Variational Modal Identification of Conservative Nongyroscopic Systems

1989 ◽  
Vol 111 (2) ◽  
pp. 160-171 ◽  
Author(s):  
L. Silverberg ◽  
S. Kang
Keyword(s):  
Longitudinal Vibration ◽  
Modal Identification ◽  
System Response ◽  
Bending Vibration ◽  
Free System ◽  
Dirac Delta ◽  
Vibration Problem ◽  
Identification Method ◽  
Delta Functions ◽  
Admissible Functions

A new modal identification method for Conservative Nongyroscopic Systems is proposed. The modal identification method is formulated as a variational problem in which stationary values of a functional quotient are sought. The computation of the functional quotient is carried out using a set of admissible functions defined over the spatial domain of the system. Measurements of the free system response at discrete points are carried out using any combination of displacements, velocities, and/or accelerations. Three types of admissible functions have been considered—global functions, spatial Dirac-delta functions, and finite element interpolation functions. The variational modal identification method is applied to a pure bending vibration problem, to a pure longitudinal vibration problem, and to a combined bending and longitudinal vibration problem. The effectiveness of the variational modal identification method using different sets of admissible functions is examined.

scholarly journals A novel identification procedure from ambient vibration data

Meccanica ◽  
2020 ◽  
Author(s):  
A. Di. Matteo ◽  
C. Masnata ◽  
S. Russotto ◽  
C. Bilello ◽  
A. Pirrotta
Keyword(s):  
Hilbert Transform ◽  
Time Domain ◽  
Operating Conditions ◽  
Modal Identification ◽  
Ambient Vibration ◽  
System Response ◽  
The Real ◽  
Vibration Data ◽  
Identification Method ◽  
Time Domain Signal

AbstractAmbient vibration modal identification, also known as Operational Modal Analysis, aims to identify the modal properties of a structure based on vibration data collected when the structure is under its operating conditions, i.e., no initial excitation or known artificial excitation. This procedure for testing and/or monitoring historic buildings, is particularly attractive for civil engineers concerned with the safety of complex historic structures. However, since the external force is not recorded, the identification methods have to be more sophisticated and based on stochastic mechanics. In this context, this contribution will introduce an innovative ambient identification method based on applying the Hilbert Transform, to obtain the analytical representation of the system response in terms of the correlation function. In particular, it is worth stressing that the analytical signal is a complex representation of a time domain signal: the real part is the time domain signal itself, while the imaginary part is its Hilbert transform. A 3DOF numerical example will be presented to show the accuracy of the proposed procedure, and comparisons with data from other methods assess the reliability of the approach. Finally, the identification method will be extended to the real case study of the Chiaramonte Palace, a historic building located in Palermo and known as “Steri”.

On Analysis of Cable Network Vibrations Using Galerkin’s Method

1970 ◽  
Vol 37 (3) ◽  
pp. 606-611 ◽  
Author(s):  
A. I. Soler ◽  
H. Afshari
Keyword(s):  
Field Equation ◽  
System Response ◽  
Galerkin’S Method ◽  
Small Oscillations ◽  
Dirac Delta ◽  
Galerkin's Method ◽  
Cable Network ◽  
Cable Networks ◽  
Delta Functions ◽  
Vibrating Membrane

Built-up systems consisting of rectangular cable networks covered by or embedded in a membrane matrix are considered; small oscillations about an initially flat, pretensioned state are studied. By employing Dirac delta functions to aid in representation of preload and weight distribution acting on the system, the system response is shown to be given by a generalized version of the equation for a vibrating membrane. A solution of the field equation is effected using Galerkin’s method and approximating functions are suggested for a wide class of boundary shapes. As an illustration of the method a rectangular boundary shape is considered and results are obtained for typical values of preload, cable distribution, etc. Results are compared with previous analyses of similar systems, and advantages of the present approach are discussed.

THE MODAL IDENTIFICATION METHOD IN NONLINEAR HEAT TRANSFER PROBLEMS

Equipment ◽  
2006 ◽  
Author(s):  
O. Balima ◽  
D. Petit ◽  
J. B. Saulnier ◽  
M. Girault ◽  
Y. Favennec
Keyword(s):  
Heat Transfer ◽  
Modal Identification ◽  
Identification Method ◽  
Nonlinear Heat Transfer ◽  
Transfer Problems

Dirac Delta Functions in the Laplace‐Type Expansion of rnYlm(θ, φ)

1969 ◽  
Vol 51 (6) ◽  
pp. 2359-2362 ◽  
Author(s):  
Kenneth G. Kay ◽  
H. David Todd ◽  
Harris J. Silverstone
Keyword(s):  
Dirac Delta ◽  
Delta Functions ◽  
Laplace Type

scholarly journals Electrostatic and magnetostatic fields of point dipoles revisited

2019 ◽  
Vol 65 (1) ◽  
pp. 71 ◽  
Author(s):  
Y. Muniz ◽  
Anderson José Fonseca ◽  
C. Farina
Keyword(s):  
Magnetic Dipole ◽  
Electric Dipole ◽  
Alternative Procedure ◽  
Dirac Delta ◽  
Delta Functions ◽  
Point Electric Dipole

After reviewing how the Dirac delta contributions to the electrostatic and magnetostatic fields of a point electric dipole and a point magnetic dipole are usually introduced, we present an alternative procedure for obtaining these terms based on a regularization prescription similar to that used in the computation of the transverse and longitudinal delta functions. We think this method may be useful for the students in other analogous calculations.

Review of basic quantum physics

Quantum 20/20 ◽  
2019 ◽  
pp. 1-20
Author(s):  
Ian R. Kenyon
Keyword(s):  
Quantum Physics ◽  
Particle Density ◽  
Electromagnetic Coupling ◽  
Black Body ◽  
Black Body Radiation ◽  
Gauge Transformations ◽  
Dirac Delta ◽  
Wave Particle Duality ◽  
Delta Functions ◽  
Lorentz Invariants

Basic experimental evidence is sketched: the black body radiation spectrum, the photoeffect, Compton scattering and electron diffraction; the Bohr model of the atom. Quantum mechanics is reviewed using the Copenhagen interpretation: eigenstates, observables, hermitian operators and expectation values are explained. Wave-particle duality, Schrödinger’s equation, and expressions for particle density and current are described. The uncertainty principle, the collapse of the wavefunction, Schrödinger’s cat and the no-cloning theorem are discussed. Dirac delta functions and the usage of wavepackets are explained. An introduction to state vectors in Hilbert space and the bra-ket notation is given. Abstracts of special relativity and Lorentz invariants follow. Minimal electromagnetic coupling and the gauge transformations are explained.

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