Dynamic response of viscoelastic foundation beams under traveling wave effect

FENG Hao; YANG Yu-sheng; YU Hai-tao

doi:10.11779/CJGE202001014

Volume 42 Issue 1

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Chinese Journal of Geotechnical Engineering > 2020 > 42(1): 126-132. > DOI: 10.11779/CJGE202001014

FENG Hao, YANG Yu-sheng, YU Hai-tao. Dynamic response of viscoelastic foundation beams under traveling wave effect[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(1): 126-132. DOI: 10.11779/CJGE202001014

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Dynamic response of viscoelastic foundation beams under traveling wave effect

Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China

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Received Date: March 10, 2019
Available Online: December 07, 2022

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Abstract

Abstract

The dynamic problem of elastic foundation beams is usually analyzed by using the analytical and numerical methods, but the numerical method has a large amount of calculation, and the analytical method is usually more efficient. The analytic solution of infinite length Euler-Bernoulli beam on viscoelastic foundation subjected to constant axial pressure and transverse traveling wave is obtained by the Laplace and Fourier transforms. Compared with the numerical simulation results, the correctness of the solution is verified. Taking a long tunnel as an example, the influences of wave frequency, wave velocity and axial force and foundation stiffness on the dynamic response of the long tunnel are analyzed, and its internal force response affected by the wave frequency is obtained. The lower the frequency, the greater the internal force response of the tunnel. The internal force response is affected by the travelling wave velocity. When the travelling wave velocity is close to the critical velocity, the internal force response of the tunnel significantly increases.
- travelling wave effect,
- elastic foundation beam,
- dynamic problems,
- analytical solution

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References (16)

References

[1]	JOHN C M S, ZAHRAH T F. Aseismic design of underground structures[J]. Tunnelling & Underground Space Technology Incorporating Trenchless Technology Research, 1987, 2(2): 165-197.
[2]	KENNEY J T. Steady-state vibrations of beam on elastic foundation for moving load[J]. Journal of Applied Mechanics -Transactions of the ASME, 1954, 21(4): 359-364. doi: 10.1115/1.4010934
[3]	MATHEWS P M. Vibrations of a beam on elastic foundation[J]. ZAMM-Journal of Applied Mathematics and Mechanics, 1958, 38(3/4): 105-115.
[4]	MATHEWS P M. Vibrations of a beam on elastic foundation II[J]. Journal of Applied Mathematics and Mechanics, 1959, 39(1/2): 13-19.
[5]	ACHENBACH J D, SUN C. Dynamic response of beam on viscoelastic subgrade[J]. Journal of the Engineering Mechanics Division, 1965, 91(5): 61-76. doi: 10.1061/JMCEA3.0000678
[6]	SUN L. A closed-form solution of a bernoulli-euler beam on a viscoelastic foundation under harmonic line loads[J]. Journal of Sound & Vibration, 2001, 242(4): 619-627.
[7]	SUN L. An explicit representation of steady state response of a beam on an elastic foundation to moving harmonic line loads[J]. International Journal for Numerical & Analytical Methods in Geomechanics, 2003, 27(1): 69-84..
[8]	KIM S M, ROESSET J M. Dynamic response of a beam on a frequency-independent damped elastic foundation to moving load[J]. Canadian Journal of Civil Engineering, 2003, 30(2): 460-467. doi: 10.1139/l02-109
[9]	DIPANJAN B, KAMESWARA R N S V. Analytical solutions for Euler– Bernoulli beam on visco-elastic foundation subjected to moving load[J]. International Journal for Numerical & Analytical Methods in Geomechanics, 2013, 37(8): 945-960.
[10]	YU H. Analytical solution for an infinite euler-bernoulli beam on a viscoelastic foundation subjected to arbitrary dynamic loads[J]. Journal of Engineering Mechanics, 2014, 140(3): 542-551. doi: 10.1061/(ASCE)EM.1943-7889.0000674
[11]	YU H, CAI C, YUAN Y, et al. Analytical solutions for Euler-Bernoulli Beam on Pasternak foundation subjected to arbitrary dynamic loads[J]. International Journal for Numerical & Analytical Methods in Geomechanics, 2017.
[12]	YU H, YUAN Y, QIAO Z, et al. Seismic analysis of a long tunnel based on multi-scale method[J]. Engineering Structures, 2013, 49: 572-587. doi: 10.1016/j.engstruct.2012.12.021
[13]	CLOUGH R W, PENZIEN J. Dynamics of Structures[M]. 3rd ed. Berkeley: Computers & Structures, Inc, 2003.
[14]	禹海涛, 张正伟, 段科萍, 等. 反应位移法在圆形隧道抗震分析中的适用性评价[J]. 结构工程师, 2018, 34(14): 211-218. YU Hai-tao, ZHANG Zheng-wei, DUAN Ke-ping, et al. Adaptability evaluation of response displacement method in seismic analysis of circular tunnel[J]. Structural Engineers, 2018, 34(14): 211-218. (in Chinese)
[15]	HASHASH Y M A, HOOK J J, SCHMIDT B, et al. Seismic design and analysis of underground structures[J]. Tunnelling and Underground Space Technology, 2001, 16(4): 247-293. doi: 10.1016/S0886-7798(01)00051-7
[16]	WANG J N. Seismic Design of Tunnels: A Simple State-of-the-art Design Approach[M]. New York: Parsons Brinckerhoff, 1993.