Analysis of transverse oscillations of drilling rig derrick as Timoshenko beam with variable parameters along the length
1
Department of Strength of Materials and Structural Mechanics, Lviv Polytechnic National, Ukraine
2
Department of Robotics and Integrated Mechanical Engineering Technologies, Lviv Polytechnic National, Ukraine
Submission date: 2025-04-09
Acceptance date: 2025-05-27
Online publication date: 2025-06-02
Publication date: 2025-06-02
Corresponding author
Yevhen Kharchenko
Department of Strength of Materials and Structural Mechanics, Lviv Polytechnic National, Ukraine
Department of Strength of Materials and Structural Mechanics, Lviv Polytechnic National, Ukraine
Diagnostyka 2025;26(2):2025214
KEYWORDS
TOPICS
ABSTRACT
Free and forced transverse oscillations of a drilling rig tower are considered. The computational model is represented as a Timoshenko beam with variable bending stiffness, running mass, and longitudinal force along the length. It is assumed that the tower is mounted on a rigid platform supported by an elastic base. Additionally, the tower is connected to the base by means of elastic braces. The crown block and rig service platforms attached to the tower are treated as rigid bodies. For the case of harmonic oscillations of a Timoshenko beam with variable parameters along its length, the differential equations of the amplitude functions are obtained and reduced to Volterra integral equations. Oscillations of a multi-span structure are calculated using the matrix method of initial parameters. An analysis of the results of calculations of transverse oscillations of a drill tower is presented.
FUNDING
This research received no external funding.
REFERENCES (31)
1.
Eugster SR, Harsch J. A variational formulation of classical nonlinear beam theories. In: Abali B, Giorgio I, eds. Developments and novel approaches in nonlinear solid body mechanics. Vol 130. Cham: Springer; 2020. https://doi.org/10.1007/978-3-....
2.
Sohani F, Eipakchi H. Linear and nonlinear vibrations of variable cross-section beams using shear deformation theory. Z Angew Math Mech. 2021; 101:e202000265; https://doi.org/10.1002/zamm.2....
3.
Xiao Z, Zhang R, Dai H. Dynamic characteristics analysis of variable cross-section beam under thermal vibration environment. Structures. 2024;61:105941. https://doi.org/10.1016/j.istr....
4.
Krutii Y, Surianinov M, Vandynsky V. Exact solution of the differential equation of transverse oscillations of the rod taking into account its own weight. MATEC Web Conference. 2017; 116:02022. https://doi.org/10.1051/matecc....
5.
McAleenan M, Nagem R. Sound and vibration in composite tubes of variable cross section. Proceedings of the ASME 1996 International Mechanical Engineering Congress and Exposition. 1996; 257-259. https://doi.org/10.1115/IMECE1....
6.
El Kaimbillah A, Braikat B, Mohri F, Damil N. A one-dimensional model for computing forced nonlinear vibration of thin-walled composite beams with open variable cross-sections. Thin-Walled Structures. 2021; 159:107211. https://doi.org/10.1016/j.tws.....
7.
Wang Z, Shi C, Gong C, Cao C, Peng Z, Sun Y. Difference solutions for responses of foundation-beams with arbitrary boundary conditions considering spatial soil variability and its applications. Computers and Geotechnics. 2022;151:105002 \https://doi.org/10.1016/J.COMP....
8.
(Stevanovic) Hedrih KR. Forced longitudinal fractional type vibrations of a rod with variable cross section. In: Abali B, Giorgio I, eds. Developments and novel approaches in nonlinear solid body mechanics. Vol 130. Cham: Springer; 2020. https://doi.org/10.1007/978-3-....
9.
Burlayenko V, Altenbach H, Dimitrova S. Modal characteristics of functionally graded porous Timoshenko beams with variable cross-sections. Composite Structures. 2024;342:118273. https://doi.org/10.1016/j.comp....
10.
Sofi A. Nonlinear vibrations of beams with fractional derivative elements crossed by moving loads. nternational Journal of Non-Linear Mechanics. 2024; 159:104567. https://doi.org/10.1016/j.ijno....
11.
Lee C, Hwang Y, Jang TS. Application of pseudo-parameter iteration method to nonlinear deflection analysis of an infinite beam with variable beam cross-sections on a nonlinear elastic foundation. Heliyon. 2024;10(7):e28176. https://doi.org/10.1016/j.heli....
12.
Li Z, Huang D. Analytical solution for vibration of functionally graded beams with variable cross-sections resting on Pasternak elastic foundations. International Journal of Mechanical Sciences. 2021; 191:106084. https://doi.org/10.1016/j.ijme....
13.
