### ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

## 2pEA7. Low-frequency underwater transducer modeling using the direct
global stiffness method.

**J. Robert Fricke
**

**
Mark A. Hayner
**

**
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*Dept. of Ocean Eng., MIT, Cambridge, MA 02139
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*
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The direct global stiffness matrix method (DGSM), described by Fricke and
Hayner [direct global stiffness matrix method for 3-D Truss Dynamics, submitted
to the ASME 15th Biennial Conference on Mechanical Vibration and Noise, 17--21
September 1995], provides an efficient method for analyzing two-dimensional and
axisymmetric, low-frequency, underwater, transducer geometries. The DGSM method
is a wave-type solution based on the Euler--Bernoulli beam element. The
mechanical motion of the transducer element is modeled using a collection of
beam elements welded together at joints. By imposing dynamic equilibrium
conditions at these joints, a banded symmetric stiffness matrix is formed. The
matrix is then solved using Gaussian elimination to find joint displacements
and rotations with beam energies calculated on a post-processing basis. The
radiation load due to the surrounding water is included using a compact source
assumption. Thus fluid loading interaction effects, important for low quality
factor transducers, are properly addressed. Analysis of a class IV
flextensional transducer is offered as an example of the usefulness of this
approach.