Free Vibrations of Fluid-Conveying Cylindrical Shells

1974 ◽  
Vol 96 (2) ◽  
pp. 420-426 ◽  
Author(s):  
S. S. Chen ◽  
G. S. Rosenberg
Keyword(s):  
Potential Flow ◽  
Cylindrical Shells ◽  
Low Frequency ◽  
Free Vibrations ◽  
Frequency Equation ◽  
Frequency Range ◽  
Frequency Spectra ◽  
Flowing Fluid ◽  
Shell Motion ◽  
Conveying Fluid

This paper treats the free vibrations of cylindrical shells conveying fluid. The shell motion is described by the Flu¨gge’s equations, whereas the hydrodynamic forces are described by the linearized potential flow theory. Frequency spectra are presented for symmetric and asymmetric modes and the effects of flow velocity and other parameters are discussed. In the low-frequency range, a modified water-hammer theory and an approximate bending frequency equation including the effect of the flowing fluid are developed.

Geometrically Nonlinear Forced Vibrations of Circular Cylindrical Shells Containing Flowing Fluid

2000 ◽  
Author(s):  
F. Pellicano ◽  
M. Amabili ◽  
M. P. Païdoussis
Keyword(s):  
Stochastic Dynamics ◽  
Cylindrical Shells ◽  
Harmonic Excitation ◽  
Linear Potential ◽  
Stochastic Motion ◽  
Flowing Fluid ◽  
Periodic Response ◽  
Shell Motion ◽  
Circular Cylindrical Shells ◽  
Flow Velocities

Abstract The response of a shell conveying fluid to harmonic excitation, in the spectral neighbourhood of one of the lowest natural frequencies, is investigated for different flow velocities. Nonlinearities due to moderately large amplitude shell motion are considered by using the nonlinear Donnell shallow shell theory. Linear potential flow theory is applied to describe the fluid-structure interaction by using the model proposed by Païdoussis and Denise. For different amplitude and frequency of the excitation and for different flow velocities, the following are investigated numerically: (i) periodic response of the system; (ii) unsteady and stochastic motion; (iii) loss of stability by jumps to bifurcated branches. The effect of the flow velocity on the nonlinear periodic response of the system has also been investigated. Poincaré maps and bifurcation diagrams are used to study the unsteady and stochastic dynamics of the system. Amplitude-modulated motions, multi-periodic solutions, chaotic responses and the so-called “blue sky catastrophe” phenomenon have been observed for different values of the system parameters; the latter two have been predicted here probably for the first time for the dynamics of circular cylindrical shells.

Characteristics of Modal Sound Radiation of Finite Cylindrical Shells

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Tian Ran Lin ◽  
Chris Mechefske ◽  
Peter O’Shea
Keyword(s):  
Cylindrical Shells ◽  
Low Frequency ◽  
Sound Radiation ◽  
Sound Field ◽  
Radiation Efficiency ◽  
Boundary Element Methods ◽  
Frequency Range ◽  
Nodal Lines ◽  
Infinite Cylindrical Shell ◽  
Modal Index

Characteristics of modal sound radiation of finite cylindrical shells are studied using finite element and boundary element methods in this paper. In the low frequency range, modal radiation efficiencies of finite cylindrical shells are found to asymptotically approach those of the corresponding infinite cylindrical shell when structural trace wavelengths of the cylindrical shells are greater than the acoustic wavelength. Modal radiation efficiencies for each group of modes having the same circumferential modal index decrease as the axial modal index increases. They converge to each other when the axial trace wavelength is much greater than the circumferential trace wavelength. The mechanism leading to lower radiation efficiency of modes with higher circumferential modal index of short cylinders is explained. Similar to those of flat plate panels, change in slope or waviness is observed in modal radiation efficiency curves of modes with higher order axial modal index at medium frequencies. This is attributed to the interference of sound radiated by neighboring vibrating cells when the distance between nodal lines of a vibrating mode is in the same order or smaller than the acoustic wavelength. The effects of the internal sound field on modal radiation efficiencies of a finite open-end cylinder are discussed.

Theoretical Analysis of Free Vibrations Based on a New High Order Shell Theory for Cylindrical Shells Conveying Fluid

2017 ◽  
Author(s):  
Ming Ji ◽  
Kazuaki Inaba
Keyword(s):  
Boundary Conditions ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Fluid Pressure ◽  
Free Vibrations ◽  
High Order ◽  
Out Of Plane ◽  
Conveying Fluid

The natural frequencies of free vibrations for thick cylindrical shells with clamped-clamped ends conveying fluid are investigated. Equations of motion and boundary conditions are derived by Hamilton’s principle based on the new high order shell theory. The hydrodynamic force is derived from the linearized potential flow theory. Besides, fluid pressure acting on the shell wall is gotten by the assumption of non-penetration condition. The out-of-plane and in-plane vibrations are coupled together due to the existence of fluid-solid-interaction (FSI). Under the assumption of harmonic motion, the dispersion relationships are presented. Using the method of frequency sweeping, the natural frequencies of symmetric modes and asymmetric modes corresponding to each flow velocity are found by satisfying the dispersion relationship equations and boundary conditions. Several numerical examples with different flow velocities and thickness are presented compared with previous thin shell theory and FEM results and show reasonable agreement. The effects of thickness are discussed.

