Translator Disclaimer
June 2007 On the Quintic Nonlinear Schrödinger Equation Created by the Vibrations of a Square Plate on a Weakly Nonlinear Elastic Foundation and the Stability of the Uniform Solution
Ben T. Nohara, Akio Arimoto
Japan J. Indust. Appl. Math. 24(2): 161-179 (June 2007).

Abstract

Plates are common structural elements of most engineering structures, including aerospace, automotive, and civil engineering structures. The study of plates from theoretical perspective as well as experimental viewpoint is fundamental to understanding of the behavior of such structures. The dynamic characteristics of plates, such as natural vibrations, transient responses for the external forces and so on, are especially of importance in actual environments. In this paper, we conside the envelope surface created by the vibrations of a square plate on a weakly nonliner elastic foundation and analyze the stability of the uniform solution of the governing equation for the envelope surface. We derive the two-dimensional equation that governs the spatial and temporal evolution of the envelope surface on cubic nonlinear elastic foundation. The fact that the governing equation becomes the quintic nonlinear Schrödinger equation is shown. Also we obtain the stability condition of the uniform solution of the quintic nonlinear Schrödinger equation.

Citation

Download Citation

Ben T. Nohara. Akio Arimoto. "On the Quintic Nonlinear Schrödinger Equation Created by the Vibrations of a Square Plate on a Weakly Nonlinear Elastic Foundation and the Stability of the Uniform Solution." Japan J. Indust. Appl. Math. 24 (2) 161 - 179, June 2007.

Information

Published: June 2007
First available in Project Euclid: 17 December 2007

zbMATH: 1159.74016
MathSciNet: MR2338152

Rights: Copyright © 2007 The Japan Society for Industrial and Applied Mathematics

JOURNAL ARTICLE
19 PAGES


SHARE
Vol.24 • No. 2 • June 2007
Back to Top