This paper presents a new analytical solution for the vibration response of a beamstiffened Mindlin plate having a completely free boundary condition by utilizing a finite cosine integral transform.In the solution,the...This paper presents a new analytical solution for the vibration response of a beamstiffened Mindlin plate having a completely free boundary condition by utilizing a finite cosine integral transform.In the solution,the unknown coupling force and moments at the beam/plate interface and the unknown modal constants from the integral transform are determined by the continuity and compatibility conditions at the interface as well as the boundary conditions.It provides an easily implemented tool for exploring complex edge value problems for a class of higher-order partial differential equations represented by fully free‐stiffened Mindlin thick plates.The validity of the model is evaluated by comparing the calculated free and forced vibration responses of the beam‐stiffened plate with those calculated using a beamstiffened thin plate and those from finite element analysis.展开更多
We consider a family of optimal control problems where the control variable is given by a boundary condition of Neumann type. This family is governed by parabolic variational inequalities of the second kind. We prove ...We consider a family of optimal control problems where the control variable is given by a boundary condition of Neumann type. This family is governed by parabolic variational inequalities of the second kind. We prove the strong convergence of the optimal control and state systems associated to this family to a similar optimal control problem. This work solves the open problem left by the authors in IFIP TC7 CSMO2011.展开更多
基金The financial support from the Qingdao Postdoctoral Applied Research Program(No.862205040040)for this work is gratefully acknowledged.
文摘This paper presents a new analytical solution for the vibration response of a beamstiffened Mindlin plate having a completely free boundary condition by utilizing a finite cosine integral transform.In the solution,the unknown coupling force and moments at the beam/plate interface and the unknown modal constants from the integral transform are determined by the continuity and compatibility conditions at the interface as well as the boundary conditions.It provides an easily implemented tool for exploring complex edge value problems for a class of higher-order partial differential equations represented by fully free‐stiffened Mindlin thick plates.The validity of the model is evaluated by comparing the calculated free and forced vibration responses of the beam‐stiffened plate with those calculated using a beamstiffened thin plate and those from finite element analysis.
基金partly supported by the Institut Camille Jordan ST-Etienne Universitythe projects Argentine ANPCyT PICTO Austral 2008 # 73 and SOARD-AFOSR (No. FA9550-10-1-0023)
文摘We consider a family of optimal control problems where the control variable is given by a boundary condition of Neumann type. This family is governed by parabolic variational inequalities of the second kind. We prove the strong convergence of the optimal control and state systems associated to this family to a similar optimal control problem. This work solves the open problem left by the authors in IFIP TC7 CSMO2011.
