfer of the zygote to the uterus where it implants and pregnancy takes place. It also prevents pathogen entry. Recent developments in three-dimensional (3D) organoid systems from the FRT now provide crucial experimental models that recapitulate the cellular heterogeneity and physiological, anatomical and functional properties of the organ in vitro. In this review, we summarise the state of the art on organoids generated from different regions of the FRT. We discuss the potential applications of these powerful in vitro models to study normal physiology, fertility, infections, diseases, drug discovery and personalised medicine.

Mathematical Theory of Transversally Isotropic Shells of Arbitrary Thickness at Static Load

2019 ◽  
Vol 968 ◽  
pp. 496-510
Author(s):  
Anatoly Grigorievich Zelensky
Keyword(s):  
Mathematical Theory ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Theory Of Elasticity ◽  
Elastic Plates ◽  
Dimensional Problem ◽  
Boundary Problems ◽  
Complex Boundary ◽  
Plates And Shells ◽  
Basic Equations

Classical and non-classical refined theories of plates and shells, based on various hypotheses [1-7], for a wide class of boundary problems, can not describe with sufficient accuracy the SSS of plates and shells. These are boundary problems in which the plates and shells undergo local and burst loads, have openings, sharp changes in mechanical and geometric parameters (MGP). The problem also applies to such elements of constructions that have a considerable thickness or large gradient of SSS variations. The above theories in such cases yield results that can differ significantly from those obtained in a three-dimensional formulation. According to the logic in such theories, the accuracy of solving boundary problems is limited by accepted hypotheses and it is impossible to improve the accuracy in principle. SSS components are usually depicted in the form of a small number of members. The systems of differential equations (DE) obtained here have basically a low order. On the other hand, the solution of boundary value problems for non-thin elastic plates and shells in a three-dimensional formulation [8] is associated with great mathematical difficulties. Only in limited cases, the three-dimensional problem of the theory of elasticity for plates and shells provides an opportunity to find an analytical solution. The complexity of the solution in the exact three-dimensional formulation is greatly enhanced if complex boundary conditions or physically nonlinear problems are considered. Theories in which hypotheses are not used, and SSS components are depicted in the form of infinite series in transverse coordinates, will be called mathematical. The approximation of the SSS component can be adopted in the form of various lines [9-16], and the construction of a three-dimensional problem to two-dimensional can be accomplished by various methods: projective [9, 14, 16], variational [12, 13, 15, 17]. The effectiveness and accuracy of one or another variant of mathematical theory (MT) depends on the complex methodology for obtaining the basic equations.

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