Vibration analysis of thin-walled composite beams with I-shaped cross-sections

A general analytical model applicable to the vibration analysis of thin-walled composite I-beams with arbitrary lay-ups is developed. Based on the classical lamination theory, this model has been applied to the investigation of load–frequency interaction curves of thin-walled composite beams under various loads. The governing differential equations are derived from the Hamilton’s principle. A finite element model with seven degrees of freedoms per node is developed to solve the problem. Numerical results are obtained for thin-walled composite I-beams under uniformly distributed load, combined axial force and bending loads. The effects of fiber orientation, location of applied load, and types of loads on the natural frequencies and load–frequency interaction curves as well as vibration mode shapes are parametrically studied.

[1]  R. Barsoum.  Finite element method applied to the problem of stability of a non‐conservative system , 1971 .

[2]  M. Attard,et al.  Stability of thin-walled open beams under nonconservative loads , 1987 .

[3]  Kappyo Hong,et al.  Lateral buckling of I-section composite beams , 2002 .

[5]  Gábor M. Vörös.  On coupled bending–torsional vibrations of beams with initial loads , 2009 .

[6]  Samir A. Emam,et al.  Postbuckling and free vibrations of composite beams , 2009 .

[7]  J. R. Banerjee,et al.  Free vibration of axially loaded composite Timoshenko beams using the dynamic stiffness matrix method , 1998 .

[8]  Jaehong Lee,et al.  Flexural–torsional buckling of thin-walled I-section composites , 2001 .

[9]  M. Ohga,et al.  Natural frequencies and mode shapes of thin-walled members , 1995 .

[10]  Dinar Camotim,et al.  Local and global vibration of thin-walled members subjected to compression and non-uniform bending , 2008 .

[11]  Metin O. Kaya,et al.  Flexural torsional-coupled vibration analysis of axially loaded closed-section composite Timoshenko beam by using DTM , 2007 .

[12]  V. Vlasov.  Thin-walled elastic beams , 1961 .

[13]  George Z. Voyiadjis,et al.  Mechanics of Composite Materials with MATLAB , 2005 .

[14]  Hongxing Hua,et al.  Dynamic stiffness analysis for free vibrations of axially loaded laminated composite beams , 2008 .

[15]  Seunghye Lee,et al.  Flexural–torsional behavior of thin-walled composite beams , 2004 .

[16]  A. Leung.  Dynamic buckling of columns by biaxial moments and uniform end torque , 2010 .

[17]  Jaehong Lee,et al.  Free vibration of thin-walled composite beams with I-shaped cross-sections , 2002 .

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

[19]  L. Azrar,et al.  Vibration analysis of buckled thin-walled beams with open sections , 2004 .

[20]  Andrew Y. T. Leung,et al.  Exact dynamic stiffness for axial-torsional buckling of structural frames , 2008 .

[21]  Frederic Ward Williams,et al.  EXACT DYNAMIC STIFFNESS MATRIX FOR COMPOSITE TIMOSHENKO BEAMS WITH APPLICATIONS , 1996 .

[22]  Stephen P. Timoshenko,et al.  Vibration problems in engineering , 1928 .

[23]  Víctor H. Cortínez,et al.  Free vibration of thin-walled composite beams with static initial stresses and deformations , 2007 .

[24]  Andrew Y. T. Leung,et al.  Dynamic Axial-Moment Buckling of Linear Beam Systems by Power Series Stiffness , 2009 .

[25]  Dinar Camotim,et al.  GBT-BASED LOCAL AND GLOBAL VIBRATION ANALYSIS OF LOADED COMPOSITE OPEN-SECTION THIN-WALLED MEMBERS , 2006 .

[26]  S. Suryanarayan,et al.  Unified analytical solution for various boundary conditions for the coupled flexural-torsional vibration of beams subjected to axial loads and end moments , 1989 .

[27]  Hongxing Hua,et al.  Bending-torsional coupled dynamic response of axially loaded composite Timosenko thin-walled beam with closed cross-section , 2004 .

[28]  Dinar Camotim,et al.  Vibration behaviour of axially compressed cold-formed steel members , 2006 .

[29]  S. Timoshenko.  Theory of Elastic Stability , 1936 .