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Crack Estimation of Beam Under the Moving Mass Using the Dynamic Characteristics Based on Two Contact Point Theory

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Iranian Journal of Science and Technology, Transactions of Mechanical Engineering Aims and scope Submit manuscript

Abstract

It is important to identify the presence of damage present in the structures like bridge which undergoes the excitation due to moving vehicles. In such type of problems, modal analysis and dynamic displacement response analysis are not sufficient to portray the crack presence. The presented work emphases on the analysis of acceleration response to investigate the crack presence. A mathematical model is developed by considering the two masses with fixed distance between them traversing on the Euler–Bernoulli beam having a crack. The acceleration response analysis can be effective to present the qualitative explanation of the fault present in the beam. A key features of the acceleration response of beam having a crack includes discontinuity at the crack location which vary with change in distance between the front and rear wheel and a greater response value compare to that for healthy in the last phase of travel from the time front wheel exits the beam. However, the effectiveness of the presentation of the crack through acceleration response depends upon the fixed distance between the front and rear wheel and the bridge length. The discontinuity will be higher for the higher ratio of distance between the front and rear wheel to the bridge length.

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Abbreviations

\(c\) :

Sectional flexibility

\(\vartheta\) :

Poissons ratio

E :

Young’s modulus

I :

Moment of inertia

h :

Height of the beam

a :

Depth of crack

\(Y_{1} \left( x \right)\) :

Displacement response of first segment

\(Y_{2} \left( x \right)\) :

Displacement response of second segment

\(\beta\) :

Non-dimensional natural frequency

\(x\) :

Variable distance traveled by vehicle from left end

\(l_{1}\) :

Crack located at distance from the left end of beam

L :

Total length of beam

t :

Time

ν :

Velocity of vehicle

d :

Distance between front and rear wheel

M 1 :

Mass on the front wheel (farthest from the left end)

M 2 :

Mass on the rear wheel

g :

Gravitational acceleration

q(t):

Modal response

m :

Mass of the beam

ρ :

Density of the beam

A :

Cross section of beam

ω n :

nth Natural frequency

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Authors and Affiliations

  1. Department of Mechanical Engineering, Visvesvaraya National Institute of Technology, Nagpur, India

    Tanuja Vaidya & Animesh Chatterjee

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  1. Tanuja Vaidya
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  2. Animesh Chatterjee
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Correspondence to Tanuja Vaidya.

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Vaidya, T., Chatterjee, A. Crack Estimation of Beam Under the Moving Mass Using the Dynamic Characteristics Based on Two Contact Point Theory. Iran J Sci Technol Trans Mech Eng 43 (Suppl 1), 307–326 (2019). https://doi.org/10.1007/s40997-018-0159-8

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  • DOI: https://doi.org/10.1007/s40997-018-0159-8

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