Analytical-experimental investigation of free-vibration characteristics of rotating composite I-beams

This article presents a free-vibration analysis of coupled composite I-beams with couplings under rotation. A linear analysis based upon Vlasov theory was developed to obtain coupled flap-lag-torsion equations of motion for I-beams made out of general composite laminates. Constrained warping and transverse shear effects were included. Free-vibration characteristics were obtained by solving these equations using Galerkin's method. In order to validate the theory, graphite-epoxy and kevlar-epoxy I-beams with bending-torsion coupling were fabricated using an autoclave molding technique and tested in an in vacuo rotor test facility for their vibration characteristics. Induced-strain actuation by piezoceramic elements was used to excite the I-beams in the rotating frame. Strain gauges were used to measure the response of these beams over a range of rotational speeds up to 1000 rpm. Natural frequencies and strain mode shapes were determined by carrying out signal analysis using a spectrum analyzer. Good correlation between theory and experiment was achieved. About 600% increase in torsional frequency due to constrained warping occurs for graphite-epoxy beams with a slenderness ratio of 18. Nomenclature A = cross-sectional area of blade b, h = semiwidth and semiheight of I-beam Eh Et — Young's moduli in principal directions of plies of beam Glt - shear modulus of plies in principal plane Ixx, Iyy = blade cross-sectional moment of inertia about x and y axes, respectively K] - stiffness matrix for beam Kf] = flap bending stiffness matrix Kft] — flap bending-torsion coupling stiffness matrix K] = lag bending stiffness matrix K!t] - lag bending-torsion coupling stiffness matrix [Kt] = torsion stiffness matrix KA = effective polar radius of gyration of blade cross-section V(/vv + IXX)IA