Relation between creeping waves and normal modes of vibration of a curved body

1977 ◽  
Vol 61 (3) ◽  
pp. 711-715 ◽  
Author(s):  
H. Überall ◽  
L. R. Dragonette ◽  
L. Flax
Keyword(s):  
Normal Modes ◽  
Modes Of Vibration

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.

scholarly journals Normal modes of a "cylindrical valley" of alluvium

1989 ◽  
Vol 22 (2) ◽  
pp. 76-80 ◽  
Author(s):  
W. R. Stephenson
Keyword(s):  
Shear Modulus ◽  
Structural Damage ◽  
Travelling Waves ◽  
Soft Soil ◽  
Normal Modes ◽  
Modes Of Vibration ◽  
Rigid Material ◽  
Cylindrical Volume ◽  
High Bulk ◽  
Low Shear

Some normal modes of vibration are deduced for a cylindrical volume of high bulk modulus, low shear modulus material, embedded in an infinite half space of rigid material. The manner in which they may be excited by travelling waves in the rigid material is examined. The relevance of such processes is discussed with regard to the enhancement of structural damage on soft soil during an earthquake.

Identification of the Reduced Dynamics of a Physical Flexible Three-Beam Structure

2009 ◽  
Author(s):  
Ioannis T. Georgiou
Keyword(s):  
Normal Modes ◽  
Rigid Motion ◽  
Slow Dynamics ◽  
Beam Structure ◽  
Cantilevered Beam ◽  
Modes Of Vibration ◽  
Long Time ◽  
Single Sensor ◽  
Time Term ◽  
The Right

An experimental spatiotemporal database for the free dynamics of the local transverse acceleration field of a flexible three-beam structure is created by employing a single sensor. A POD-based dimension reduction reveals that the database is dominated by a single POD mode with slow dynamics and a shape that reflects the acceleration discontinuities at the right corners of the structure. This mode interacts with the second POD mode with dynamics evolving at a relatively faster time scale. In the long time term, the dominant POD mode is dominated by a single harmonic indicating that the dynamics have entered a reduced subspace containing only slow dynamics. The dominant POD mode as well as the second one of the database generated by a relocating sensor seems to be related to normal modes of vibration. The shape of the dominant POD mode reveals the dominant physics of the specific three-beam structure: the cantilevered beam moves in its first mode while the horizontal and the other vertical beams perform a near rigid motion. This should be true for a wide rage of three-beam structures.

Detection of Coherence in Collocated Experimental Acceleration Signals in a Flexible Aluminum Multi-Beam Structure

2011 ◽  
Author(s):  
Ioannis T. Georgiou
Keyword(s):  
State Of The Art ◽  
Normal Modes ◽  
Piezoelectric Sensors ◽  
Beam Structure ◽  
Original Result ◽  
Unit Space ◽  
Modes Of Vibration ◽  
Proper Orthogonal ◽  
The Impact ◽  
Acceleration Signals

The present work concerns the study of the experimental Proper Orthogonal Decomposition (POD) modes of three simultaneously acquired ensembles of collocated impulse-induced acceleration signals in a complex multi-beam aluminum structure. The impact-induced locally transverse acceleration of a three-beam structure is measured simultaneously at three fixed points with state-of-the-art piezoelectric sensors. Each ensemble of collocated databases is processed by the POD Transform to find out that it is underlined by strong coherence in space and time manifested by a small number of POD modes. It is found that the unit space modulations of the first-the dominant-POD modes of the three databases of experimental acceleration signals form an orthonormal set. The same is true for their companion unit time modulations. This original result leads to the identification of three normal modes of vibration for the complex beam structure.

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