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Research Papers

Elastic Response of Acoustic Coating on Fluid-Loaded Rib-Stiffened Cylindrical Shells

[+] Author and Article Information
Christopher Gilles Doherty

Department of Mechanical Engineering,
Virginia Polytechnic Institute and
State University,
Blacksburg, VA 24061
e-mail: dohertyc@vt.edu

Steve C. Southward

Department of Mechanical Engineering,
Virginia Polytechnic Institute and
State University,
Blacksburg, VA 24061
e-mail: scsouth@vt.edu

Andrew J. Hull

Undersea Warfare Weapons, Vehicles and
Defensive Systems Department,
Naval Undersea Warfare Center Division,
Newport, RI 02841
e-mail: andrew.hull@navy.mil

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received February 17, 2018; final manuscript received August 22, 2018; published online October 16, 2018. Assoc. Editor: Stefano Lenci. This work is in part a work of the U.S. Government. ASME disclaims all interest in the U.S. Government's contributions.

J. Vib. Acoust 141(1), 011020 (Oct 16, 2018) (9 pages) Paper No: VIB-18-1071; doi: 10.1115/1.4041306 History: Received February 17, 2018; Revised August 22, 2018

Reinforced cylindrical shells are used in numerous industries; common examples include undersea vehicles, aircraft, and industrial piping. Current models typically incorporate approximation theories to determine shell behavior, which are limited by both thickness and frequency. In addition, many applications feature coatings on the shell interior or exterior that normally have thicknesses which must also be considered. To increase the fidelity of such systems, this work develops an analytic model of an elastic cylindrical shell featuring periodically spaced ring stiffeners with a coating applied to the outer surface. There is an external fluid environment. Beginning with the equations of elasticity for a solid, spatial-domain displacement field solutions are developed incorporating unknown wave propagation coefficients. These fields are used to determine stresses at the boundaries of the shell and coating, which are then coupled with stresses from the stiffeners and fluid. The stress boundary conditions contain double-index infinite summations, which are decoupled, truncated, and recombined into a global matrix equation. The solution to this global equation results in the displacement responses of the system as well as the exterior scattered pressure field. An incident acoustic wave excitation is considered. Thin-shell reference models are used for validation, and the predicted system response to an example simulation is examined. It is shown that the reinforcing ribs and coating add significant complexity to the overall cylindrical shell model; however, the proposed approach enables the study of structural and acoustic responses of the coupled system.

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References

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Figures

Grahic Jump Location
Fig. 1

Cross section view of the coated shell system

Grahic Jump Location
Fig. 2

Thin and thick-shell radial (top), tangential (middle), and axial (bottom) normalized error in dB for plane wave: 50 Hz, φi = π/12, and mpts = 31 for elastic model and 201 for reference model, npts = 7. Rib is located between the left edge (z = 0) and the dashed line.

Grahic Jump Location
Fig. 3

Normalized magnitude of displacement modes for each circumferential index, n and axial index, m

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Fig. 4

Coating surface radial (top), tangential (middle), and axial (bottom) displacement response for acoustic wave: 5000 Hz, φi = 15 deg, mpts = 31, and npts = 7. Rib located between z = 0 and z = 0.025 m.

Grahic Jump Location
Fig. 5

Radial displacement field of coated system for cross section of cylinder thickness at angle θ = 10 deg, for acoustic wave loading (φi = 15 deg and f = 5000 Hz); box at lower left represents rib location

Grahic Jump Location
Fig. 6

Tangential displacement field of coated system for cross section of cylinder thickness at angle θ = 10 deg, for acoustic wave loading (φi = 15 deg and f = 5000 Hz); box at lower left represents rib location

Grahic Jump Location
Fig. 7

Axial displacement field of coated system for cross section of cylinder thickness at angle θ = 10 deg, for acoustic wave loading (φi = 15 deg and f = 5000 Hz); box at lower left represents rib location

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