scholarly journals Non-stationary dynamics of anisotropic Kirchhoff-Love type shel

2020 ◽  
pp. 101-106
Author(s):  
Наталья Александровна Локтева ◽  
Дмитрий Олегович Сердюк ◽  
Павел Дмитриевич Скопинцев
Keyword(s):  
Cylindrical Shell ◽  
Applied Pressure ◽  
Side Surface ◽  
Constant Thickness ◽  
Median Surface ◽  
Rectangular Region ◽  
Shell Material ◽  
Dirac Delta ◽  
Infinite Cylindrical Shell ◽  
Delta Functions

Строится нестационарная функция прогиба для тонкой бесконечной цилиндрической оболочки постоянной толщины при воздействии на ее боковую поверхность вынужденной нестационарной движущейся нагрузки, распределенной по прямоугольной области. Материал рассматриваемой цилиндрической оболочки принят упругим и анизотропным, обладающим симметрией относительно ее срединной плоскости. Теория тонких упругих оболочек строится на гипотезах Кирхгофа-Лява. Для математического описания мгновенно приложенной нагрузки используются дельта-функции Дирака. A non-stationary deflection function is determined for a thin infinite cylindrical shell of constant thickness under the influence of non-stationary moving pressure. The pressure is distributed over a rectangular region, which belongs to the side surface of the shell. The shell material is elastic, anisotropic, and has symmetry to the median surface. The theory of thin elastic shells is based on the Kirchhoff-Love’s hypotheses. The Dirac delta-functions are used to describe an instantaneously applied pressure.

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.

Power Flow and Sound Radiation of a Submerged Cylindrical Shell with Internal Structural

2011 ◽  
Vol 105-107 ◽  
pp. 321-325 ◽  
Author(s):  
Jin Yan ◽  
Juan Zhang
Keyword(s):  
Cylindrical Shell ◽  
Power Flow ◽  
Coupled System ◽  
Engineering Practice ◽  
Coupling Condition ◽  
Space Harmonics ◽  
In Series ◽  
Infinite Cylindrical Shell ◽  
Radiated Sound ◽  
Vibrational Power Flow

The vibrational power flow in a submerged infinite cylindrical shell with internal rings and bulkheads are studied analytically. The harmonic motion of the shell and the pressure field in the fluid is described by Flügge shell theory and Helmholtz equation, respectively. The coupling condition on the outer surface of the shell wall is introduced to obtain the vibrational equation of this coupled system. Both four kinds of forces (moments) between rings and shell and between bulkheads and shell are considered. The solution is obtained in series form by expanding the system responses in terms of the space harmonics of the spacing of both ring stiffeners and bulkheads. The vibrational power flow and radiated sound power are obtained and the influences of various complicating effects such as the ring, bulkhead and fluid loading on the results are analyzed. The analytic model is close to engineering practice, which will be valuable to the application on noise and vibration control of submarines and underwater pipes.

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