Reaction of the preloaded rotation shell with the rigid nose part of the apparatus to a shock wave in the liquid

The article investigates the problem of hydro-elastic interaction of a weak shock wave with a rigid nosed rotation shell preloaded with axial forces. The shell is enclosed in a rigid parabolic screen, i.e. the impact of the end face and the shock wave diffraction are not considered. Liquid is regarded to be perfectly compressible. Its applied summing hydrodynamic pressure during complex interaction with the shell surface can be classified into the incident, reflected and radiated waves. The problem of hydro-elastic interaction of these shock fronts with a preloaded parabolic rigid nosed shell in a related setting is reduced to the solution of the wave equations of nonlinear system of equations for shell motion under particular initial and boundary conditions, in which the dimensionless displacement of this nose section under the impact of hydrodynamic forces is determined by integrating its motion equation. The equations, describing the dependences of nose section displacements on shock wave interaction time, take into account generalized hydrodynamic forces, including the second category directly related to the mass of the attached fluid. Determination of stress-strain state in case of interaction with the shock wave in the liquid of elastic rotation paraboloid in the form of the shell containing a rigid insertion in the nose section is reduced to the solution of a nonlinear equations system of shell motion considering the boundary conditions along fastenings at the end face of the shell and interface conditions of the shell and insertion. Dimensionless displacements of the nose section caused by hydrodynamic forces are defined by integrating the equations of motion under the initial conditions along insertion offsets in the axial directions.

Accurate compact solution of fluid-filled FG cylindrical shell inducting fluid term: Frequency analysis

Shell motion equations are framed with first order shell theory of Love. Vibration investigation of fluid-filled three layered cylindrical shells is studied here. It is also exhibited that the effect of frequencies is investigated by varying the different layers with constituent material. The coupled and uncoupled frequencies changes with these layers according to the material formation of fluid-filled FG-CSs. A cylindrical shell is immersed in a fluid which is a non-viscous one. These equations are partial differential equations which are usually solved by approximate technique. Robust and efficient techniques are favored to get precise results. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel’s functions of second kind designate the fluid influence. Mathematically the integral form of the Lagrange energy functional is converted into a set of three partial differential equations.

Spectral Properties

The spectral properties of the nonequilibrium Green’s functions are explored. Causality and sum rules are shown to be completed by the extended quasiparticle picture. The off-shell motion is seen to become visible in satellite structures of the spectral function. Different forms of ansatz to reduce the two-time Green’s function to a one-time reduced density matrix are discussed with respect to the consistency to other approximations. We have seen from the information contained in the correlation function that the statistical weight of excitations with which the distributions are populated are given by the spectral function. This momentum-resolved density of state can be found by the retarded and advance functions.

Revealing Phenomena of Heat Energy, Levity, Gravity and Photons Characteristic Current to Light on Dealing Matter to Sub-Atom

Technology has almost reached to its climax but the basic understanding of science in many phenomena is still awaited. Scientific research reveals strong analogy between electron and photon. Atoms that execute electronic transitions, on absorbing heat energy, excite electrons. De-excitation of electron results into depicting energy in the shape of Gaussian distribution and where inertia is involved. The wavelength of photon at point of generation remains in inter-shell distance and atoms of all those elements that glitter perform like magician, throwing one and catching other, where an electron excites at shunt energy and configure trajectory under levity and de-excites at free fall configuring trajectory under gravity and silicon atom is a model system. In band gap of such atoms, heat energy of merged photons is cultivated and that shunt energy perturb the balance of inherent energy between electron and nucleus, which is not the case in atoms do not glitter. Uninterrupted confined inter-shell motion of electron results into photon that can travel immeasurable length. Such photons increase wavelength on decreasing frequency, propagate to hard X-ray, to visible spectrum, and to beyond. Here, I discuss that heat energy is due to merged photons, current due to photons wavelength in inter-shell distance and light photons wavelength in visible spectrum. Force of repulsion or attraction in certain materials engages phenomenon of levitism or gravitism instead of magnetism where inertia is exempted. All structural motifs and dynamics are subject to characteristic photons. A structural design delivers straight-forward application on coordinating overt photons or merged photons. The various gadgets, devices and instruments only operate energy as per need of necessity. Here, materials science explores matter to sub-atom while coordinating energy and devises science to describe.

