Abstract
Vibrations of angle ply laminated beams are studied using the higher order theory and isoparametric 1d finite element formulations through proper constitution of elasticity matrix. Subsequent to the validation of the formulation, deep sandwich and composite beams are critically analyzed for various boundary conditions. Frequencies classified based on their spectrum are presented along with those of first order theories for comparison.
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References
Chandrashekhara K, Krishnamurthy K, Roy S (1990) Free vibration of composite beams including rotary inertia and shear deformation. J Compos Struct 14:269–279
Chandrashekhara K, Bangera KM (1993) Vibration of symmetrically laminated clamped-free beam with a mass at the free end. J Sound Vibrat 160:93–101
Teh KK, Huang CC (1979) The vibrations of generally orthotropic beams—a finite element approach. J Sound Vibrat 62:195–206
Ahmed KM (1972) Dynamic analysis of sandwich beams. J Sound Vibrat 21:263–276
Abramovich H, Livshits A (1994) Free vibrations of non-symmetric cross-ply laminated composite beams. J Sound Vibrat 176:597–612
Marur SR, Kant T (1996) Free vibration analysis of fiber reinforced composite beams using higher order theories and finite element modeling. J Sound Vibrat 194:337–351
Marur SR, Kant T (1998) A higher order finite element model for the vibration analysis of laminated beams. Am. Soc Mech Eng J Vibrat Acoust 120:822–824
Yildirim V, Sancaktar E, Kiral E (1999) Comparison of the in-plane natural frequencies of symmetric cross-ply laminated beams based on the Bernoulli–Euler and Timoshenko beam theories. Am Soc Mech Eng J Appl Mech 66:410–417
Matsunaga H (2001) Vibration and buckling of multilayered composite beams according to higher order deformation theories. J Sound Vibrat 246:47–62
Lo KH, Christensen RM, Wu EM (1977) A higher order theory of plate deformation—part1: homogenous plates. Am Soc Mech Eng J Appl Mech 44:663–668
Jones RM (1975) Mechanics of composite materials. McGraw-Hill Kogakusha, Tokyo
Vinayak RU, Prathap G, Naganarayana BP (1996) Beam elements based on a higher order theory—I. Formulation and analysis of performance. Comput Struct 58:775–789
Bathe KJ (1982) Finite element procedures in engineering analysis. Prentice Hall, New Jersey
Chen JK, Sun CT (1985) Nonlinear transient responses of initially stressed composite plates. Comput Struct 21:513–520
Allen HG (1969) Analysis and design of structural sandwich panels. Pergamon Press, London
Reddy JN (1982) On the solutions to forced motions of rectangular composite plates. Am Soc Mech Eng J Appl Mech 49:403–408
Timoshenko SP (1921) On the correction for shear in differential equation for transverse vibrations of prismatic bars. Philos Mag Ser 41:744–746
Kant T, Marur SR, Rao GS (1998) Analytical solution to the dynamic analysis of laminated beams using higher order refined theory. Compos Struct 40:1–9
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Marur, S.R., Kant, T. On the angle ply higher order beam vibrations. Comput Mech 40, 25–33 (2007). https://doi.org/10.1007/s00466-006-0079-0
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DOI: https://doi.org/10.1007/s00466-006-0079-0