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Accession Number ADA564441
Title Analytical Approximate Solution of Coupled Wave Equations with a Nonlinear Stiffness.
Publication Date Apr 2012
Media Count 26p
Personal Author D. B. Segala
Abstract By utilizing the Euler-Lagrange equations, a set of coupled partial differential equations was derived for two crossing strings with a spring at the crossover point. This report considers three types of springs: a nonlinear softening spring, a nonlinear hardening spring, and a linear spring. The Adomian decomposition method was used to obtain an analytical approximate solution from the derived coupled wave equations. The dynamic responses of the analytical solutions for both the nonlinear softening and nonlinear hardening springs were compared to the response from the linear spring. In both the nonlinear softening and nonlinear hardening springs, higher frequency oscillations were observed at the spring location; however, when a linear spring was used, the strings did not exhibit higher frequency oscillations and only oscillated in the mode by which they were excited.
Keywords Adomian decomposition
Close form solutions
Coupled wave equations
Euler equations
Euler lagrange equations
Partial differential equations
Wave equations

Source Agency Non Paid ADAS
NTIS Subject Category 72B - Algebra, Analysis, Geometry, & Mathematical Logic
Corporate Author Naval Undersea Warfare Center Div., Newport, RI. Ranges Engineering and Analysis Dept.
Document Type Technical report
Title Note Technical rept.
NTIS Issue Number 1303
Contract Number N/A

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