On optimum design of a vibrating plate with respect to its thickness and eigen-frequencies

• Autorzy: Bock I. , Lovíšek J.
• Konferencja: Conference on Numerical Method in Continuum Mechanics (6 ; 16-18.09.1996 ; Stará Lesná, Słowacja)
• Języki publikacji: EN

Abstrakty

EN

The eigenvalue optimization problem for anisotropic plates has been dealt with. The variable thickness of a plate plays the role of a design variable. The state problem arises considering free vibrations of a plate. The demand of the lowest first eigenfrequency means the maximal first eigenvalue of the elliptic eigenvalue problem. The continuity and differentiability properties of the first eigenvalue have been examined. The existence theorem for the optimization problem has been stated and verified. The finite elements approximation has been analyzed. The shifted penalization and the method of nonsmooth optimization can be used in order to obtain numerical results.

Słowa kluczowe

EN

vibratory plate; eigenfrequency

PL

płyta wibracyjna; częstotliwość drgań własnych

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 1998
• Tom: Vol. 5, nr 2
• Strony: 139--150
• Opis fizyczny: Bibliogr. 10 poz., tab.

Twórcy

autor

Bock I.

• Dept. of Mathematics, Faculty of Electr. Engineering and Inform. Technology, Slovak Tech. Untv., 81219 Bratislava,

autor

Lovíšek J.

• Dept. of Mechanics, Faculty of Constructions, Slovak Tech. Univ., 81368 Bratislava

Bibliografia

• [1] I. Bock, J.Lovíšek. Optimal control of a viscoelastic plate bending with respect to a thickness. Math. Nachr., 125: 135-151, 1986.
• [2] I. Bock, J. Lovíšek. Optimal control problems for variational inequalities with controls in coefficients and in unilateral constraints. Application of Math., 32: 301-314, 1987.
• [3] W. Findeisen, J. Szymanowski, A. Wierzbicki. Theory and numerical methods of optimization (in Polish). Polish Scientific Publisher, Warsaw, 1980.
• [4] E.J. Haug, B. Rousselet. Design sensitivity analysis in structural mechanics. Eigenvalue variations. J. Structural Mech., 8: 161-186, 1980.
• [5] I. Hlaváček, I. Bock, J. Lovíšek. Optimal control of a variational inequality with application to structural analysis II, III. Appl. Math. and Optim., 13: 117-139, 1985.
• [6] J.E. Lagnese, J.L. Lions. Modelling analysis and control of thin plates. Masson-Springer Verlag, Paris-Berlin, 1989.
• [7] C. Lemarechal, R. Mifflin. Nonsmooth optimization. Pergamon Press, Oxford, 1978.
• [8] J. Lovíšek, J. Štangl. Optimal design of a thickness a thin isotropic plate with respect to the spectral problem. In: Dynamics of Structures. Proc. of the Conference, Karlovy Vary, 1989.
• [9] A. Myslinski, J. Sokolowski. Nondifferentiable optimization problems for elliptic systems. SIAM J. Control and Optimization, 23: 632-648, 1985.
• [10] J. Nečas, I. Hlaváček. Mathematical theory of elastic and elasto-plastic bodies. Elsevier, Amsterdam-Oxford-New York, 1981.