Free Vibration Analysis of a Laminated Shallow Curved Beam Based on Trigonometric Shear Deformation Theory

REFERENCES

• Banerjee , J. R. ( 1997 ). Dynamic stiffness formulation for structural elements: A general approach . Computers and Structures 63 : 101 – 103 .
   Web of Science ®Google Scholar
• Bhimaraddi , A. , Carr , A. J. , Moss , P. J. ( 1989 ). Generalized finite element analysis of laminated curved beams with constant curvature . Computers and Structures 31 : 309 – 317 .
   Web of Science ®Google Scholar
• Chidamparam , P. , Leissa , A. W. ( 1993 ). Vibrations of planar curved beams, rings, and arches . Applied Mechanics Review 46 : 467 – 483 .
   Google Scholar
• Collins , J. S. , Johnson , E. R. ( 1992 ). Static and dynamic response of graphite-epoxy curved frames . Journal of Composite Materials 26 : 792 – 803 .
   Web of Science ®Google Scholar
• DiTaranto , R. A. ( 1973 ). Free and forced response of a laminated ring . Journal of the Acoustical Society of America 53 : 748 – 757 .
   Web of Science ®Google Scholar
• Ecsedi , I. , Dluhi , K. ( 2005 ). A linear model for the static and dynamic analysis of non-homogeneous curved beams . Applied Mathematical Modelling 29 : 1211 – 1231 .
   Web of Science ®Google Scholar
• Hajianmaleki , M. , Qatu , M. S. ( 2012a ). Static and vibration analyses of thick, generally laminated deep curved beams with different boundary conditions . Composites Part B 43 : 1767 – 1775 .
   Web of Science ®Google Scholar
• Hajianmaleki , M. , Qatu , M. S. ( 2012b ). A rigorous beam model for static and vibration analysis of generally laminated composite thick beams and shafts . International Journal of Vehicle Noise and Vibration 8 : 166 – 184 .
   Google Scholar
• Hajianmaleki , M. , Qatu , M. S. ( 2013a ). Transverse vibration analysis of generally laminated two-segment composite shafts with a lumped mass using generalized differential quadrature . Journal of Vibration and Control 19 : 2013 – 2021 .
   Web of Science ®Google Scholar
• Hajianmaleki , M. , Qatu M. S. ( 2013b ). Vibrations of straight and curved composite beams: A review . Composite Structures 100 : 218 – 232 .
   Web of Science ®Google Scholar
• Jones , R. M. ( 1976 ). Mechanics of Composite Materials . New York : McGraw-Hill .
   Google Scholar
• Khdeir , A. A. , Reddy , J. N. ( 1997 ). Free and forced vibration of cross-ply laminated composite shallow arches . International Journal of Solids and Structures 34 : 1217 – 1234 .
   Web of Science ®Google Scholar
• Kim , J. G. ( 2006 ). An effective composite laminated curved beam element . Communications in Numerical Methods in Engineering 22 : 453 – 466 .
   Web of Science ®Google Scholar
• Kovacs , B. ( 2001 ). Free vibration of a laminated circular ring segment . Journal of Sound and Vibration 245 : 653 – 667 .
   Web of Science ®Google Scholar
• Laura , P. A. A. , Maurizi , M. J. ( 1987 ). Recent research on vibrations of arch type structures . Shock and Vibration Digest 19 : 6 – 9 .
   Google Scholar
• Lin , K. C. , Hsieh , C. M. (2007). The closed form general solutions of 2-D curved laminated beams of variable curvatures. Composite Structures 79:606–618.
   Web of Science ®Google Scholar
• Lu , Q. , Lu , C. F. ( 2008 ). Exact two-dimensional solutions for in-plane natural frequencies of laminated circular arches . Journal of Sound and Vibration 318 : 982 – 990 .
   Web of Science ®Google Scholar
• Malekzadeh , P. , Setoodeh , A. R. ( 2009 ). DQM in-plane free vibration of laminated moderately thick circular deep arches . Advances in Engineering Software 40 : 798 – 803 .
