Frecuencias de resonancia de un aluminio esférico

Resonance frequencies of a spherical aluminum

shell subject to static internal pressure

Andrew A. Piacsek and Sami Abdul-Wahid

Department of Physics, Central Washington University, Ellensburg, Washington 98926

piacsek@cwu.edu, sipho.1989@gmail.com

Robert Taylor

Department of Industrial Engineering and Technology, Central Washington University,

Ellensburg, Washington 98926

terebigemuwan@gmail.com

Abstract: Measurements of the vibrational response of a spherical

aluminum shell subject to changes in the interior pressure clearly

demonstrate that resonance frequencies shift higher as the pressure is

increased. The frequency shift appears to be smaller for longitudinal

modes than for bending wave modes. The magnitude of frequency shift

is comparable to analytical predictions made for thin cylindrical shells.

Changes in the amplitudes of resonance peaks are also observed. A

possible application of this result is a method for noninvasively monitoring

pressure changes inside sealed containers, including intracranial

pressure in humans.

VC 2012 Acoustical Society of America

PACS numbers: 43.40.Ey, 43.25.Gf [JGM]

Date Received: February 16, 2012 Date Accepted: April 20, 2012

1. Introduction

Recent interest in developing noninvasive techniques for measuring intracranial pressure

(ICP) has led to investigations of the vibrational response of skulls subject to internal

pressure changes. A significant result of these limited studies, both experimental1

and computational,2 is that an increase in ICP produces an upward shift in certain

resonance frequencies of ovine and human skulls. Although the maximum ICP investigated

was less than 0.5 psi, this result is consistent with the predictions of early theoretical

studies of thin cylindrical shells subject to much larger pressures.3–10 In addition

to ICP monitoring, this phenomenon has the potential to be exploited as a diagnostic

tool for the pressure inside any thin-walled container that should remain sealed, such

as an industrial tank containing hazardous waste.

It should be emphasized that we are concerned only with the effect on shell resonance

frequencies due to static internal pressure, regardless of the specific fluid contained

in the shell, rather than acoustic pressures associated with spherical cavity modes.

The mechanism by which prestress within a shell causes the resonance frequencies to

shift is clearly nonlinear. In shell vibrations, there are two distinct sources of nonlinearity:

the interaction of shell curvature and finite thickness gives rise to nonlinear straindisplacement

relations5 (“geometric nonlinearity”), and the stress-strain relations

...