Some measurements in the self-preserving jet

1969 ◽  
Vol 38 (3) ◽  
pp. 577-612 ◽  
Author(s):  
I. Wygnanski ◽  
H. Fiedler
Keyword(s):  
Low Frequency ◽  
Convection Velocity ◽  
Hot Wire ◽  
Frequency Range ◽  
Mean Velocity ◽  
Frequency Spectra ◽  
Velocity Fluctuations ◽  
Taylor’S Hypothesis ◽  
Velocity Turbulence ◽  
Made In

The axisymmetric turbulent incompressible and isothermal jet was investigated by use of linearized constant-temperature hot-wire anemometers. It was established that the jet was truly self-preserving some 70 diameters downstream of the nozzle and most of the measurements were made in excess of this distance. The quantities measured include mean velocity, turbulence stresses, intermittency, skewness and flatness factors, correlations, scales, low-frequency spectra and convection velocity. The r.m.s. values of the various velocity fluctuations differ from those measured previously as a result of lack of self-preservation and insufficient frequency range in the instrumentation of the previous investigations. It appears that Taylor's hypothesis is not applicable to this flow, but the use of convection velocity of the appropriate scale for the transformation from temporal to spatial quantities appears appropriate. The energy balance was calculated from the various measured quantities and the result is quite different from the recent measurements of Sami (1967), which were obtained twenty diameters downstream from the nozzle. In light of these measurements some previous hypotheses about the turbulent structure and the transport phenomena are discussed. Some of the quantities were obtained by two or more different methods, and their relative merits and accuracy are assessed.

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.

On the Equivalence of Dispersion Relations Resulting from Rayleigh-Lamb Frequency Equation and the Operator Plate Model

2001 ◽  
Vol 123 (4) ◽  
pp. 417-420 ◽  
Author(s):  
Nikolay A. Losin
Keyword(s):  
Velocity Dispersion ◽  
Free Vibrations ◽  
Frequency Equation ◽  
Dispersion Relations ◽  
Plate Model ◽  
Elastic Plates ◽  
Flexural Waves ◽  
Frequency Spectra ◽  
Infinite Power ◽  
Antisymmetric Vibrations

The Rayleigh-Lamb frequency equations for the free vibrations of an infinite isotropic elastic plate are expanded into the infinite power series and reduced to the polynomial frequency and velocity dispersion relations. The latter are compared to those of the operator plate model developed in [Losin, N. A., 1997, “Asymptotics of Flexural Waves in Isotropic Elastic Plates,” ASME J. Appl. Mech., 64, No. 2, pp. 336–342; Losin, N. A., 1998, “Asymptotics of Extensional Waves in Isotropic Elastic Plates,” ASME J. Appl. Mech., 65, No. 4, pp. 1042–1047] for both symmetric and antisymmetric vibrations. As a result of comparative analysis, the equivalence of the corresponding dispersion polynomials is established. The frequency spectra, generated by Rayleigh-Lamb equations, are illustrated graphically and briefly discussed with reference to those published in [Potter, D. S., and Leedham, C. D., 1967, “Normalized Numerical Solution for Rayleigh’s Frequency Equation,” J. Acoust. Soc. Am., 41, No. 1, pp. 148–153].

scholarly journals How well are FREQUENCY SENSITIVITIES OF grasshopper ears tuned to species-specific song spectra?

1996 ◽  
Vol 199 (7) ◽  
pp. 1631-1642
Author(s):  
J Meyer ◽  
N Elsner
Keyword(s):  
High Frequency ◽  
Broad Band ◽  
Low Frequency ◽  
Attachment Site ◽  
The Body ◽  
Frequency Range ◽  
Frequency Spectra ◽  
Interspecific Differences ◽  
Tympanal Membrane ◽  
Species Specific

