An optimal control problem with respect to variable thicknesses for a vibrating elastic plate in a contact with a rigid obstacle

作     者：Bock, Igor 

作者机构：Institute of Computer Science and Mathematics FEI Slovak University of Technology Ilkovičova 3 Bratislava 81219 Slovakia 

出 版 物：《SeMA Journal》 (SeMA. J.)

年 卷 期：2025年第82卷第2期

页      面：251-266页

学科分类：0820[工学-石油与天然气工程] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 0702[理学-物理学] 

基　　金：Ministerstvo školstva, vedy, výskumu a športu Slovenskej republiky, (VEGA-1/0637/23) Ministerstvo školstva, vedy, výskumu a športu Slovenskej republiky 

主　　题：Optimal control Penalization Rigid obstacle Variable thickness Vibrating elastic plate 

摘      要：We deal with an optimal control problem governed by a hyperbolic variational inequality describing perpendicular vibrations of a simply supported anisotropic elastic plate against a rigid obstacle. A variable thickness of a plate plays the role of a control variable. The state problem is not uniquely solved. In order to overcome the problem of a priori estimates of states we restrict the admissible set to solutions obtained through a penalization method. We verify the existence of an optimal thickness function as a limit of the sequence of thicknesses solving the case of the penalized state problem. © The Author(s) 2025.