scholarly journals THE PROBLEM OF THE OSCILLATION OF THE ELASTIC LAYER BOUNDED BY RIGID BOUHDARIES

2018 ◽  
pp. 42-48
Author(s):  
Seitmuratov Angisin ◽  
Tileubay Sarsenkul ◽  
Toxanova Sveta ◽  
Ibragimova Nuraim ◽  
Doszhanov Bayanalui ◽  
...  
Keyword(s):  
Cylindrical Shell ◽  
Phase Velocity ◽  
Elastic Layer ◽  
Direct Relation ◽  
Anisotropic Layer ◽  
Harmonic Oscillations ◽  
Natural Oscillations ◽  
Integral Transformations ◽  
Oscillation Frequencies ◽  
Rotational Shear

In the case of harmonic oscillations of a cylindrical shell, the phase velocity is expressed in terms of the frequency of natural oscillations freely supported along the edges of the shell, and therefore, the study of waves in plane and circular elements has the most direct relation to the problem of determining its own forms and oscillation frequencies shells finite length. Below let us consider some problems of oscillation of an elastic layer bounded by rigid boundaries under the influence of a normal or rotational shear stress. The solutions of the problems under consideration are obtained by using integral transformations by the coordinate. Key words: harmonic oscillations, cylindrical shells, phase velocity, frequency, eigenvibrations, Bessel function, wave, anisotropic, layer.

scholarly journals Phase Velocity and Attenuation of Longitudinal Shear Vibrations of Hollow Poroelastic Cylinders

2014 ◽  
Vol 19 (2) ◽  
pp. 337-346
Author(s):  
S. Ahmed Shah ◽  
S. Javvad Hussaini
Keyword(s):  
Cylindrical Shell ◽  
Phase Velocity ◽  
Longitudinal Shear ◽  
Frequency Equation ◽  
Circular Cylinders ◽  
Physical Parameters ◽  
Flexural Mode ◽  
Second Mode ◽  
Phase Velocity And Attenuation ◽  
Frequency Phase

Abstract The present paper is devoted to the study of phase velocity and attenuation of longitudinal shear vibrations of hollow poroelastic circular cylinders in the presence of dissipation. The explicit expressions for phase velocity and attenuation of longitudinal shear vibrations are derived. The frequency equation of longitudinal shear vibrations and modes obtained in a previous paper are used to compute the phase velocity and attenuation for different dissipations for thin and thick poroelastic cylindrical shells and poroelastic solid cylinder. The physical parameters of sandstone saturated with kerosene and sandstone saturated with water are used for the purpose of computation. It is found that the phase velocity is linear beyond certain frequency. Phase velocity is smaller for a typical anti-symmetric mode compared to the flexural mode. It is greater for the second mode than that of the first mode. Also the phase velocity is larger for a thin poroelastic cylindrical shell than that of a thick poroelastic cylindrical shell. The same is true for attenuation also. Attenuation is very high for the considered dissipations and it increases with the increase in dissipation.

scholarly journals Rotational shear effects on edge harmonic oscillations in DIII-D quiescent H-mode discharges

2016 ◽  
Vol 56 (7) ◽  
pp. 076011 ◽  
Author(s):  
Xi Chen ◽  
K.H. Burrell ◽  
N.M. Ferraro ◽  
T.H. Osborne ◽  
M.E. Austin ◽  
...  
Keyword(s):  
Harmonic Oscillations ◽  
Shear Effects ◽  
Rotational Shear

scholarly journals Elastic Stability Analysis of a Two-Layered Functionally Graded Cylindrical Shell under Axial Compression with the use of Energy Approach

2009 ◽  
Vol 18 (6) ◽  
pp. 096369350901800 ◽  
Author(s):  
H. Sepiani ◽  
A. Rastgoo ◽  
M. Ahmadi ◽  
A.Ghorbanpour Arani ◽  
K. Sepanloo
Keyword(s):  
Cylindrical Shell ◽  
Potential Energy ◽  
Axial Compression ◽  
Elastic Layer ◽  
Elastic Stability ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Minimum Potential Energy ◽  
Equilibrium Equations ◽  
Minimum Potential

This paper investigates the elastic axisymmetric buckling of a thin, simply supported functionally graded (FG) cylindrical shell embedded with an elastic layer under axial compression. The analysis is based on energy method and simplified nonlinear strain-displacement relations for axial compression. Material properties of functionally graded cylindrical shell are considered graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. Using minimum potential energy together with Euler equations, equilibrium equations are obtained. Consequently, stability equation of functionally graded cylindrical shell with an elastic layer is acquired by means of minimum potential energy theory and Trefftz criteria. Another analysis is made using the equivalent properties of FG material. Numerical results for stainless steel-ceramic cylindrical shell and aluminum layer are obtained and critical load curves are analyzed for a cylindrical shell with an elastic layer. A comparison is made to the results in the literature. The results show that the elastic stability of functionally graded cylindrical shell with an elastic layer is dependent on the material composition and FGM index factor, and the shell geometry parameters and it is concluded that the application of an elastic layer increases elastic stability and significantly reduces the weight of cylindrical shells.