Grasshoppers of 20 acridid species were examined using spectral analysis, laser vibrometry and electrophysiology to determine whether the song spectra, the best frequencies of tympanal-membrane vibrations and the threshold curves of the tympanal nerves are adapted to one another. The songs of almost all species have a relatively broad-band maximum in the region between 20 and 40 kHz and a narrower peak between 5 and 15 kHz. There are clear interspecific differences in the latter, which are not correlated with the length of the body or of the elytra. At the site of attachment of the low-frequency receptors (a-cells), the tympanal membrane oscillates with maximal amplitude in the region from 5 to 10 kHz. At the attachment site of the high-frequency receptors (d-cells), there is also a maximum in this region as well as another around 15-20 kHz. The tympanal nerve is most sensitive to tones between 5 and 10 kHz, with another sensitivity maximum between 25 and 35 kHz. The species may differ from one another in the position of the low-frequency peaks of the membrane oscillation, of the nerve activity and of the song spectra. No correlation was found between the characteristic frequency of the membrane oscillation and the area of the tympanal membrane. Within a given species, the frequency for maximal oscillation of the membrane at the attachment site of the low-frequency receptors and the frequency for maximal sensitivity of the tympanal nerve are in most cases very close to the low-frequency peak in the song spectrum. In the high-frequency range, the situation is different: here, the position of the peak in the song spectrum is not correlated with the membrane oscillation maximum at the attachment site of the high-frequency receptors, although there is a correlation between the song spectrum and the sensitivity of the tympanal nerve. On the whole, therefore, hearing in acridid grasshoppers is quite well adjusted to the frequency spectra of the songs, partly because the tympanal membrane acts as a frequency filter in the low-frequency range.

Free and Forced Vibrations of an Infinitely Long Cylindrical Shell in an Infinite Acoustic Medium

1954 ◽  
Vol 21 (2) ◽  
pp. 167-177
Author(s):  
H. H. Bleich ◽  
M. L. Baron
Keyword(s):  
Surrounding Medium ◽  
Low Frequency ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
Acoustic Medium ◽  
Frequency Range ◽  
Stiffened Shells ◽  
Free And Forced Vibrations ◽  
Water Tables ◽  
Radial Forces

Abstract The paper presents a general method for the treatment of free and forced-vibration problems of infinitely long thin cylindrical shells. Surprisingly simple results are obtained by utilizing the known and tabulated modes of the shell in vacuo as generalized co-ordinates describing the response of the shell. The frequencies of free vibrations of submerged shells are obtained, and the response of the shell and medium to sinusoidally distributed, periodic, radial forces is determined. The results indicate that there is a low-frequency range where no radiation occurs and a high-frequency range where energy is radiated. Free vibration, or resonance in the case of forced vibrations, occurs only in the low-frequency range. The results of the paper may be applied to obtain the response to arbitrarily distributed, periodic, or nonperiodic forces by expanding such forces in Fourier series and/or integrals. The results for free and forced vibrations are discussed in general and for the specific case of steel shells in water. Tables are provided to facilitate numerical computations. With limitations the method is also applicable to ring-stiffened shells, and to the case of a static pressure in the surrounding medium.

scholarly journals Radio synchrotron spectra of star-forming galaxies

2018 ◽  
Vol 611 ◽  
pp. A55 ◽  
Author(s):  
U. Klein ◽  
U. Lisenfeld ◽  
S. Verley
Keyword(s):  
Supernova Remnants ◽  
Thermal Flux ◽  
Low Frequency ◽  
Cosmic Ray ◽  
Power Laws ◽  
Radio Continuum ◽  
Frequency Range ◽  
Frequency Spectra ◽  
Star Forming ◽  
Simple Power

We investigated the radio continuum spectra of 14 star-forming galaxies by fitting nonthermal (synchrotron) and thermal (free-free) radiation laws. The underlying radio continuum measurements cover a frequency range of ~325 MHz to 24.5 GHz (32 GHz in case of M 82). It turns out that most of these synchrotron spectra are not simple power-laws, but are best represented by a low-frequency spectrum with a mean slope αnth = 0.59 ± 0.20 (Sν ∝ ν−α), and by a break or an exponential decline in the frequency range of 1–12 GHz. Simple power-laws or mildly curved synchrotron spectra lead to unrealistically low thermal flux densities, and/or to strong deviations from the expected optically thin free-free spectra with slope αth = 0.10 in the fits. The break or cutoff energies are in the range of 1.5–7 GeV. We briefly discuss the possible origin of such a cutoff or break. If the low-frequency spectra obtained here reflect the injection spectrum of cosmic-ray electrons, they comply with the mean spectral index of Galactic supernova remnants. A comparison of the fitted thermal flux densities with the (foreground-corrected) Hα fluxes yields the extinction, which increases with metallicity. The fraction of thermal emission is higher than believed hitherto, especially at high frequencies, and is highest in the dwarf galaxies of our sample, which we interpret in terms of a lack of containment in these low-mass systems, or a time effect caused by a very young starburst.

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