Welcome to Francis Academic Press

International Journal of Frontiers in Sociology, 2021, 3(8); doi: 10.25236/IJFS.2021.030806.

Application of Mathematical Model in Dynamic Analysis and Monitoring of Mechanical System


Ting Li

Corresponding Author:
Ting Li

School of Mathematics and Statistics Zaozhuang University, Zaozhuang 277160, P.R. China


With the increasing popularity of mechanical system power, mechanical system plays an increasingly important role in various projects in China. It is not only directly related to personal safety, but also affects the enormous economic benefits brought by mechanical engineering applications. Therefore, it is necessary to analyze and monitor its operation status in order to detect potential dangerous signals in advance and ensure the stable operation of its mechanical system equipment. The purpose of this paper is to give us a deeper understanding of the dynamic characteristics of rotating machinery systems. It also provides a dynamic basis for parameter optimization design, fault diagnosis, vibration control and so on. In this paper, the steady and transient steering characteristics of an automobile train system consisting of one tractor and five trailers with double axle steering are studied by using the concept of ADAMS. The research methods of design research analysis, experiment design analysis and optimum design analysis are adopted. The effects of structural parameters such as lateral stiffness of tire, length of tractor rod, position of articulation point, front wheel rotation angle and service parameters on trajectory follow ability of tractor and Trailer (i.e., the same rut of tractor and trailer) are analyzed. The optimization schemes of the Steady-state circular motion and the figure-8 motion of the train under different working conditions are put forward. The experimental results show that: the trajectory deviation obtained by the experimental method in this paper decreases by 70% to 80%, the deviation is smaller, and the operation of mechanical system equipment tends to be more stable.


Mathematical Model, Mechanical System, Dynamic Analysis, Automobile and Train System

Cite This Paper

Ting Li. Application of Mathematical Model in Dynamic Analysis and Monitoring of Mechanical System. International Journal of Frontiers in Sociology (2021), Vol. 3, Issue 8: 36-46. https://doi.org/10.25236/IJFS.2021.030806.


[1] Feigel A. Dynamics of a mechanical system with multiple degrees of freedom out of thermal equilibrium.[J]. Phys.rev.e, 2017, 95(5):052106.

[2] PaTajaddodianfar F, Yazdi M R H, Pishkenari H N, et al. Classification of the nonlinear dynamics in an initially curved bistable micro/nano-electro-mechanical system resonator[J]. Iet Micro & Nano Letters, 2015, 10(10):583-588.

[3] Ruan X, Wang X, et al. Analysis and Design of Current Control Schemes for LCL-Type Grid-Connected Inverter Based on a General Mathematical Model[J]. IEEE Transactions on Power Electronics, 2016, 32(6):1-1.

[4] Benson J D, Benson C T, Critser J K. Mathematical model formulation and validation of water and solute transport in whole hamster pancreatic islets.[J]. Mathematical Biosciences, 2014, 254(1):64-75.

[5] Munoz A I, Tello J I. On a mathematical model of bone marrow metastatic niche[J]. Mathematical Biosciences & Engineering Mbe, 2017, 14(1):289.

[6] Zagzoule M, Marcvergnes J P. A global mathematical model of the cerebral circulation in man[J]. Journal of Biomechanics, 2017, 19(12):1015-1022.

[7]Shiri T, Garira W, Musekwa S D. A two-strain hiv-1 mathematical model to assess the effects of chemotherapy on disease parameters[J]. Mathematical Biosciences & Engineering Mbe, 2017, 2(4):811-832.

[8] Gan C, Todd R, Apsley J M. Drive System Dynamics Compensator for a Mechanical System Emulator[J]. Industrial Electronics IEEE Transactions on, 2015, 62(1):70-78.

[9] Szalai R, Jeffrey M R. Nondeterministic dynamics of a mechanical system[J]. Physical Review E Statistical Nonlinear & Soft Matter Physics, 2014, 90(2):860-877.

[10] Cascarano G, Giacovazzo C, M. Lui&#x. Direct methods and structures showing superstructure effects. III. A general mathematical model[J]. Acta Crystallographica, 2014, 44(2):176-183.

[11] Brady J M, Tobin J M, Jean‐Claude Roux. Continuous fixed bed biosorption of Cu2+ ions: application of a simple two parameter mathematical model[J]. Journal of Chemical Technology & Biotechnology, 2015, 74(1):71-77.

[12] Pokhilko A V, Ataullakhanov F I, Holmuhamedov E L. Mathematical model of mitochondrial ionic homeostasis: Three modes of Ca 2+ transport[J]. Journal of Theoretical Biology, 2017, 243(1):152-169.

[13] Klein C, Rumpe B, Broy M. A stream-based mathematical model for distributed information processing systems - the SysLab system model -[J]. 2014,58(2):143

[14] Marton K, Campanelli L, Eichorn N, et al. Information Processing and Proactive Interference in Children With and Without Specific Language Impairment[J]. J Speech Lang Hear Res, 2014, 57(1):106-119.

[15] Jiang L Y, Qin G, Xu X X, et al. Dynamics and nonclassical properties of an opto-mechanical system prepared in four-headed cat state and number state[J]. Optics Communications, 2016, 369:179-188.

[16] Habib G, Rega G, Stepan G. Bifurcation analysis of a two-DoF mechanical system subject to digital position control. Part I: theoretical investigation[J]. Nonlinear Dynamics, 2014, 76(3):1781-1796.

[17] Ibănescu R, Ungureanu C. Lagrange's Equations versus Bond Graph Modeling Methodology by an Example of a Mechanical System[J]. Applied Mechanics & Materials, 2015, 809-810:914-919.

[18] Rudra S, Barai R K, Maitra M. Nonlinear state feedback controller design for underactuated mechanical system: A modified block backstepping approach[J]. Isa Transactions, 2014, 53(2):317-326.

[19] Lemu H G. Advances in numerical computation based mechanical system design and simulation[J]. Advances in Manufacturing, 2015, 3(2):130-138.

[20] Schoeder S, Ulbrich H, Schindler T. Discussion of the Gear–Gupta–Leimkuhler method for impacting mechanical systems[J]. Multibody System Dynamics, 2014, 31(4):477-495.