Suspension Bridge Estimation Method using the Fokker-Planck Model
DOI:
https://doi.org/10.56741/jnest.v3i02.536Keywords:
estimation method, finite element, fokker-planck model, mathematical models, weakly damped waveAbstract
The failure of the suspension bridge has been known since the beginning of the bridge collapse. Most of these failures form the basis of current engineering knowledge. One of the factors of failure is human-made factors related to the calculation of the bridge estimate. This paper presents an indirect estimation method using numerical simulation using finite elements by analyzing the Fokker-Planck model when dynamic excitation is associated with bridge loads. The results show that the Fokker-Planck model's homogeneous form can take into account the solution for the bridge analysis approach. It leads to a stable state when giving mass variations to the model. The indirect estimation method using finite elements can estimate the cable tension with controllable weak damping. It can be concluded that the method in this study is more accurate and convenient for the application technique.
Downloads
References
Berchio E. & Gazzola F. A Qualitative Explanation of The Origin of Torsional Instability in Suspension Bridges. Nonlinear Analysis: Theory, Methods & Applications, 121, pp. 54-72, 2015.
Blekherman A. Internal Resonance in Pedestrian Bridges. International Journal of Bridge Engineering. 3(3), pp. 1-33, 2015.
Gould H., Murray D.R. & Sanfratello. Mathematical Modeling Handbook. Teacher College Columbia University: COMAP, Columbia, 2012.
Bochicchio I., Giorgi C. & Vuk E. Well-Posedness and Longtime Behaviour of A Coupled Nonlinear System Modeling A Suspension Bridge. Meccanica. 50(3), pp. 665-673, 2015.
Ming C.Y. Solution of Differential Equations with Applications to Engineering Problems. Dynamical Systems Analytical and Computational Techniques.11, pp. 233-264, 2017.
Zhukovsky K.V. A Method of Inverse Differential Operators Using Orthogonal Polynomials and Special Functions for Solving Some Types of Differential Equations and Physical Problems. Moscow University Physics Bulletin. 70(2), pp. 93-100, 2015.
Feng L., Liu F., Turnerra I., Yang Q. & Zhuang P. Unstructured Mesh Finite Difference/Finite Element Method for The 2D Time-Space Riesz Fractional Diffusion Equation on Irregular Convex Domains. Applied Mathematical Modelling. 59, pp. 441-463, 2018.
Arioli G. & Gazzola F. On A Nonlinear Nonlocal Hyperbolic System Modeling Suspension Bridges. Milan Journal of Mathematics. 83(2), pp. 211-236, 2015.
Ferrero A. & Gazzola F. A Partially Hinged Rectangular Plate as A Model for Suspension Bridges. Discrete & Continuous Dynamical Systems-A. 35(12), pp. 5879-5908, 2015.
Sokolov I.M., Klafter J. & Blumen A. Fractional kinetics. Physics Today. 55(11), pp. 48-54, 2002.
Zaslavsky G.M. & Chaos. Fractional Kinetics, and Anomalous Transport. Physics Reports, 371(6), pp 461-580, 2002.
Berchio E., Ferrero A. & Gazzola F. Structural Instability of Nonlinear Plates Modelling Suspension Bridges: Mathematical Answers to Some Long-Standing Questions. Nonlinear Analysis: Real World Applications, 28, pp. 91-125, 2016.
Sapagovas M., Novickij J. & Stikonas A. Stability Analysis of A Weighted Difference Scheme for Two-Dimensional Hyperbolic Equations with Integral Conditions. Electronic Journal of Differential Equations. 2019(04), pp. 1-13, 2019.
Meng Z.J., Cheng H., Ma, L.D. & Cheng Y.M. The Hybrid Element‐Free Galerkin Method for Three‐Dimensional Wave Propagation Problems. International Journal for Numerical Methods in Engineering, 117(1), pp. 15-37, 2019.
Ohene K.R., Osei – Frimpo E., Mends–Brew E. & King A.T. A Mathematical Model of A Suspension Bridge – Case Study: Adomi Bridge, Atimpoku, Ghana. Global Advanced Research Journal of Engineering, Technology and Innovation. 1(3), pp. 047-062, 2012.
Spiegel M.R. Schaum's Outlines Advanced Mathematics For Engineers And Scientists. McGraw-Hill, New York, 1976.
McKenna P.J. & Moore K.S. The Global Structure of Periodic Solutions to A Suspension Bridge Mechanical Model. IMA journal of applied mathematics. 67(5), pp. 459-478, 2002.
Tajčová G. Mathematical Models of Suspension Bridges. Applications of Mathematics. 42(6), pp. 451-480, 1997.
Tajčová G. Mathematical Models of Suspension Bridges: Existence of Unique Solutions. Proceedings of Equadiff. 9, pp. 281-305, 1998.
McKenna P.J. & Walter W. Nonlinear Oscillations in A Suspension Bridge. Archive for Rational Mechanics and Analysis, 98(2), pp. 167-177, 1987.
Lazer A.C. & McKenna P.J. Large-Amplitude Periodic Oscillations in Suspension Bridges: Some New Connections with Nonlinear Analysis. SIAM Review, 32(4), pp. 537-578, 1990.
