A Thick-Beam Library Solution Method for Vibration-Based Characterization of Thick Composite Plates

Abstract

A method is presented for obtaining the modal solutions to the free lateral vibrations of a rectangular orthotropic plate of thickness appreciable enough that through-the-thickness shear and rotary inertia are important. The Rayleigh method is applied to the Timoshenko beam in this approach, which also utilizes optimized modes. The plate solution was synthesized from those of beams lying wholly in each of the two transverse directions. For thin plates, the Rayleigh method with optimized modes gives results of comparable accuracy with other methods employing 36 (six per direction) modes, and thus presents a significant advantage. However, the necessary numerical solution of the hyperbolic thick beam frequency equations takes much more computer resources than for a thin beam. Many important procedures, such as the material identification and damage characterization of thick plates, generally utilize multitudes of trial solutions of this forward problem. Procedures for speeding up the forward solution are therefore of great importance. Possible pathways for arriving at such procedures are examined. Investigation of the behavior of the fundamental vibration mode, which is usually the most important structural mode, suggests the feasibility of setting up of a solution library for a thick beam rather than for a plate directly. The thick beam solution library is developed and an interpolation algorithm is created. The library is utilized for the forward plate problem. Results with and without the library are compared, and they show that the beam solution library method is indeed accurate and achieves significant savings on computation time.