Structural acoustic problem and dynamic nonlinear plate equations

ABSTRACT

The purpose of this paper is to investigate a structural interaction model coupled with dynamic von Karman equations, without neither rotational inertia nor clamped boundary conditions. Our fundamental goal is to establish the existence and the uniqueness of the weak solution for the so-called global functional energy. The stability is also discussed. At the end, a numerical study based on the finite difference method is presented as well.

Keywords:

• von Karman equation
• nonlinear plates
• structural acoustic
• rotational inertia
• non-coupled method
• finite difference method

2010 Mathematics Subject Classifications:

• 74F10
• 74B20
• 74K25
• 65N05

Acknowledgements

The authors would like to thank the three anonymous referees for their valuable comments and suggestions which substantially improved the final version of the present manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).