   Web of Science ®Google Scholar
• Malekzadeh , P. , Setoodeh , A. R. , Barmshouri , E. ( 2008 ). A hybrid layerwise and differential quadrature method for in-plane free vibration of laminated thick circular arches . Journal of Sound and Vibration 315 : 212 – 225 .
   Web of Science ®Google Scholar
• Markus , S. , Nanasi , T. ( 1981 ). Vibration of curved beams . Shock and Vibration Digest 13 : 3 – 14 .
   Google Scholar
• Matsunaga , H. ( 2004 ). Free vibration and stability of laminated composite circular arches subjected to initial axial stress . Journal of Sound and Vibration 271 : 651 – 670 .
   Web of Science ®Google Scholar
• Patel , B. P. , Ganapathi , M. , Saravanan , J. ( 1999 ). Shear flexible field-consistent curved spline beam element for vibration analysis . International Journal for Numerical Methods in Engineering 46 : 387 – 407 .
   Web of Science ®Google Scholar
• Qatu , M. S. ( 1992 ). In-plane vibration of slightly curved laminated composite beams . Journal of Sound and Vibration 159 : 327 – 338 .
   Web of Science ®Google Scholar
• Qatu , M. S. ( 1993 ). Theories and analyses of thin and moderately thick laminated composite beams . International Journal of Solids and Structures 30 : 2743 – 2756 .
   Web of Science ®Google Scholar
• Qatu , M. S. , Elsharkawy , A. A. ( 1993 ). Vibration of laminated composite arches with deep curvature and arbitrary boundaries . Computers and Structures 47 : 305 – 311 .
   Web of Science ®Google Scholar
• Raveendranath , P. , Singh , G. , Pradhan , B. ( 2000 ). Application of coupled polynomial displacement fields to laminated beam elements . Computers and Structures 78 : 661 – 670 .
   Web of Science ®Google Scholar
• Rossettos , J. N. ( 1971 ). Vibration of slightly curved beams of transversely isotropic composite materials . AIAA Journal 9 : 2273 – 2275 .
   Web of Science ®Google Scholar
• Rossettos , J. N. , Squires , D. C. ( 1973 ). Modes and frequencies of transversely isotropic slightly curved Timoshenko beams . ASME Journal of Applied Mechanics 40 : 1029 – 1033 .
   Web of Science ®Google Scholar
• Surana , K. S. , Nguyen , S. H. ( 1990 ). Two-dimensional curved beam element with higher-order hierarchical transverse approximation for laminated composites . Computers and Structures 36 : 499 – 511 .
   Web of Science ®Google Scholar
• Touratier , M. ( 1991 ). An efficient standard plate theory . International Journal of Engineering Science 29 : 901 – 916 .
   Web of Science ®Google Scholar
• Tseng , Y. P. , Huang , C. S. , Kao , M. S. ( 2000 ). In-plane vibration of laminated curved beams with variable curvature by dynamic stiffness analysis . Composite Structures 50 : 103 – 114 .
   Web of Science ®Google Scholar
• Wittrick , W. H. , Williams , F. W. ( 1971 ). A general algorithm for computing natural frequencies of elastic structures . The Quarterly Journal of Mechanics and Applied Mathematics 24 : 263 – 284
   Web of Science ®Google Scholar
• Wolfram , S. ( 1991 ). Mathematica: A System for Doing Mathematics by Computer. , 2nd ed. Reading , MA : Addison-Wesley .
   Google Scholar
• Yildirim , V. ( 1999a ). In-plane free vibration of symmetric cross-ply laminated circular bars . ASCE Journal of Engineering Mechanics 125 : 630 – 636 .
   Web of Science ®Google Scholar
• Yildirim , V. (1999b). Rotary inertia, axial and shear deformation effects on the in-plane natural frequencies of symmetric cross-ply laminated circular arches. Journal of Sound and Vibration 224:575–589.
   Web of Science ®Google Scholar
• Yildirim , V. ( 2001 ). Common effects of the rotary inertia and shear deformation on the out-of-plane natural frequencies of composite circular bars . Composites Part B: Engineering 32 : 687 – 695 .
   Web of Science ®Google Scholar
• #Communicated by S. Sinha.
   Google Scholar