Revealing Phenomena of Heat Energy, Levity, Gravity, Photons Characteristic Current to Light on Dealing Matter to Sub-Atom

Technology has reached to its climax but the basic understanding of science in many phenomena is still awaited. Scientific research reveals strong analogy between electron and photon. Atoms that execute electronic transitions, on absorbing heat energy, excite electrons. De-excitation of electron results into depicting energy in the shape of Gaussian distribution. The wavelength of photon at point of generation remains in inter-shell distance and atoms of all those elements that glitter perform like magician, throwing one and catching other, where an electron excites at shunt energy and configure trajectory under levity and de-excites at free fall configuring trajectory under gravity and silicon atom is a model system. In band gap of such atoms, heat energy of merged photons is cultivated and that shunt energy perturb the balance of inherent energy between electron and nucleus, which is not the case in atoms do not glitter. Uninterrupted confined inter-shell motion of electron results into photon that can travel immeasurable length. Such photons increase wavelength on decreasing frequency, propagate to hard X-ray, to visible spectrum, and to beyond. Here, I discuss that heat energy is due to merged photons, current due to photons wavelengths in inter-shell distance and light photons wavelengths in visible spectrum. Force of repulsion or attraction in certain materials engages phenomenon of levitism or gravitism instead of magnetism. All structural motifs and dynamics are subject to characteristic photons. A structural design delivers straight-forward application on coordinating overt photons or merged photons. The various gadgets, devices and instruments only operate energy as per need of necessity. Here, materials science explores matter to sub-atom while coordinating energy and devises science to describe.

Dynamic Model of Elastically Mounted Machinery with Cylindrical Shell

Mounting machinery by isolators can reduce vibration transmitted to the base and attenuated environmental noise. In this paper the machine having cylindrical shell such as electric motors is modeled by thin-wall cylindrical shell motion equation. The reaction force exerted by isolator is considered as point force and integrated in the shell equation. The typical vibration excitation of machinery is represented by point and line excitations. The forces transmitted to the base through isolators are then calculated under different excitations. Conclusions with respect to machinery and isolation system design are presented based on numerical results.

Investigation on Vibro-Acoustic Characteristics from Submerged Cylindrical Shell with Double Damping Layers

The vibration and sound radiation from submerged cylindrical shell with double damping layers are presented. The cylindrical shell motion was described with classical thin shell theory. The double damping layers motion was described with the Navier viscoelasticity theory. For different Youngs modulus parameters of double damping layers, the sound radiated power and the radial quadratic velocity of cylindrical shell models were calculated and analyzed. The results show that the sound radiated power and radial quadratic velocity are reduced to varying degrees due to double damping layers in a large frequency domain except low frequency. The double damping layer with soft inner layer and hard outer layer can make the sound radiated peaks move to high frequency, can help to reduce the radial quadratic velocity on outer surface of damping layer, and can help to reduce the vibration of model at antiresonance frequency.

On high-altitude projectile motion

In this study, the formulas for projectile velocity components and coordinates in a vacuum were derived with the altitude decrease in gravitational acceleration factored in. A model of cannon shell motion in the air is presented that accounts for the altitude dependence of gravitational acceleration, air density, the speed of sound up to an altitude of 84 km, and the speed dependence of the drag coefficient at trans- and supersonic speeds. The drag coefficient function is obtained by fitting to experimental data taken for the US M101 155 mm shell. The model gives flight parameters that agree with the published ones. The motion of the Paris Gun projectile is then modeled. The model shows that a range of 120 km is possible if the projectile mass is about 150 kg. A flat Earth approximation was used in the computations. Changing the launch angle to 90°, super high-altitude vertical ascent and free fall are modeled.