Free Vibration Analysis of Fiber-Reinforced Plastic Composite Cantilever I-Beams

An analytical study for dynamic behavior of pultruded fiber-reinforced plastic (FRP) composite cantilever I-beams is presented. Based on a Vlasov-type linear hypothesis, dynamic beam mass and stiffness coefficients, which account for both cross-section geometry and material anisotropy of the beam, are obtained. The eigenfrequency problem is solved by a Ritz energy method, and both exact transcendental and polynomial shape functions satisfying the boundary conditions of cantilever beams are used to describe the modal shapes. Good agreement between the proposed analytical method and finite-element analysis is obtained. The effect of beam span length, fiber orientation, and fiber volume fraction on natural frequencies is investigated. The proposed analytical solution can be used to effectively predict the vibration behavior of FRP cantilever I-beams.

[1]  Vladimir Kobelev,et al.  Model of thin-walled anisotropic rods , 1988 .

[2]  Julio F. Davalos,et al.  Equations facilitate composite designs , 1999 .

[3]  Ohseop Song,et al.  DYNAMIC RESPONSE OF ANISOTROPIC THIN-WALLED BEAMS TO BLAST AND HARMONICALLY OSCILLATING LOADS , 1998 .

[4]  I. Elishakoff,et al.  Novel closed – form solutions in buckling of inhomogeneous columns under distributed variable loading , 2001 .

[5]  E. H. Mansfield.  The Stiffness of a Two-Cell Anisotropic Tube , 1981 .

[6]  Erian A. Armanios,et al.  Theory of composite thin-walled opened-cross-section beams , 1993 .

[7]  Julio F. Davalos,et al.  On the Mechanics of Thin-Walled Laminated Composite Beams , 1993 .

[8]  C. Libove.  Stresses and rate of twist in single-cell thin-walled beams with anisotropic walls , 1988 .

[9]  Julio F. Davalos,et al.  Analysis and design of pultruded FRP shapes under bending , 1996 .

[10]  Inderjit Chopra,et al.  Experimental and theoretical analysis of composite I-beams with elastic couplings , 1991 .

[11]  Noel W. Murray,et al.  Introduction to the theory of thin-walled structures , 1984 .

[12]  C. Sun,et al.  Simplified theory for composite thin-walled beams , 1992 .

[13]  Coupled elastic response of open section laminated composite beams subject to generalized beam loading , 1992 .

[14]  E. Barbero.  Introduction to Composite Materials Design , 1998 .

[15]  Ever J. Barbero,et al.  A Strength of Materials Formulation for Thin Walled Composite Beams with Torsion , 1998 .

[16]  Shive K. Chaturvedi,et al.  Laminated composite open profile sections: non-uniform torsion of I-sections , 2000 .

[17]  Olivier A. Bauchau,et al.  Composite Box Beam Analysis: Theory and Experiments , 1987 .

[18]  An exact symplectic geometry solution for the static and dynamic analysis of Reissner plates , 1998 .

[19]  A. Gjelsvik,et al.  The Theory of Thin-Walled Bars , 1981 .

[20]  Ohseop Song,et al.  VIBRATION AND STABILITY OF PRETWISTED SPINNING THIN-WALLED COMPOSITE BEAMS FEATURING BENDING–BENDING ELASTIC COUPLING , 2000 .

[21]  Nelson R. Bauld,et al.  A Vlasov theory for fiber-reinforced beams with thin-walled open cross sections , 1984 .

[22]  Leonard Meirovitch,et al.  Convergence of the classical Rayleigh-Ritz method and the finite element method , 1990 .

[23]  W. R. Dean.  On the Theory of Elastic Stability , 1925 .

[24]  Liviu Librescu,et al.  Free Vibration Of Anisotropic Composite Thin-Walled Beams Of Closed Cross-Section Contour , 1993 .