Group velocity of wave propagation in carbon nanotubes

2008 ◽  
Vol 464 (2094) ◽  
pp. 1423-1438 ◽  
Author(s):  
Lifeng Wang ◽  
Wanlin Guo ◽  
Haiyan Hu
Keyword(s):  
Carbon Nanotubes ◽  
Cylindrical Shell ◽  
Dispersion Relation ◽  
Phase Velocity ◽  
Group Velocity ◽  
Continuum Mechanics ◽  
Flexural Wave ◽  
Multi Walled Carbon Nanotubes ◽  
Non Local ◽  
Walled Carbon Nanotubes

The group velocities of longitudinal and flexural wave propagations in single- and multi-walled carbon nanotubes are studied in the frame of continuum mechanics. The dispersion relations between the group velocity and the wavenumber for flexural and longitudinal waves, described by a beam model and a cylindrical shell model, are established for both single- and multi-walled carbon nanotubes. The effect of microstructures in carbon nanotubes on the wave dispersion is revealed through the non-local elastic models of a beam and a cylindrical shell, including the second-order gradient of strain and a parameter of microstructure. It is shown that the microstructures in the carbon nanotubes play an important role in the dispersion of both longitudinal and flexural waves. In addition, the non-local elastic models predict that the cut-off wavenumber of the dispersion relation between the group velocity and the wavenumber is approximately 2×10 10  m −1 for the longitudinal and flexural wave propagations in both single- and multi-walled carbon nanotubes. This may explain why the direct molecular dynamics simulation cannot give a proper dispersion relation between the phase velocity and the wavenumber when the wavenumber approaches approximately 2×10 10  m −1 , much lower than the cut-off wavenumber for the dispersion relation between the phase velocity and the wavenumber predicted by continuum mechanics.

scholarly journals AN ELECTROMAGNETIC METHOD FOR FREQUENCY ANALYSIS OF TRANSVERSE VIBRATIONS OF A BEAM

2020 ◽  
pp. 112-120
Author(s):  
F.Yu. Kuznetsov ◽  
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Frequency Analysis ◽  
Natural Oscillation ◽  
Theoretical Description ◽  
Natural Oscillations ◽  
Technical Procedure ◽  
Transverse Vibrations ◽  
Sample Testing ◽  
Oscillation Frequencies

Vibration-based diagnostics of constructions is an obligatory technical procedure in mechanical engineering. In this regard, there is a problem of an adequate theoretical description of vibration processes in various structures with account for end fixity conditions, as well as the creation of experimental facilities for non-contact testing. The paper presents a theoretical basis and experimental verification results for a method of electromagnetic frequency analysis of rod systems. The essence of the method is the experimental determination of natural oscillation frequencies and their comparison with reference values. The main attention is paid to a theoretical description of transverse vibrations of a cantilever conductive rod in an external magnetic field in order to determine reference frequencies of a defect-free sample. The presence of the external magnetic field gives rise to the distributed electromagnetic force exerted on the rod. In the case of natural oscillations, the magnetic force is damping, which leads to a change in damping factors of partial oscillations. The electromagnetic effect is selective towards vibrational modes; hence, the damping factors of various partial oscillations of the rod vary to different degrees. This fact allows one to determine an optimal location of the area with acting magnetic field, as well as its width when measuring a given frequency of sample testing. The proposed method has several advantages: indestructibility of the sample, non-contact measurements, invariability of mechanical properties of the sample during the tests.

scholarly journals Investigation of the Influence of a Cavity Type Defect on the Frequencies of the Natural Rail Oscillations by the Radar Method

2019 ◽  
pp. 1006-1012
Author(s):  
Vadim S. Potylitsyn ◽  
Danil S. Kudinov ◽  
Ekaterina A. Kokhonkova
Keyword(s):  
Doppler Radar ◽  
Natural Oscillation ◽  
Rolling Stock ◽  
Destructive Testing ◽  
Natural Oscillations ◽  
Type Defect ◽  
Radar Method ◽  
Impulse Load ◽  
Oscillation Frequencies ◽  
Non Destructive

