Analytical modeling on the vibration response of a beam‐stiffened Mindlin thick plate with free boundary conditions

Abstract

Abstract This paper presents a new analytical solution for the vibration response of a beam‐stiffened 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 beam‐stiffened thin plate and those from finite element analysis.

Keywords

• vibration
• beam‐stiffened mindlin thick plate
• free boundary condition
• finite integral transform