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A numerical study on an infinite linear elastic Bernoulli-Euler beam on a viscoelastic foundation subjected to harmonic line loads

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Abstract

This paper presents a numerical study on the low-amplitude responses of an infinite Bernoulli-Euler beam resting on a viscoelastic foundation subjected to harmonic line loads. To simulate the linear response, a semi-analytical solution procedure that was theoretically proposed by Jang (2016) is utilized and several numerical experiments are conducted to investigate the influence of key model parameters characterizing stiffness and damping. The properties of the viscoelastic foundation are based on theoretical and empirical values for cohesionless sand type foundation. According to the numerical experiments, the obtained responses are compared with those from the closed-form solution and found to have a good agreement with them.

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Abbreviations

A :

Cross sectional area

b :

Width of the beam cross-section

C :

Damping coefficient

E :

Young’s modulus of beam

E s :

Young’s modulus of foundation

g :

Gravity acceleration

G,G t :

Kernel function

H :

Half-maximum convention (Heaviside step function)

h :

Height

I :

Second moment of area

K :

Spring coefficient

K p :

Pseudo-spring coefficient

P :

Amplitude of the applied external load

r 0 :

Half-width of the line load

u,v :

Iterative (response) solutions

X 0 :

Constant

W :

External load

α, β, β p :

Parameters

γ :

Rate of the vertical displacement decreasing with depth

γ s :

Unit weight of soil

K :

Loading frequency

V s :

Poisson’s ratio of foundation

ρ :

Density

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Acknowledgments

The present study was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2018R1D1A1B06049813). And it was also supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MSIP) (NRF-2017R1A5A1015722 and 2011-0030013).

Author information

Authors and Affiliations

  1. Wessex Institute, Southampton, SO40 7AA, UK

    S. Syngellakis

  2. Department of Naval Architecture and Ocean Engineering, Pusan National University, Busan, 46241, Korea

    Jinsoo Park, Dae Seung Cho & Taek Soo Jang

Authors
  1. S. Syngellakis
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  2. Jinsoo Park
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  3. Dae Seung Cho
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  4. Taek Soo Jang
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Corresponding author

Correspondence to Taek Soo Jang.

Additional information

Stavros Syngellakis is an Adjunct Professor at the Wessex Institute of Technology, Southampton, UK. He received his Ph.D. in Civil Engineering from Princeton University, USA. For most of his academic career, he taught mechanics of solids and structures at the University of Southampton, UK. His research interests include wave propagation in solids, structural stability, fracture and contact mechanics.

Jinsoo Park is a post-doctoral researcher under the supervision of Prof. T.S. Jang at the Department of Naval Architecture and Ocean Engineering, Pusan National University in Busan, Republic of Korea. He is a member of Ocean Engineering Laboratory (Supervisor Prof. TS Jang) and his main fields of research are marine hydrodynamics and its numerical simulation.

Dae Seung Cho is a Professor at the Department of Naval Architecture and Ocean Engineering at Pusan National University in Busan, Republic of Korea. He received his Ph.D degree from Seoul National University. His main fields of research are noise, vibration and radar cross section analysis and control of marine structures.

Taek Soo Jang is a Professor at the Department of Naval Architecture and Ocean Engineering at Pusan National University in Busan, Republic of Korea. He received his Ph.D. degree from Seoul National University. His main fields of research are nonlinear (ocean) system identification (inverse problems), techniques to remedy the ill-posedness, developing nonlinear numerical schemes for ODE & PDE and water waves and wave mechanics.

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Syngellakis, S., Park, J., Cho, D.S. et al. A numerical study on an infinite linear elastic Bernoulli-Euler beam on a viscoelastic foundation subjected to harmonic line loads. J Mech Sci Technol 34, 3587–3595 (2020). https://doi.org/10.1007/s12206-020-0810-3

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  • DOI: https://doi.org/10.1007/s12206-020-0810-3

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