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Dynamic Investigation of FRP Cracked Beam Using Neural Network Technique

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Journal of Vibration Engineering & Technologies Aims and scope Submit manuscript

Abstract

Purpose

In the present investigation, vibration signatures have been used for identifying the place of crack and depth in pre-cracked FRP beams. Bidirectional (woven) FRP composite beams are consisting of 13 layers of epoxy–glass fibres (0°/7.5°/15°/22.5°/30°/37.5°/45°). Effects of clamped–free and clamped–clamped end conditions have been studied in the current investigation.

Methods

Fibre orientations effect on dynamics of FRP beam by the altering transverse crack location and its depth have been observed by applying analytical, finite element method, and neural network techniques.

Results

The results obtained have been verified experimentally. The outcomes of both methods have deviation within 6% during comparison.

Conclusion

From the investigation, it has been concluded that the natural frequencies and mode shapes can be used for identifying crack location and crack depth for different fibre orientation in FRP beam.

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Abbreviations

A:

Cross-sectional area of the of FRP beam

C-F:

Clamp–free end condition

Cij :

Flexibility influence matrix

E:

Modulus of elasticity of the FRP beam material

FRP:

Fibre-reinforced plastic composite

F i (i = 1, 2):

Function determined experimentally

H :

Thickness of the beam

h 1 :

Pre-crack depth

I :

Moment of inertia

i, j :

Variables

J C :

Release rate of strain energy

K Ii (i = 1, 2):

Intensity factor of stress used for Pi load

K ij :

Local flexible element matrix

L :

Length of the FRP beam

L 1 :

Crack locale in FRP beam from one end

M i (i = 1, 4):

Compliance constant

P i (i = 1, 2):

Pi = axial force (i = 1) and Pj = bending load (i = 2)

K :

Stiffness matrix

u i (i = 1, 2):

Additional displacement functions

U c :

Strain energy caused by pre-crack

W :

FRP beam breadth

X, Y, and Z :

Reference co-ordinate for FRP beam

Y 0 :

Exciting vibration amplitude

y i (i = 1, 2):

Standard function (transverse) yi(x)

ω n :

Natural frequency of un-cracked FRP composite beam (NFUCB)

ω c :

Frequency of cracked FRP composite beam (FCCB)

∆ω :

(ωn) − (ωc)

(∆ω/ω n):

Relative eigen frequency (REF)

(ω c/ω n):

Relative natural frequency (RNF)

χ :

Relative crack depth (RCD = \(\frac{{h_{1} }}{H}\)) 

\(\psi\) :

Relative crack location (RCL = L1/L)

\(\rho_{\text{C}}\) :

FRP composite beam mass density

\(\delta \,\) :

Constant of characteristic equation

\(\varUpsilon\) :

Coefficient of independent force

\(g\) :

Complex constants

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Authors and Affiliations

  1. Department of Production Engineering, Veer Surendra Sai University of Technology, Burla, Odisha, 768018, India

    Pankaj Charan Jena

  2. Department of Mechanical Engineering, N.I.T, Rourkela, Odisha, 769008, India

    Dayal R. Parhi

  3. Department of Mechanical Engineering, Jadavpur University, Jadavpur, Kolkata, 700032, India

    G. Pohit

Authors
  1. Pankaj Charan Jena
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  2. Dayal R. Parhi
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  3. G. Pohit
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Correspondence to Pankaj Charan Jena.

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Jena, P.C., Parhi, D.R. & Pohit, G. Dynamic Investigation of FRP Cracked Beam Using Neural Network Technique. J. Vib. Eng. Technol. 7, 647–661 (2019). https://doi.org/10.1007/s42417-019-00158-5

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  • DOI: https://doi.org/10.1007/s42417-019-00158-5

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