Formulation of Mindlin-Engesser model for stiffened plate vibration

In this paper, a Mindlin-Engesser model is developed for the vibration analysis of moderately thick plates with arbitrarily oriented stiffeners. The theoretical derivation incorporates the Mindlin theory to account for the effects of transverse shear deformation and rotary inertia of plates, and the Engesser theory to account for the shear deformation of stiffeners with the inclusion of torsion effect. In the method of solution, the resulting energy functionals are minimized using the Ritz procedure with a set of admissible two-dimensional functions expressed in the form of simple polynomials. The key kinematic feature of these shape functions is that they are boundary oriented and no boundary losses are introduced as in discretization methods. With the aim of demonstrating the applicability and versatility of the method, numerical examples including plates of various shapes with arbitrarily oriented stiffeners are presented. Several findings and conclusions regarding the method have been highlighted and discussed.