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

  • Igor Bock Slovak University of Technology in Bratislava
  • Ján Lovíšek Slovak University of Technology in Bratislava


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.



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May 31, 2023
How to Cite
BOCK, Igor; LOVÍŠEK, Ján. On optimum design of a vibrating plate with respect to its thickness and eigen-frequencies. Computer Assisted Methods in Engineering and Science, [S.l.], v. 5, n. 2, p. 139-150, may 2023. ISSN 2956-5839. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/1350>. Date accessed: 18 july 2024.