Liu L, Yang G. Transverse vibration analysis for a type of variable cross-section beam subjected to moving mass. Gongcheng Lixue/Eng Mech. 2015;32:212-219. http://doi.org/10.6052/j.issn.....
14.
Kharchenko L, Kharchenko Y. Fluctuations of multi-section aboveground pipeline region under the influence of moving diagnostic piston. Vibrations in Physical Systems. 2014; 26:105-112.
15.
Ren Y, Qu S, Yang J, Luo J, Zhu S, Zhai W. Implementation of variable cross-section curved beam in train-turnout dynamic interactions. International Journal of Mechanical Sciences. 2024;283:109662. http://doi.org/10.1016/j.ijmec....
16.
Zhao L, Deng T, Jin F, Shao Z. Nonlinear analysis on electro-elastic coupling properties in bent piezoelectric semiconductor beams with variable cross section. Applied Mathematical Modelling. 2024; 133:20-40. https://doi.org/10.1016/j.apm.....
17.
Iwaniec J, Iwaniec M, Kasprzyk S. Transverse vibrations of transmission tower of variable geometrical structure. Journal of Low Frequency Noise, Vibration and Active Control. 2018; 38(2): 774-786. https://doi.org/10.1177/146134....
18.
Yan T, Han C. Research on the vibration of drilling derrick. Advanced Materials Research. 2010; 139-141:2368-2371. ttps://doi.org/10.4028/www.scientific.net/AMR.139-141.2368.
19.
Tan Z, Chen H, Wan F, Liao F, Gao Y, Cai C. Influence of complex load on the strength and reliability of offshore derrick by using APDL and Python. Applied Sciences. 2022;12(22):11693. https://doi.org/10.3390/app122....
20.
Kharchenko Y, Blikharskyy Y, Bilovus A, Vira V, Selejdak J, Blikharskyy Z. Influence of nonstationary processes in drill rigs on the durability of structural elements. Applied Sciences. 2024; 14(13):5930. https://doi.org/10.3390/app141....
21.
Hu J, Zhang X, Tan S, Liang Y, Wang J. Fatigue damage analysis of steel truss suspension bridge under non-stationary and non-Gaussian buffeting. International Journal of Structural Stability and Dynamics. 2024; 25(06):2550055. https://doi.org/10.1142/S02194....
22.
da Silva AX, Sorokin V, Brennan M, Gonçalves P. The dynamic behavior of a finite periodic structure comprising either symmetrical or asymmetrical exponential- and conical-shaped rods. Journal of Sound and Vibration. 2024; 595:118741. https://doi.org/10.1016/j.jsv.....
23.
Civalek O, Akgöz B. Size-dependent stability of embedded beams with variable cross section. International Journal of Engineering Science. 2025; 208:104210. https://doi.org/10.1016/j.ijen....
24.
Qin M, Yang J, Wei S. Calculation of precast prestressed beam with variable cross-sections on Pasternak foundation under anchoring force. KSCE Journal of Civil Engineering. 2024; 28(9): 3941-3950. https://doi.org/10.1007/s12205....
25.
Ling T, Wu X, Huang F, Xiao J, Sun Y, Feng W. Variable cross-sections of functionally graded beams on Pasternak foundations: An enhanced interaction theory for construction applications. Archive of Applied Mechanics. 2024; 94:1005–1020. https://doi.org/10.1007/s00419....
26.
Nešić N, Cajić M, Karličić D, et al. Nonlinear vibration of a nonlocal functionally graded beam on a fractional visco-Pasternak foundation. Nonlinear Dynamics. 2022;107:2003-2026. https://doi.org/10.1007/s11071....
27.
Cheng F, Tseng W. Dynamic matrix of Timoshenko beam columns. Journal of the Structural Division. 1973; 99(3):527-549. https://doi.org/10.1061/JSDEAG....
28.
Howson W, Williams F. Natural frequencies of frames with axially loaded Timoshenko Members. Journal of Sound and Vibration. 1973; 26(4):503-515. https://doi.org/10.1016/S0022-....
29.
Thornton W, Gorzynski J. - Discussion of "Dynamic matrix of Timoshenko beam columns". Journal of the Structural Division. 1973;99(12);2502-2504. https://doi.org/10.1061/JSDEAG....
30.
Rychlik A, Vrublevskyi O, Prokhorenko A. Modelling of the diagnostic station operation process to identify damage to the wheel rim structure. J Mech Sci Technol. 2019;33(9):4129-4138. https://doi.org/10.1007/s12206...
31.
Wang T, Kinsman T. Vibrations of frame structures according to the Timoshenko theory. Journal of Sound and Vibration. 1971; 14(2):215-227. https://doi.org/10.1016/0022-4....
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