#### Date of Award

1995

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Physics and Astronomy

#### First Advisor

Warren W. Johnson

#### Abstract

A spherical gravitational wave detector can be equally sensitive to a wave from any direction, and also able to measure its direction and polarization. We derive a set of equations to describe the mechanics of a spherical antenna coupled to an arbitrary number of attached mechanical resonators. A special arrangement of 6 resonators is proposed, which we term a Truncated Icosahedral Gravitational Wave Antenna, or TIGA. An analytic solution to the equations of motion is found for this case. We find that direct deconvolution of the gravitational tensor components can be accomplished with a specified set of linear combinations of the resonator outputs, which we call the mode channels. We develop one simple noise model for this system and calculate the resulting strain noise spectrum. We conclude that the angle-averaged energy sensitivity will be 56 times better than for the typical equivalent bar-type antenna with the same noise temperature. We have constructed a prototype TIGA. This shape was machined from an Al 6063 cylindrical bar, is 84 cm in diameter, has its first quadrupole resonances near 3200 Hz, and is suspended from its center of mass. The frequencies of the lowest seven multiplets were found to closely match those calculated for a sphere. We observed the motion of the prototype's surface using 6 accelerometers attached to its surface in the symmetric truncated icosahedral arrangement. We have tested a first order direction finding algorithm, which uses fixed linear combinations of six accelerometer responses to first infer the relative amplitudes of the quadrupole modes and from these the location of the impulse. The six accelerometers were then replaced by six mechanical resonators. A strain gauge was used to monitor the radial motion of each resonator. The frequency response of the of coupled system was measured and compared to the eigenvalue solutions of the equations of motion. It was concluded that deviations from perfect symmetry have a second order effect on our ability to observe the prototype's quadrupole modes and thus determine the location and direction of the initial excitation.

#### Recommended Citation

Merkowitz, Stephen Michael, "Truncated Icosahedral Gravitational Wave Antenna." (1995). *LSU Historical Dissertations and Theses*. 6033.

https://digitalcommons.lsu.edu/gradschool_disstheses/6033

#### Pages

134

#### DOI

10.31390/gradschool_disstheses.6033