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Transient point load induced response of Kirchhoff’s plate with translationally constrained edges: aircraft landing on floating airports

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Abstract

Dynamic analysis of thin rectangular elastically supported plates to transient loads is presented. A floating airport is modeled as a horizontal Kirchhoff’s plate, which is elastically supported at the ends, and is subjected to the impact of aircrafts landing and deceleration over its length. This sets the free–free–free–free plate into high-frequency vibration, causing flexural stress waves to travel over the plate. First, the beam natural frequencies and modeshapes in either direction are generated with these complexities. The eigenvalue analysis of the governing differential equation is done, using the weighted summation of the product of the beam modes. The radiation pressure on the bottom side of the plate is included to reduce the frequencies by the added-mass effect. The plate is then subjected to decelerating shock loads. The vibratory response is analyzed by the computationally efficient normal mode analysis. The amplification factor versus the taxiing time of the moving load is generated. This gives insights into the maximum stress encountered under the transient load, as function of taxiing time and support.

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Abbreviations

L :

Length of the plate

B :

Width of the plate

h :

Thickness of the plate

ρ :

Density of the beam material

ρ water :

Density of water

ρ material :

Density of plate material

E :

Elastic modulus of the material

I :

Second moment of area of the cross section of the beam about the horizontal neutral axis

x :

Space variable along x-direction

y :

Space variable along y-direction

t :

Time variable

ϕ j (x):

jth beam modeshape in the x-direction

ϕ l (y):

lth beam modeshape in the y-direction

Φ k (x, y):

kth plate modeshape

q j (t):

Principal coordinate

Ψ(x, y, z, t):

Velocity potential of the fluid

Ψ k :

kth velocity potential of the fluid

Ψ * k :

kth velocity potential of the fluid per unit velocity of the kth principal coordinate

A kn :

kth generalized added mass under the nth plate modeshapes

F(x, y, t):

Transient load

ω n1 :

Fundamental natural frequency of the plate

T n1 :

Fundamental natural period of the plate

z(x, y, t):

Dynamic flexural deflection of the plate

z st(x, y, t):

Static flexural deflection of the plate

References

  1. N.J. Robinson, S.C. Palmer, A modal analysis of a rectangular plate floating on an incompressible fluid. J. Sound Vib. 142(3), 453–460 (1990)

    Article  Google Scholar 

  2. H. Kagemoto, M. Fujino, M. Murai, Theoretical and experimental predictions of the hydroelastic response of a very large floating structure in waves. Appl. Ocean Res. 20, 135–144 (1998)

    Article  Google Scholar 

  3. H. Endo, The behavior of a VLFS and an airplane during takeoff/landing run in wave condition. Mar. Struct. 13, 477–491 (2000)

    Article  Google Scholar 

  4. H. Seto et al., Integrated hydrodynamic-structural analysis of VLFS. Mar. Struct. 18, 181–200 (2005)

    Article  Google Scholar 

  5. S.H. Hashemi et al., Vibration analysis of rectangular Mindlin’s plates on elastic foundations and vertically in contact with stationary fluid by the Ritz method. Ocean Eng. 37, 174–185 (2010)

    Article  Google Scholar 

  6. N. Datta, Hydroelastic response of marine structures to impact-induced vibrations, Dissertation for Doctor of Philosophy, Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, 2010

  7. N. Datta, Y. Verma, Accurate Eigenvector-based generation and computational insights of Mindlin’s plate modeshapes for twin frequencies. Int. J. Mech. Sci. 123, 64–73 (2017)

    Article  Google Scholar 

  8. N. Datta, A.W. Troesch, Hydroelastic response of Kirchhoff plates to transient hydrodynamic impact loads. Mar. Syst. Ocean Technol. 7(2), 77–94 (2012)

    Google Scholar 

  9. N. Datta, J.D. Thekinen, Wet vibration of axially loaded elastically supported plates to moving loads: aircraft landing on floating airports, 32nd International Conference on Ocean, Offshore and Arctic Engg, Nantes, 2013

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Authors and Affiliations

  1. Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology, Kharagpur, India

    N. Datta

  2. Department of Mechanical Engineering, Purdue University, West Lafayatte, USA

    J. D. Thekinen

Authors
  1. N. Datta
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  2. J. D. Thekinen
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Correspondence to N. Datta.

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Datta, N., Thekinen, J.D. Transient point load induced response of Kirchhoff’s plate with translationally constrained edges: aircraft landing on floating airports. Mar Syst Ocean Technol 12, 252–261 (2017). https://doi.org/10.1007/s40868-017-0038-y

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  • DOI: https://doi.org/10.1007/s40868-017-0038-y

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