Low‐frequency underwater transducer modeling using the direct global stiffness method

Abstract

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.