N112-156 TITLE: High Frequency Elastic Analysis Tool

TECHNOLOGY AREAS: Information Systems, Ground/Sea Vehicles

ACQUISITION PROGRAM: PMS450, Virginia program office

OBJECTIVE: Development of modeling methods and software that accurately predicts flank array self-noise levels.

DESCRIPTION: This topic seeks innovative approaches for transitioning modeling methods that can extend self-noise modeling of hull arrays where conventional finite element approaches fail (or takes an enormous amount of time to converge on a solution). Currently, a comprehensive set of fully elastic analytical models for submarine coatings, UUV coatings, flank array sonar systems and torpedo sonar windows does not exist.

Acoustic modeling requires mathematically propagating a plane wave onto a structure. When sound is incident on a hull array, it creates both dilatational (sound) waves and shear waves. Shear waves have a much slower propagation speed than dilatational waves and hence a shorter wavelength. Since finite element methods require on the order of ten elements per wavelength for accurate modeling [1,2], this means that such systems cannot be accurately modeled. The sound waves can be accurately modeled, but the shear waves (with their shorter wavelengths) cannot. As a result, the design of such arrays are severely hindered using the finite element method, since there is no way to predict shear wave behavior (which leads to noise) and hence there is no way to use design approaches to mitigate such noise.

Previous analytical models were restricted to low frequency, low wave number analysis based on governing equations that contain only a flexural wave component [3,4]. Recent analytical modeling methods incorporate higher order elastic terms [5,6], allowing undersea vehicles and their corresponding sonar systems to be modeled in high frequency regimes, fully supporting all of the dynamic wave propagation and interaction with the structure. These new methods provide a modeling capability and insight at high frequencies and high wave numbers that is unavailable through previous analytical methods. This SBIR topic seeks advanced approaches to better understand Navy systems in this regime, including UUV coatings, submarine hull coatings, weapon sonar systems, and especially hull array sonar systems.

PHASE I: Develop and validate analytical methods for a transitioning model applicable for high frequency and wave number regimes for fully elastic structures. The model should include a fluid that supports acoustic pressure, an acoustic coating, a backing plate, and ribs having three degrees of freedom.

PHASE II: Further refine analytical methods from Phase I by extending this to a multi-layer array system and develop a modeling tool that can be made available to the Navy design community. Predict the noise due to shear waves and its potential impact on system performance. Test against experimental data and key benchmarks.

PHASE III: Transition MATLAB code to the acquisition community.

PRIVATE SECTOR COMMERCIAL POTENTIAL/DUAL-USE APPLICATIONS: The tools developed under this effort should find a wide variety of uses for modeling of fully elastic structures when conventional finite element methods fail.

REFERENCES:
[1] O.C. Zienkiewicz and R.L. Taylor, The Finite Element Method for Solid and Structural Mechanics, Sixth Edition, Butterworth-Heinmann, 2005.

[2] R.T. Fenner, Finite Element Methods for Engineers, Imperial College Press, London, 1997.

[3] C.J. Chapman, S.V. Sorokin, "The Forced Vibration of an Elastic Plate Under Significant Fluid Loading", Journal of Sound and Vibration, Volume 281, 2005, pp. 719 � 741.

[4] B.A. Cray, "Acoustic Radiation from Periodic and Sectionally Aperiodic Rib-Stiffened Plates", Journal of the Acoustical Society of America", Volume 95, 1994, pp 256-264.

[5] A.J. Hull, "Dynamic response of an elastic plate containing periodic masses," Journal of Sound and Vibration, Volume 310, 2008, pp. 1 � 20.

[6] A.J. Hull, "Elastic Response of a Four Layer Hull Array Sonar System Subjected to Acoustic Plane Wave Excitation," NUWC Technical Report 11965, February 2010, Naval Undersea Warfare Center, Newport, RI.

KEYWORDS: flank array; hull array, sonar, periodic structures, self noise, fully elastic models

** TOPIC AUTHOR (TPOC) **

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