scholarly journals VIBRATIONS REINFORCED BY LONGITUDINAL RIBS OF AN INHOMOGENEOUS ORTHOTROPIC CYLINDRICAL PANEL CONTACTING WITH A VISCOUS-ELASTIC MEDIUM

2020 ◽  
Vol 2 (32) ◽  
pp. 144-155
Author(s):  
A.H. Movsumova
Keyword(s):  
Variational Principle ◽  
Elastic Medium ◽  
Cylindrical Panel ◽  
Frequency Equation ◽  
Geometric Parameters ◽  
Vibration Frequencies ◽  
Viscoelastic Foundation ◽  
Longitudinal Ribs

Vibrations of an orthotropic cylindrical panel, non-uniform in thickness, supported by longitudinal ribs, lying on a linearly viscoelastic foundation, were investigated. The Hamilton – Ostrogradsky variational principle was used to find the vibration frequencies of the panel. A frequency equation is constructed, its roots are found, and the influence of physical and geometric parameters characterizing the system is studied.

scholarly journals The effect of an enclosed air cavity on a rectangular drum

1983 ◽  
Vol 24 (3) ◽  
pp. 343-349 ◽  
Author(s):  
H. P. W. Gottlieb
Keyword(s):  
Green’S Function ◽  
Frequency Shift ◽  
Green's Function ◽  
Natural Vibration ◽  
Frequency Equation ◽  
Vibration Frequencies ◽  
Air Cavity ◽  
First Order ◽  
Degenerate Mode ◽  
Function Formulation

AbstractThe effect of an enclosed air cavity on the natural vibration frequencies of a rectangular membrane is investigated. The modes specified by an even integer are not affected. For the odd-odd modes, the frequency equation is found via a Green's function formulation and is solved to first order in a parameter representing the effect of the cavity of the rectangular drum. The frequencies are raised, with the fundamental being most affected. In the case of degeneracies, each degenerate mode contributes to the frequency shift, but the degeneracy itself is not broken to first order.

Vibrations of Transversely Isotropic Finite Circular Cylinders

1994 ◽  
Vol 61 (4) ◽  
pp. 964-970 ◽  
Author(s):  
K. T. Chau
Keyword(s):  
Hyperbolic Equations ◽  
Longitudinal Vibration ◽  
Transversely Isotropic ◽  
Frequency Equation ◽  
Circular Cylinders ◽  
Finite Cylinder ◽  
Mode Shapes ◽  
Axisymmetric Vibration ◽  
Vibration Frequencies ◽  
Axisymmetric Mode

This paper investigates the exact frequency equations for all the possible natural vibrations in a transversely isotropic cylinder of finite length. Two wave potentials are used to uncouple the equations of motion; the resulting hyperbolic equations are solved analytically for the vibration frequencies of a finite cylinder with zero shear tractions and zero axial displacement on the end surfaces and with zero tractions on the curved surfaces. In general, the mode shapes and the frequency equations of vibrations depend on both the range of the frequency and the elastic properties of the material. The vibration frequencies for sapphire cylinders are studied as an example. Two limiting cases are also considered: the long bar limit equals the frequency equation for the longitudinal vibration of bars obtained by Morse (1954) and by Lord Rayleigh (1945); and the frequency equation for thin disks (small length/radius ratio) is also obtained. The frequency for the first axisymmetric mode agrees with the experimental observation by Lusher and Hardy (1988) to within one percent. Natural frequencies for the first three longitudinal and circumferential modes are plotted for all cylinder geometries. The lowest frequency always corresponds to the first nonsymmetric mode regardless of the dimension of the cylinder. For axisymmetric vibration modes, numerical plots show that double roots exist in the frequency equations; such doublets were observed experimentally by Booker and Sagar (1971).

