Bimodal optimal design of vibrating plates using theory and methods of nondifferentiable optimization

• Published in: Journal of Optimization Theory and Applications Vol. 46; no. 2; pp. 187 - 203
• Main Author: Myslinski, A.
• Format: Journal Article
• Language: English; Japanese
• Published: New York, NY Springer Science and Business Media LLC 01.06.1985; Springer
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Design; Optimization; Vibrating plate
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1007/bf00938423

An optimal design problem of vibrating plates, under an assumption that the smallest eigenvalue is multiple which implies that the optimization problem is nondifferentiable with respect to the design variable, is examined. The optimization problem involves maximizing the smallest eigenvalue of the elliptic eigenvalue problem describing the free-plate vibration. The variable subject to optimization is the thickness of the plate. The finite-element method is used as an approximation method and to obtain a numerical solution of the problem, a shifted penalty function method and a nonsmooth optimization method are used.