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Response Analysis of Inclined Edge Cracked Beam Under Moving Mass

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Vibration Engineering and Technology of Machinery, Volume I (VETOMAC 2021)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 137))

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Abstract

The dynamic behavior of structure with the presence of inclined edge crack is an emerging topic in the era of structural dynamics. In the present analogy, a novel method is focused to investigate the dynamic response of an inclined edge cracked simply supported structure subjected to moving mass. The responses of the beam structure subjected to traversing load are calculated with different crack inclination angles and crack depth using Duhamel integral approach. For the authentication of the numerical approach, the finite element analyzes (FEA) is accomplished to corroborate the exactness of computational approach (Duhamel integral approach). The FEA approach has been conducted using the commercial ANSYS WORKBENCH software. The significance of the crack parameters (crack inclination angle and crack depth) and moving mass parameters (moving speed and magnitude of moving mass) on the responses of the beam are investigated. The numerical analyzes followed by FEA approaches are illustrated for different crack angles, crack depth, moving speed and moving mass. The results which are obtained from both the numerical method as well as FEA approach are compared with each other. As per the results are concerned, the applied numerical analogy converges well towards the FEA approach. So the Duhamel integral method is found to be convergent and can be useful to obtain the response of structure under transit mass.

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Abbreviations

M:

Moving or Transit mass magnitude,

v:

Transit velocity

L:

Beam length

d:

Crack depth

b:

Beam width

H:

Beam thickness

δ:

Dirac Delta function

λ:

Eigen function

Tn(t):

Amplitude function

Y(x):

Shape function

y(x, t):

Response function

n:

Number of modes

α:

Relative depth of crack at the intact positions

\(l \,\):

Crack length at the crack opening

β = vt:

Position of the transit mass

ωn:

Frequency at nth mode of the beam

EI:

Flexural rigidity

m̄= ρA:

Beam mass per unit length

ρ:

Density of the structure

A:

Area of cross-section of the beam

θ:

Crack inclination angle

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Nalanda Institute of Technology, Bhubaneswar, India

    Shakti P. Jena

  2. Department of Mechanical Engineering, JNTU Kakinada, Vardhaman College of Engineering, Hyderabad, India

    Naresh Kumar Sarella

  3. School of Mechanical Engineering, KIIT University, Bhubaneswar, India

    Sasmita Sahu

  4. Department of Mechanical Engineering, National Institute of Technology, Rourkela, India

    Dayal R. Parhi

Authors
  1. Shakti P. Jena
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  2. Naresh Kumar Sarella
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  3. Sasmita Sahu
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  4. Dayal R. Parhi
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Corresponding author

Correspondence to Shakti P. Jena .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam, India

    Rajiv Tiwari

  2. Department of Mechanical Engineering, B.M.S. College of Engineering, Bengaluru, Karnataka, India

    Y. S. Ram Mohan

  3. Department of Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India

    Ashish K. Darpe

  4. Department of Mechanical Engineering, B.M.S. College of Engineering, Bengaluru, Karnataka, India

    V. Arun Kumar

  5. Department of Mechanical Engineering, Indian Institute of Technology Patna, Patna, Bihar, India

    Mayank Tiwari

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Jena, S.P., Sarella, N.K., Sahu, S., Parhi, D.R. (2023). Response Analysis of Inclined Edge Cracked Beam Under Moving Mass. In: Tiwari, R., Ram Mohan, Y.S., Darpe, A.K., Kumar, V.A., Tiwari, M. (eds) Vibration Engineering and Technology of Machinery, Volume I. VETOMAC 2021. Mechanisms and Machine Science, vol 137. Springer, Singapore. https://doi.org/10.1007/978-981-99-4721-8_6

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  • DOI: https://doi.org/10.1007/978-981-99-4721-8_6

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-99-4720-1

  • Online ISBN: 978-981-99-4721-8

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