Bending Vibrations of a Pipe Line Containing Flowing Fluid

1952 ◽  
Vol 19 (2) ◽  
pp. 205-208
Author(s):  
G. W. Housner
Keyword(s):  
Dynamic Instability ◽  
Fluid Velocity ◽  
Normal Modes ◽  
Beam Theory ◽  
Free Vibrations ◽  
Bending Vibrations ◽  
Flowing Fluid ◽  
Fluid Velocities ◽  
Modes Of Vibration ◽  
Pipe Line

Abstract Both free vibrations and forced motions due to crosswinds may create important problems in the design of pipe lines supported above ground. An analytic investigation, based on simple beam theory, shows that the flow of fluid in such a pipe line has no beneficial effect upon the vibrations. The fluid velocity causes a dynamic coupling of the simple modes of vibration so that the normal modes of vibration are of complex shape with 90-deg out-of-phase components. The solution is presented for free vibrations and for steady-state forced vibrations, and it is shown that large amplitudes may be developed if the amount of damping is too small. It is shown that at low fluid velocities there is negligible effect upon the vibration of the pipe line, and at a certain high critical velocity the fluid flow causes a dynamic instability. The present analysis revises the conclusions which appeared in an earlier publication.

Bending Vibrations of a Pipe Line Containing Flowing Fluid

1950 ◽  
Vol 17 (3) ◽  
pp. 229-232
Author(s):  
Holt Ashley ◽  
George Haviland
Keyword(s):  
Beam Theory ◽  
Free Vibrations ◽  
Analytic Investigation ◽  
Bending Vibrations ◽  
Flowing Fluid ◽  
Flow Rates ◽  
Simply Supported ◽  
End Conditions ◽  
Pipe Line ◽  
Mass Flow Rates

Abstract Free vibrations and forced motions due to cross winds may both create important problems in the design of pipe lines supported above ground. An analytic investigation, based on simple beam theory, shows that the flow of fluid in such a pipe line produces marked damping tendencies and thus may reduce the severity of loading encountered. The time dependence of the fundamental mode of a simply supported pipe line is calculated for a number of mass-flow rates, the damping being observed to increase rapidly and the frequency to remain nearly constant over the practically important range. A method is outlined for studying forced vibration, higher modes, and other end conditions. Finally the problem is discussed in terms of traveling waves on an “infinite” unsupported pipe line.

scholarly journals Geometry, and Normal Modes of Vibration (3N-6) for Di and Tetra-Rings Layer (6, 0) Linear (Zigzag) SWCNTs; A DFT Treatment

2019 ◽  
Vol 16 (3(Suppl.)) ◽  
pp. 0726
Author(s):  
Kubba Et al.
Keyword(s):  
Density Functional ◽  
Point Group ◽  
Normal Modes ◽  
Dft Method ◽  
Basis Set ◽  
Single Wall Carbon Nanotubes ◽  
Equilibrium Geometry ◽  
Vibration Frequencies ◽  
Bending Vibrations ◽  
Modes Of Vibration

            Density Functional Theory (DFT) method of the type (B3LYP) and a Gaussian basis set (6-311G) were applied for calculating the vibration frequencies and absorption intensities for normal coordinates (3N-6) at the equilibrium geometry of the Di and Tetra-rings layer (6, 0) zigzag single wall carbon nanotubes (SWCNTs) by using Gaussian-09 program. Both were found to have the same symmetry of D6d point group with C--C bond alternation in all tube rings (for axial bonds, which are the vertical C--Ca bonds in rings layer and for circumferential bonds C—Cc in the outer and mid rings bonds). Assignments of the modes of vibration IR active and inactive vibration frequencies (symmetric and asymmetric modes) based on the image modes applied by the Gaussian 09 display. The whole relations for the vibration modes were also done including nCH stretching, nC--C stretching, δCH, δring (δC--C--C) deformation in plane of the molecule) and gCH, gring (gC--C--C) deformation out of plane of the molecule. The assignment also included modes of puckering, breathing and clock-anticlockwise bending vibrations.

scholarly journals Preparation and the Microwave and Infrared Spectra of Vinyl Ketene

