0
Research Papers

A Higher-Order Shear Deformation Model of a Periodically Sectioned Plate

[+] Author and Article Information
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 2, 2016; final manuscript received April 20, 2016; published online June 2, 2016. Assoc. Editor: Matthew Brake.This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

J. Vib. Acoust 138(5), 051010 (Jun 02, 2016) (9 pages) Paper No: VIB-16-1063; doi: 10.1115/1.4033495 History: Received February 02, 2016; Revised April 20, 2016

This paper develops a higher-order shear deformation model of a periodically sectioned plate. A parabolic deformation expression is used with periodic analysis methods to calculate the displacement field as a function of plate spatial location. The problem is formulated by writing the transverse displacement field and the in-plane rotations as a series solution of unknown wave propagation coefficients multiplied by an exponential indexed wavenumber term in the direction of varying structural properties multiplied by an exponential constant term in the direction of constant structural properties. These expansions, along with various structural properties written using Fourier summations, are inserted into the governing differential equations that were derived using Hamilton's principle. The equations are now algebraic expressions that can be orthogonalized and written in a global matrix format whose solution is the wave propagation coefficients, thus yielding the transverse and in-plane displacements of the system. This new model is validated with finite-element theory and Kirchhoff plate theory for a thin plate simulation and verified with comparison to experimental results for a 0.0191 m thick sectional plate.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

Periodically sectioned plate with a Cartesian coordinate system

Grahic Jump Location
Fig. 2

Schematic of the (a) validation problem and the magnitude of the displacement versus x-direction position at (b) 100 Hz, (c) 300 Hz, and (d) 500 Hz for the sectioned plate with a thickness of 0.001 m. The solid lines are the higher-order shear deformation plate solution, the circular markers are the Kirchhoff plate solutions, and the square markers are finite-element results. The vertical dashed line is the location where the periodic sections abut one another.

Grahic Jump Location
Fig. 3

Magnitude of the wave propagation coefficients Wm versus m index at (a) 100 Hz, (b) 300 Hz, and (c) 500 Hz for the sectioned plate with a thickness of 0.001 m. The horizontal dashed line is the location that is −90 dB down from the maximum value in each plot.

Grahic Jump Location
Fig. 4

The experimental setup showing the mechanical shaker attached to the plate. The spacing of the adjacent individual vertical strips is 0.0572 m (2.25 in.).

Grahic Jump Location
Fig. 5

Model (a) and experimental results (b) of plate normal displacement in the decibel scale versus x- and y-wavenumbers at 400 Hz

Grahic Jump Location
Fig. 6

Model (a) and experimental results (b) of plate normal displacement in the decibel scale versus x- and y-wavenumbers at 800 Hz

Grahic Jump Location
Fig. 7

Model (a) and experimental results (b) of plate normal displacement in the decibel scale versus x- and y-wavenumbers at 1200 Hz

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In