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On the angle ply higher order beam vibrations

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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

  1. Chandrashekhara K, Krishnamurthy K, Roy S (1990) Free vibration of composite beams including rotary inertia and shear deformation. J Compos Struct 14:269–279

    Article  Google Scholar 

  2. 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

    Article  MATH  Google Scholar 

  3. Teh KK, Huang CC (1979) The vibrations of generally orthotropic beams—a finite element approach. J Sound Vibrat 62:195–206

    Article  MATH  Google Scholar 

  4. Ahmed KM (1972) Dynamic analysis of sandwich beams. J Sound Vibrat 21:263–276

    Article  MATH  Google Scholar 

  5. Abramovich H, Livshits A (1994) Free vibrations of non-symmetric cross-ply laminated composite beams. J Sound Vibrat 176:597–612

    Article  MATH  Google Scholar 

  6. 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

    Article  Google Scholar 

  7. 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

    Google Scholar 

  8. 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

    Google Scholar 

  9. Matsunaga H (2001) Vibration and buckling of multilayered composite beams according to higher order deformation theories. J Sound Vibrat 246:47–62

    Article  Google Scholar 

  10. 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

    MATH  Google Scholar 

  11. Jones RM (1975) Mechanics of composite materials. McGraw-Hill Kogakusha, Tokyo

    Google Scholar 

  12. 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

    MATH  Google Scholar 

  13. Bathe KJ (1982) Finite element procedures in engineering analysis. Prentice Hall, New Jersey

    Google Scholar 

  14. Chen JK, Sun CT (1985) Nonlinear transient responses of initially stressed composite plates. Comput Struct 21:513–520

    Article  MATH  Google Scholar 

  15. Allen HG (1969) Analysis and design of structural sandwich panels. Pergamon Press, London

    Google Scholar 

  16. Reddy JN (1982) On the solutions to forced motions of rectangular composite plates. Am Soc Mech Eng J Appl Mech 49:403–408

    MATH  Google Scholar 

  17. Timoshenko SP (1921) On the correction for shear in differential equation for transverse vibrations of prismatic bars. Philos Mag Ser 41:744–746

    Article  Google Scholar 

  18. 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

    Article  Google Scholar 

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Correspondence to Sudhakar R. Marur.

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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

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