Sage Journals: Discover world-class research

Abstract

The free vibration characteristics of a nonsymmetric cross-ply laminated composite beam coupled in bending and longitudinal deformation is studied using a wave approach. The effects of shear deformation and rotary inertia are included in the analysis. Exact analytical expressions are derived for the natural frequencies, mode shapes, and the power flow of the propagating waves. The derived expressions are validated using the results from past literature and provide a benchmark for numerical models. The advantages of the wave approach over conventional free vibration analysis methods are highlighted. Specifically, the wave approach is used to derive a simplified expression for the mode count function of the composite beam. Additionally, the wave approach is also used to investigate the power flow and cross-conversion of the propagating wavetypes across various classical boundary conditions. The influence of the number of cross-ply layers on the natural frequencies and power flow are also investigated. The efficacy of the wave analysis is illustrated through several numerical examples.

Keywords

Composite beam mode count nonsymmetric cross-ply power flow wave analysis

Get full access to this article

View all access options for this article.

References

Sahoo

Panda

Singh

VK.

Experimental and numerical investigation of static and free vibration responses of woven glass/epoxy laminated composite plate. Proc IMechE, Part L: J Materials: Design and Applications 2017; 231: 463–478.

Foster

NG.

Designing composite structures for optimum inservice performance with reference to the Firefly aircraft and the Jetstream baggage pod. Proc IMechE, Part L: J Materials: Design and Applications 2000; 214: 51–60.

Vinson

Sierakowski

RL.

The behavior of structures composed of composite materials. 2nd ed. Dordrecht: Springer, 2006.

Chen

Yang

TY.

Static and dynamic formulation of a symmetrically laminated beam finite element for a microcomputer. J Compos Mater 1985; 19: 459–475.

Chandrashekhara

Krishnamurthy

Roy

Free vibration of composite beams including rotary inertia and shear deformation. Compos Struct 1990; 14: 269–279.

Singh

Abdelnaser

AS.

Random response of symmetric cross-ply composite beams with arbitrary boundary conditions. AIAA J 1992; 30: 1081–1088. https://doi.org/10.2514/3.11030.

Abramovich

Livshits

Free vibrations of non-symmetric cross-ply laminated composite beams. J Sound Vib 1994; 176: 1512–1520.

Eisenberger

Abramovich

Shulepov

Dynamic stiffness analysis of laminated beams using a first order shear deformation theory. Compos Struct 1995; 31: 265–271.

Abramovich

Eisenberger

Shulepov

Vibrations of multi-span non-symmetric composite beams. Compos Eng 1995; 5: 397–404.

10.

Abramovich

Eisenberger

Shulepov

Vibrations and buckling of cross-ply nonsymmetric laminated composite beams. AIAA J 1996; 34: 1064–1069.

11.

Polyanin

Chernoutsan

A concise handbook of mathematics, physics, and engineering sciences. 1st ed. Boca Raton, FL: CRC Press, 2010.

12.

Mei

Effect of material coupling on wave vibration of composite Timoshenko beams. J Vib Acoust 2005; 127: 333–340.

13.

Mace

BR.

Wave reflection and transmission in beams. J Sound Vib 1984; 97: 237–246.

14.

Cremer

Heckl

Petersson

BA.

Structure-borne sound: structural vibrations and sound radiation at audio frequencies. Berlin: Springer Science Business Media, 2005.

15.

Xie

Thompson

Jones

CJC.

Mode count and modal density of structural systems: relationships with boundary conditions. J Sound Vib 2004; 274: 621–651.

16.

Hansen

CH.

Foundations of vibroacoustics. Boca Raton, FL: CRC Press, 2018.

17.

Jones

RM.

Buckling and vibration of unsymmetrically laminated cross-ply rectangular plates. AIAA J 1973; 11: 1626–1632.

18.

Bachoo

Bridge

Random vibration analysis and modal energy characteristics of fiber reinforced composite beams.

Proc IMechE, Part L: J Materials: Design and Applications 2020. DOI: 10.1177/1464420720958746.

19.

Lyon

DeJong

RG.

Theory and application of statistical energy analysis. Cambridge, MA: MIT Press, 1995.

20.

Maxit

Guyader

JL.

Extension of SEA model to subsystems with non-uniform modal energy distribution. J Sound Vib 2003; 265: 337–358.

Wave characteristics of nonsymmetric cross-ply laminated composite beams

Abstract

Keywords

Get full access to this article

References