1979 ◽  
Vol 34 (11) ◽  
pp. 1269-1274 ◽  
Author(s):  
Erik Bjarnov
Keyword(s):  
Dipole Moment ◽  
Gas Phase ◽  
Infrared Spectra ◽  
Room Temperature ◽  
Normal Modes ◽  
Spectroscopic Constants ◽  
Electrical Dipole ◽  
Electrical Dipole Moment ◽  
Vacuum Pyrolysis ◽  
Modes Of Vibration

Vinyl ketene (1,3-butadiene-1-one) has been synthesized by vacuum pyrolysis of 3-butenoic 2-butenoic anhydride. The microwave and infrared spectra of vinyl ketene in the gas phase at room temperature have been studied. The trans-rotamer has been identified, and the spectroscopic constants were found to be Ã= 39571(48) MHz, B̃ = 2392.9252(28) MHz, C̃ = 2256.0089(28) MHz, ⊿j = 0.414(31) kHz, and ⊿JK = - 34.694(92) kHz. The electrical dipole moment was found to be 0.987(23) D with μa = 0.865(14) D and μb = 0.475(41) D. A tentative assignment has been made for 17 of the 21 normal modes of vibration

Normal modes of vibration of a model peptide adopting the C7 C5 structure

2009 ◽  
Vol 24 (6) ◽  
pp. 543-552 ◽  
Author(s):  
P. LAGANT ◽  
G. VERGOTEN ◽  
G. FLEURY ◽  
M.H. LOUCHEUX-LEFEBVRE
Keyword(s):  
Normal Modes ◽  
Model Peptide ◽  
Modes Of Vibration

Vibration of Rectangular Plates by the Ritz Method

1950 ◽  
Vol 17 (4) ◽  
pp. 448-453 ◽  
Author(s):  
Dana Young
Keyword(s):  
Ritz Method ◽  
Normal Modes ◽  
Approximate Solutions ◽  
The Other ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Modes Of Vibration ◽  
Ritz’S Method ◽  
Square Plate ◽  
Set Up

Abstract Ritz’s method is one of several possible procedures for obtaining approximate solutions for the frequencies and modes of vibration of thin elastic plates. The accuracy of the results and the practicability of the computations depend to a great extent upon the set of functions that is chosen to represent the plate deflection. In this investigation, use is made of the functions which define the normal modes of vibration of a uniform beam. Tables of values of these functions have been computed as well as values of different integrals of the functions and their derivatives. With the aid of these data, the necessary equations can be set up and solved with reasonable effort. Solutions are obtained for three specific plate problems, namely, (a) square plate clamped at all four edges, (b) square plate clamped along two adjacent edges and free along the other two edges, and (c) square plate clamped along one edge and free along the other three edges.

Localization of Vibration in Disordered Multi-Span Beams With Damping

1993 ◽  
Author(s):  
Djamel Bouzit ◽  
Christophe Pierre
Keyword(s):  
Weak Coupling ◽  
Normal Modes ◽  
Structural Damping ◽  
Coupling Case ◽  
Effects Of Disorder ◽  
Transfer Matrix Approach ◽  
Modes Of Vibration ◽  
Comparable Magnitude ◽  
Localization Of Vibration ◽  
Statistical Perturbation

Abstract The combined effects of disorder and structural damping on the dynamics of a multi-span beam with slight randomness in the spacing between supports are investigated. A wave transfer matrix approach is chosen to calculate the free and forced harmonic responses of this nearly periodic structure. It is shown that both harmonic waves and normal modes of vibration that extend throughout the ordered, undamped beam become spatially attenuated if either small damping or small disorder is present in the system. The physical mechanism which causes this attenuation, however, is one of energy dissipation in the case of damping but one of energy confinement in the case of disorder. The corresponding rates of spatial exponential decay are estimated by applying statistical perturbation methods. It is found that the effects of damping and disorder simply superpose for a multi-span beam with strong interspan coupling, but interact less trivially in the weak coupling case. Furthermore, the effect of disorder is found to be small relative to that of damping in the case of strong interspan coupling, but of comparable magnitude for weak coupling between spans. The adequacy of the statistical analysis to predict accurately localization in finite disordered beams with boundary conditions is also examined.

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