Frequency Determination Techniques for Cantilevered Plates with Bending-Torsion Coupling.

Abstract

Various techniques for solution of the variational statement governing vibration of cantilevered composite plates are compared. The partial Ritz (Kantorovich) method assumes mode shapes only in the chordwise direction and reduces the problem to a set of ordinary differential equations. The important nondimensional parameters for cantilevered plates with bending-torsion coupling then are identified easily, including two that express the relative contribution of the warping stiffness to torsional vibration (/366) and chordwise vibration (£22)- The Rayleigh-Ritz solution, requiring assumed mode shapes in both directions, reveals the fundamental coupling mechanisms affecting the natural mode shapes and frequencies. The finite element method yields direct accurate results, yet masks the fundamental behavior. Experiments were performed to provide data for correlation with the analyses. The various solution techniques provide different levels of insight into the fundamental vibration characteristics of cantilevered plates with bending-torsion coupling, including the importance of chordwise flexure in the torsional vibration modes.