scholarly journals Longitudinal Wave in a Thermally Conducting Elastic Medium

2019 ◽  
Vol 8 (4) ◽  
pp. 8769-8771
Keyword(s):  
Temperature Field ◽  
Phase Velocity ◽  
Elastic Medium ◽  
Longitudinal Wave ◽  
Frequency Equation ◽  
Damping Coefficient ◽  
Wave Number ◽  
Longitudinal Wave Propagation ◽  
Thermally Conducting ◽  
Equations Of Motions

The longitudinal wave propagation in a thermally conducting elastic medium has been investigated. Considering the equations of motions of longitudinal wave in displacement and temperature field, the frequency equation has been derived. The dispersion and damping equations have been derived for the propagation of longitudinal wave in four materials i.e Copper, Steel, Aluminum, and Lead. Effect of Phase velocity and damping coefficient are shown graphically. It is found that the increase in wave number results the decrease in Phase velocity and increase in damping coefficient.

scholarly journals Free vibration of a microbeam resting on Pasternak’s foundation via the Green–Naghdi thermoelasticity theory without energy dissipation

2016 ◽  
Vol 35 (4) ◽  
pp. 303-311 ◽  
Author(s):  
Ashraf M Zenkour
Keyword(s):  
Energy Dissipation ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Generalized Thermoelasticity ◽  
Frequency Equation ◽  
Vibration Frequencies ◽  
Simply Supported ◽  
Thermoelasticity Theory ◽  
Foundation Parameters ◽  
Without Energy Dissipation

This article investigates the effect of length-to-thickness ratio and elastic foundation parameters on the natural frequencies of a thermoelastic microbeam resonator. The generalized thermoelasticity theory of Green and Naghdi without energy dissipation is used. The governing frequency equation is given for a simply supported microbeam resting on Winkler–Pasternak elastic foundations. The influences of different parameters are all demonstrated. Natural vibration frequencies are graphically illustrated and some tabulated results are presented for future comparisons.

AXISYMMETRIC VIBRATIONS OF CIRCULAR AND ANNULAR PLATES WITH VARIABLE THICKNESS

2001 ◽  
Vol 01 (02) ◽  
pp. 195-206 ◽  
Author(s):  
M. EISENBERGER ◽  
M. JABAREEN
Keyword(s):  
Exact Solution ◽  
Power Series ◽  
Variable Thickness ◽  
Natural Frequencies ◽  
Plate Thickness ◽  
Frequency Equation ◽  
Axisymmetric Vibration ◽  
Vibration Frequencies ◽  
Annular Plates ◽  
Infinite Power

In this work the exact axisymmetric vibration frequencies of circular and annular variable thickness plates are found. The solution is obtained using the exact element method developed earlier. It allows for the exact solution of problems with general polynomial variation in thickness using infinite power series. The solution is exact up to the accuracy of the computer. The natural frequencies of vibration are found as the solutions of the frequency equation. Normalized values for the natural frequencies are given for linear, parabolic and cubic variations of the plate thickness, for circular and annular plates, with four types of boundary conditions on the inner and outer boundaries.

scholarly journals Asymptotic analysis of natural frequencies of axisymmetric oscillations of orthotropic cylindrical shells in an infinite elastic medium, liquid filled

2019 ◽  
Vol 15 (1) ◽  
pp. 69-74 ◽  
Author(s):  
Famil A Seyfullayev ◽  
Gulnar R Mirzayeva ◽  
Shusha A Kerimova
Keyword(s):  
Asymptotic Analysis ◽  
Elastic Medium ◽  
Asymptotic Method ◽  
Natural Frequencies ◽  
Longitudinal Direction ◽  
Frequency Equation ◽  
Infinite Length ◽  
Dynamic Calculation ◽  
Thin Walled ◽  
Oscillatory Processes

