@article{CAMES, author = {Igor Bock and JĂĄn LovĂ­ĹĄek}, title = { On optimum design of a vibrating plate with respect to its thickness and eigen-frequencies}, journal = {Computer Assisted Methods in Engineering and Science}, volume = {5}, number = {2}, year = {2023}, keywords = {}, abstract = {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.}, issn = {2956-5839}, pages = {139--150}, url = {https://cames.ippt.gov.pl/index.php/cames/article/view/1350} }