Currently, the problem of non-destructive testing of rail lashes or rolling stock is quite acute, as the demands of both speed characteristics and vehicle safety increase every year. Thus, the purpose of this study was to determine the possibility of recording frequencies of natural oscillations by the radar method for rail lashes and the influence of the dimensions of the cavity-type defect. For this purpose, a laboratory bench was created with a standard rail, the length of 1.19 m of the P-65 brand, in which free oscillations were excited using a shock impulse load. Measurements of natural oscillation frequencies of the rail were recorded on a 24-bit ADC and a specialized accelerometer ZETLAB BC110. To register the oscillations, a Doppler radar with a frequency of 10 GHz was used, which was installed at the focus of a parabolic mirror offset antenna with a 1.6-meter diameter. It was found that a “field” defect shifts the frequency mode of oscillation 750 Hz upwards. It is shown that the hole in the rail neck with a diameter of 10 mm makes a change in the frequency of about 14 Hz

Evaluation of the Composite Barrier Natural Oscillations Influence on the Generated Shock Loading

2021 ◽  
pp. 103-113
Author(s):  
A.S. Borozenets ◽  
A.V. Proskurin ◽  
A.V. Shlishevskiy
Keyword(s):  
Test Object ◽  
Shock Loading ◽  
Natural Oscillation ◽  
Operating Conditions ◽  
Signal Spectrum ◽  
Natural Oscillations ◽  
Shock Loads ◽  
Frequency Determination ◽  
Prefabricated Structure ◽  
Oscillation Frequencies

The problem of studying behavior of various structures under the influence of intense impulsive (shock) loads arising during operation of many modern facilities, machines and devices remains relevant for many years. Shock loading in laboratory conditions is generated due to interaction between the test object and the braking device (barrier). In this case, braking device or barrier could be a one-piece or a prefabricated structure. If the braking device (barrier) dimensions commensurate with the test object, the braking device natural oscillation frequencies excited during interaction between the test object and the braking device (barrier) could be found in the range of the test object natural oscillation frequencies. Frequency determination within the signal spectrum registered on the test object and caused by oscillations of the braking device (barrier) or test equipment, would assist in better assessing the test object shock loading and its compliance with real operating conditions

scholarly journals OSCILLATIONS OF SPHERICAL AND CYLINDRICAL SHELLS

2001 ◽  
Vol 15 (23) ◽  
pp. 3099-3105 ◽  
Author(s):  
SERKAN ERDIN ◽  
VALERYC L. POKROVSKY
Keyword(s):  
Cylindrical Shell ◽  
Infinite Number ◽  
Cylindrical Shells ◽  
Complete Spectrum ◽  
Harmonic Oscillations ◽  
Dependent Part ◽  
Goldstone Modes

We have found the complete spectrum and eigenstates for harmonic oscillations of ideal spherical and cylindrical shells, both being infinetely thin. The spectrum of the cylindrical shell has an infinite number of Goldstone modes corresponding to folding deformations. This infrared catastrophe is overcome by accounting for curvature-dependent part of energy.

RESULTS OF STUDIES OF OPERATION OF SPECIAL IMPEDANCE TRANSDUCERS ON THE RIGID METAL STRUCTURES OF REAL PRODUCED OBJECTS

2020 ◽  
pp. 44-49
Author(s):  
A. A. Arcentiev ◽  
A. M. Konovalov ◽  
V. I. Kugushev ◽  
S. S. Khudyakov
Keyword(s):  
Cooling System ◽  
Aggressive Medium ◽  
Non Destructive Testing ◽  
Destructive Testing ◽  
Natural Oscillations ◽  
Energy Redistribution ◽  
Metal Structures ◽  
Mechanical Filter ◽  
Oscillation Frequencies ◽  
Non Destructive

The paper presents the studies of capabilities of special impedance transducers with mechanical filter of oscillation frequencies at the input (output) as a tool of non-destructive testing of real produced objects. Objects under test were elements of a power reactor, which are exposed to high temperature aggressive medium and which are inaccessible for direct contact because of the cooling system. The use of special transducers allowed the development of a new method, which used natural oscillations of the object under test and, thus, provided a mean for monitoring of inaccessible elements of the structure. The method is based on fixation of energy redistribution by the modes of natural oscillations of the object under test, when exposed to damping factors caused by cracks, erosion and other defects. It is shown, how this method operates, when using an artificial damper and in presence of real defects. The use of the artificial damper made it possible to determine that this method allowed the non-destructive testing over the entire surface of the monitored element of the structure.

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