Free vibration analysis of ribbed plates by a combined analytical–numerical method

An easy to code and computationally efficient analytical–numerical method for quick prediction of the modal characteristics of rectangular ribbed plates is presented. The approach is suitable for low-frequency free vibration analysis of thin rectangular plates reinforced by a small number of light stiffeners. The assumed-modes method is used to formulate the equations of motion of the plate and the rib separately. The motion of the built-up structure is then obtained by enforcing appropriate continuity conditions between the two. The resulting sparse generalized eigenvalue problem can be profitably solved by reliable methods to calculate only a small set of selected eigenmodes. An alternative formulation is also proposed for the single-ribbed case which leads to a compact analytical form of the frequency equation whose solution can be easily determined either graphically or numerically. The present method demonstrates good agreement with published results and standard finite element analysis.