This article investigates the power flow of the three-beam system on Winkler–Pasternak elastic foundations under elastic boundary conditions. The time-averaged power flow of the beam on elastic foundations with elastic boundary conditions is calculated based on the internal shear force and bending moment and the wave propagation approach. The reliability and accuracy of the calculation method are verified by comparing the vibration acceleration calculated by calculation examples and the finite element method. In addition, the effects of structural parameters and boundary conditions on the power flow of the three-beam system are investigated. This contributes to the analysis of the dynamic characteristics of the beam on double parameter elastic foundations under complex boundary conditions.
AhmidaKMArrudaJRF (2001) Spectral element-based prediction of active power flow in Timoshenko beams. International Journal of Solids and Structures38(10–13): 1669–1679.
2.
AvcarM (2016) Effects of material non-homogeneity and two parameter elastic foundation on fundamental frequency parameters of Timoshenko beams. Acta Physica Polonica A130(1): 375–378.
3.
BachooR (2021) Wave characteristics of nonsymmetric cross-ply laminated composite beams. Proceedings of the Institution of Mechanical Engineers - Part L: Journal of Materials: Design and Applications235(7): 1567–1584.
4.
DengJShahroudiMLiuKF (2023) Dynamic stability and responses of beams on elastic foundations under a parametric load. International Journal of Structural Stability and Dynamics23(02): 30.
5.
DoevaOMasjediPKWeaverPM (2021) Closed form solutions for an anisotropic composite beam on a two-parameter elastic foundation. European Journal of Mechanics - A: Solids88: 10.
6.
FangWYuTVan LichL, et al. (2019) Analysis of thick porous beams by a quasi-3D theory and isogeometric analysis. Composite Structures221: 110890.
7.
GhommemMAbdelkefiANuhaitAO, et al. (2012) Aeroelastic analysis and nonlinear dynamics of an elastically mounted wing. Journal of Sound and Vibration331(26): 5774–5787.
8.
GuoXMGeHXiaoCL, et al. (2022) Vibration transmission characteristics analysis of the parallel fluid-conveying pipes system: numerical and experimental studies. Mechanical Systems and Signal Processing177: 23.
9.
LeeSYChengYC (2008) A new dynamic model of high-speed railway vehicle moving on curved tracks. Journal of Vibration and Acoustics-Transactions of the Asme130(1): 10.
10.
LeeHPLimSPKhunMS (2006) Diversion of energy flow near crack tips of a vibrating plate using the structural intensity technique. Journal of Sound and Vibration296(3): 602–622.
11.
LiTYZhangWHLiuTG (2001) Vibrational power flow analysis of damaged beam structures. Journal of Sound and Vibration242(1): 59–68.
12.
LiZYXuYPHuangD (2020) Accurate solution for functionally graded beams with arbitrarily varying thicknesses resting on a two-parameter elastic foundation. The Journal of Strain Analysis for Engineering Design55(7-8): 222–236.
13.
LiaoWZLiuKXMaC, et al. (2023) Experimental study on consistency of the impact performance between composite beams and reinforced concrete beams. Composite Structures308: 15.
14.
LiuYLuG (2012) Dynamic stability of a beam on an elastic foundation including stress wave effects. International Journal of Applied Mechanics4(2): 25.
15.
LiuSBYangBG (2019) A closed-form analytical solution method for vibration analysis of elastically connected double-beam systems. Composite Structures212: 598–608.
16.
LiuCCLiFMTangLA, et al. (2011) Vibration control of the finite L-shaped beam structures based on the active and reactive power flow. Science China Physics, Mechanics & Astronomy54(2): 310–319.
17.
LiuYJLiuJPanG, et al. (2022) Vibration analysis and isolator component design of the power system in an autonomous underwater glider. International Journal of Acoustics and Vibration27(2): 112–121.
18.
PasternakPL (1954) On a New Method of Analysis of an Elastic Foundation by Means of Two Foundation Constants. Moscow: Gosstrojizdat.
19.
StojanovicVKozicPJanevskiG (2013) Exact closed-form solutions for the natural frequencies and stability of elastically connected multiple beam system using Timoshenko and high-order shear deformation theory. Journal of Sound and Vibration332(3): 563–576.
20.
TangYQLiTJYanQY (2017) Damage analysis of one-dimensional euler-Bernoulli cracked beam with traveling wave method. International Journal of Applied Mechanics9(4): 15.
21.
WangYZhengGT (2014) Vibration power flow analysis of a submerged constrained layer damping cylindrical shell. Journal of Vibration and Acoustics-Transactions of the Asme136(1): 14.
22.
WangTQinQZhuX (2020) Reaction force and power flow analysis of an acoustic metamaterial beam with multi-band gaps. Acoustics Australia48(1): 59–67.
23.
WangMTChaiKLiuSY, et al. (2023) Dynamic characteristics and experimental study of double layer vibration isolation system. Journal of Mechanical Science and Technology37(4): 1699–1709.
24.
WinklerE (1867) Die Lehre von der Elastizität und Festigkeit. Prague: Dominicus.
25.
WuCJWhiteRG (1995a) Reduction of vibrational power in periodically supported beams by use of a neutralizer. Journal of Sound and Vibration187(2): 329–338.
26.
WuCJWhiteRG (1995b) Vibrational power transmission in a finite multi-supported beam. Journal of Sound and Vibration181(1): 99–114.
27.
WuXWZhuLFWuZM, et al. (2022) Vibrational power flow analysis of Timoshenko microbeams with a crack. Composite Structures289: 15.
28.
XieMXZhangPZhuMH, et al. (2022) Energy flow analysis of high-frequency flexural vibration of wedge beam structures. Shock and Vibration2022: 10.
29.
XuDSDuJTZhaoYH (2020) Flexural vibration and power flow analyses of axially loaded beams with general boundary and non-uniform elastic foundations. Advances in Mechanical Engineering12(5): 14.
30.
YanJLiFCLiTY (2007) Vibrational power flow analysis of a submerged viscoelastic cylindrical shell with wave propagation approach. Journal of Sound and Vibration303(1-2): 264–276.
31.
YayliMOArasMAksoyS (2014) An efficient analytical method for vibration analysis of a beam on elastic foundation with elastically restrained ends. Shock and Vibration2014: 7.
32.
YeYSWeiSWCaiDG, et al. (2023) Calculation method for internal force and deformation of the prestressed I-beam on the elastic foundation. Frontiers in Earth Science10: 10.
33.
YouJMengGALiHG (2011) Random energy flow analysis of coupled beam structures and its correlation with SEA. Archive of Applied Mechanics81(1): 37–50.
34.
ZhangJLGeRYZhangLJ (2019) Transverse free vibration analysis of a tapered Timoshenko beam on visco-Pasternak foundations using the interpolating matrix method. Earthquake Engineering and Engineering Vibration18(3): 567–578.
35.
ZhouQWangT (2019) Free vibrations of an elastically restrained Euler beam resting on a movable Winkler foundation. Shock and Vibration2019: 15.
36.
ZhuLFKeLLXiangY, et al. (2020) Vibrational power flow analysis of cracked functionally graded beams. Thin-Walled Structures150: 10.