Glover J., Lazer, A.C. & McKenna P.J. Existence and Stability of Large-Scale Nonlinear Oscillations in Suspension Bridges. Zeitschrift für angewandte Mathematik und Physik ZAMP, 40(2), pp 172-200, 1989.
Holubová–Tajčová G. Mathematical Modeling of Suspension Bridges. Mathematics and Computers in Simulation, 50(1-4), pp. 183-197, 1999.
Humphreys L.D. & McKenna, P.J. When A Mechanical System Goes Nonlinear: Unexpected Responses to Low-Periodic Shaking. The American Mathematical Monthly, 112(10), pp. 861-875, 2005.
Choudhury, J. R., & Hasnat, A. Bridge collapses around the world: Causes and mechanisms. In IABSE-JSCE Joint conference on advances in bridge engineering-III, p. 34, 2015.
Biezma, M.V., & Schanack, F. Collapse of Steel Bridges. Journal of Performance of Constructed Facilities, 21(5), pp. 398-405, 2007.
Savaliya G.M., Desai A.K. & Vasanwala S.A. Static and Dynamic Analysis of Cable-stayed Suspension Hybrid Bridge and Validation. International Journal of Advanced Research in Engineering and Technology, 6(11), pp. 91-98, 2016.
Hui Y., Kang H.J., Law SS. & Hua XG. Effect of Cut-Off Order of Nonlinear Stiffness on The Dynamics of A Sectional Suspension Bridge Model. Engineering Structures, 185, pp. 377-391, 2019.
Kawai, Y., Siringoringo, D., & Fujino, Y. Failure Analysis of The Hanger Clamps of The Kutai-Kartanegara Bridge from The Fracture Mechanics Viewpoint. Journal of JSCE, 2(1), pp. 1-6, 2014.
Wang J., Liu W., Wang L. & Han X. Estimation of Main Cable Tension Force of Suspension Bridges Based on Ambient Vibration Frequency Measurements. Struct. Eng. Mech. 56, pp. 939-957, 2015.
Cantero D., McGetrick P., Kim C.W., & OBrien E. Experimental Monitoring of Bridge Frequency Evolution During The Passage of Vehicles with Different Suspension Properties. Engineering Structures. 187, pp. 209-219, 2019.
Huang F., Peng G., & Wang X. Study on Energy Dissipation of Viscous Damper for Long-Span Suspension Bridges. In IOP Conference Series: Earth and Environmental Science. 283(1), pp. 012054 (1-7), 2019.
Gan Q., Huang Y., Wang R. & Rao R. Tension Estimation of Hangers with Shock Absorber in Suspension Bridge Using Finite Element Method. Journal of Vibroengineering 21(3), pp. 587-601, 2019.
Adewuyi A.P. & Wu Z.S. Vibration-Based Dam-Age Localization in Flexural Structures Using Normalized Modal Macrostrain Techniques from Limited Measurements. Computer-Aided Civil and Infrastructure Engineering. 26, pp. 154–172, 2011.
An Y., Jo H., Spencer Jr, B.F. & Ou J. A Damage Localization Method Based on The ‘Jerk Energy’. Smart Materials and Structures. 23(2), pp. 025020 (1-13), 2014.
Katicha S.W., Flintsch G., Bryce J. & Ferne B. Wavelet Denoising of TSD Deflection Slope Measurements for Improved Pavement Structural Evaluation. Computer-Aided Civil and Infrastructure Engineering. 29(6), pp. 399-415, 2014.
Su W.C., Liu C.Y. & Huang C.S. Identification of Instantaneous Modal Parameter of Time-Varying Systems Viaa Wavelet-Based Approach and Its Application. Computer-Aided Civil and Infrastructure Engineering. 29(4), pp. 279-98, 2014.
Liu Z., Correia J., Carvalho H., Mourão A., De Jesus A., Calçada R. & Berto F. Global‐Local Fatigue Assessment of An Ancient Riveted Metallic Bridge Based on Submodelling of The Critical Detail. Fatigue & Fracture of Engineering Materials & Structures. 42(2), pp. 546-560, 2019.
Odibat Z. & Momani S. Numerical solution of Fokker–Planch Equation with Space-and Time-Fractional Derivatives. Physics Letters A. 369(5-6), pp. 349-358, 2007.
Brudastova O. Stochastic Response Determination and Spectral Identification of Complex Dynamic Structural Systems, Doctoral Dissertation, Columbia University, 2018.
Zhou G., Li A., Li J., Duan M., Xia Z., Zhu L., Spencer B.F. & Wang B. Test and Numerical Investigations on The Spatial Mechanics Characteristics of Extra-Wide Concrete Self-Anchored Suspension Bridge During Construction. International Journal of Distributed Sensor Networks. 15(12), pp. 1-20, 2019.
Li T. & Liu Z. A Recursive Algorithm for Determining the Profile of the Spatial Self-anchored Suspension Bridges. KSCE Journal of Civil Engineering. 23(3), pp. 1283-1292, 2019.
Downloads
Published
How to Cite
Issue
Section
Categories
License
Copyright (c) 2024 Journal of Novel Engineering Science and Technology
![Creative Commons License](http://i.creativecommons.org/l/by-sa/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.