Aim of the research. Free axisymmetric fluctuation of a cylindrical orthotropic cover, the infinite length contacting to the infinite elastic medium and filled with liquid is investigated. Methods. At design of the thin-walled shell designs which are widely applied in aviation, the missile and space equipment and various fields of the industry, an important task is dynamic calculation of the intense deformed condition of these designs. At a research of dynamics of covers it is necessary to determine own frequencies and forms of small fluctuations, and frequencies from the lower part of a range are of the greatest interest. It is supposed that the rigidity of material of a cover is a little more than rigidity of material of the environment. The solution of the equations of movements of the environment is considered in two options. Results. The frequency equation is received. The analysis of frequency and a form of fluctuations of a cover is carried out. The schedule of dependence of frequency of own axisymmetric fluctuations of a system on wave formation in the longitudinal direction is constructed. By means of an asymptotic method the frequency equations of the ridge cylindrical covers filled with liquid are constructed, the approximate frequencies of the equation and simple settlement formulas allowing to find values of the minimum own frequencies of fluctuations of the considered system are received, the forced fluctuations of the supported cover filled with liquid are investigated and defined is amplitude frequency characteristics of the considered oscillatory processes.

Dependence of the frequencies of intermolecular vibrations of associated water molecules upon the size of the association complexes

1970 ◽  
Vol 23 (8) ◽  
pp. 1507 ◽  
Author(s):  
AA Vetrov ◽  
BP Shelyukhaev
Keyword(s):  
Hydrogen Bond ◽  
Hydrogen Bonds ◽  
Geometric Parameters ◽  
Force Constants ◽  
Water Molecules ◽  
Vibration Frequencies ◽  
Intermolecular Vibration ◽  
Intermolecular Vibrations

The intermolecular vibration frequencies for associated water molecules have been calculated by the Elyashevich-Wilson technique. Slight variations of the geometric parameters of the water molecules and hydrogen bridges leave the intermolecular vibration frequencies almost unaffected. The values of these frequencies depend solely upon the force constants of the hydrogen bonds and the angles adjacent to a hydrogen bond. The spectra of associations containing two, three, four, and five water molecules are found to be sufficiently distinct from each other for their differences to be detected by experiment.

The theory of longitudinal vibrations of a conical elastic body in an elastic medium

2016 ◽  
Vol 3 (1) ◽  
pp. 27-35
Author(s):  
V. Bulgakov ◽  
V. Adamchuk ◽  
I. Holovach ◽  
D. Orszaghova
Keyword(s):  
Elastic Medium ◽  
Elastic Body ◽  
Cross Sections ◽  
Ritz Method ◽  
Frequency Equation ◽  
The Body ◽  
Longitudinal Vibrations ◽  
Beet Root ◽  
Analytic Expressions ◽  
Stationary Action

Aim. To elaborate the theory of longitudinal vibrations of a solid elastic body with one fi xed end in the elastic medium. The example of such a body may be found in a sugar beet root in soil, the latter being elastic medium. Methods. The principle of stationary action of Ostrogradsky-Hamilton and the Ritz method were applied in the work. Results. The Ritz method was applied to obtain the Ritz frequency equation for the oscillating process under investigation. The analytic expressions were defi ned to determine the fi rst and second eigenfrequencies of vibration and the amplitude of constrained vibrations of any of its cross-sections. The values of the fi rst and second eigenfrequencies of the elastic body under investigation with specifi c geometric and physical pa- rameters were found. The dependency diagrams for the fi rst and second eigenfrequencies on the coeffi cient of elastic contraction of soil as the elastic medium, and the dependency diagrams for the amplitude of constrained oscillations of the mentioned body on the coeffi cient c of elastic deformation of soil and the distance of the cross-section of the body from the conditional point of fi xation were drawn. The dependency diagrams for the amplitude of constrained oscillations of the elastic body on the change in the amplitude and the frequency of perturbing force were obtained. Conclusions. The impossibility of resonance occurrence was substantiated as the frequency of the perturbing force cannot equal the frequency of eigenvibrations of the elastic body due to technological and technical reasons. It was proven that the breaking of the elastic body is impossible with lon- gitudinal deformations due to the shortness of the amplitude of longitudinal vibrations of the mentioned body.

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