Dynamic Pressure Analysis of Hemispherical Shell Vibrating in Unbounded Compressible Fluid

Abstract

This paper is the first to highlight the vibrations of a hemispherical shell structure interacting with both compressible and incompressible fluids. To precisely calculate the pressure of the shell vibrating in the air, a novel analytical approach has been established that has existed in very few publications to date. An analytical formulation that calculates pressure was developed by integrating both the ‘small-density method’ and the ‘Bessel function method’. It was considered that the hemispherical shell vibrates as a simple harmonic function, and the fluid is non-viscous. For comparison, the incompressible fluid model has been analyzed. Surprisingly, it is the first to report that the pressure of the shell surface is proportional to the vibration acceleration, and the velocity amplitude decreased at the rate of 1 r 2 when the fluid was incompressible. Otherwise, the surface pressure of the hemispherical shell was proportional to the vibration velocity, and the velocity amplitude decreased with the rate of 1 r when the fluid was compressible. The compressibility of fluid played an important role in the dynamic pressure of the shell structure. Furthermore, the scale factor derived by the theoretical approach was the product of the density and the sound velocity of the fluid ( ρ o c ) exactly. In this study, the analytical solutions were verified by the calibrated numerical simulations, and the analytical formulation were rigorously tested by extensive parametric studies. These new findings can be used to guide the optimal design of the spherical shell structure subjected to wind load, seismic load, etc.

Vibration-Induced Pressures on a Cylindrical Structure Surface in Compressible Fluid

“…Considering the rotationally symmetric deformation of this structure [30][31][32], the dynamic pressure on the boundary of the fluid affects the structure simultaneously. The governing equations include both the structure dynamics equation as Equation (1) [33,34] and the fluid dynamic equation as Equation (2) [35][36][37], namely:…”

“…In recent years, owing to the large demand for civilian buildings, ocean engineering, military structures, and membrane structures [1,2], many large-span structures have been widely designed for public uses [3][4][5]. It is well known that those structures are generally light and flexible so they are sensitive to dynamic loads, such as wind loads, seismic loads, etc.…”

A New Analytical Prediction for Energy Responses of Hemi-Cylindrical Shells to Explosive Blast Load

“…The bullet was then simulated as a sphere with the same radius and density to the bullet. In order to consider the effect of the air, it was assumed to be an elastic material with a density of 1.225 kg/m 3 Figure 6 shows the comparison of displacement time history at C1 and C2. The experiment data is expressed in a solid green line with a square and the numerical result is plotted in a dotted blue line with a circle.…”

“…Hemi-cylindrical shell structures are used in many applications in ocean engineering, aerospace, composite materials and civil engineering [1][2][3][4][5][6]. For example, submarine, sea detector, aircraft brakes, ballistic components, gymnasiums, modern libraries, buried gas pipelines, and large span roofs are some of the distinct fields of applications [7][8][9][10].…”

Experimental Investigations into Earthquake Resistance of Steel Frame Retrofitted by Low-Yield-Point Steel Energy Absorbers

“…The influence of an earthquake on building structures can tremendously cause the losses of either lives or investments. Any landmark engineering structure can be destroyed in an instant because of the occurrence of extreme motions caused by natural disasters such as earthquakes and strong winds, or even by high-speed traffic motions [7,8].…”