Dynamic Pressure Analysis of Hemispherical Shell Vibrating in Unbounded Compressible Fluid

Ping Liu, Sakdirat Kaewunruen, Bai-jian Tang

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)
124 Downloads (Pure)


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 (ρoc) 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
Original languageEnglish
Article number1938
Number of pages19
JournalApplied Sciences
Issue number10
Publication statusPublished - 16 Oct 2018


  • incompressible fluid
  • compressibility
  • hemispherical shell
  • fluid–structure interaction


Dive into the research topics of 'Dynamic Pressure Analysis of Hemispherical Shell Vibrating in Unbounded Compressible Fluid'. Together they form a unique fingerprint.

Cite this