Victor A. Leontev
PhD in Physics and Mathematics, Russian State Scientific Center for Robotics and Technical Cybernetics (RTC), Senior Research Scientist, 21, Tikhoretsky pr., Saint-Petersburg, 194064, Russia, tel.: +7(812)297-30-58, ORCID: 0000-0002-4138-1386, This email address is being protected from spambots. You need JavaScript enabled to view it., This email address is being protected from spambots. You need JavaScript enabled to view it.
Received 25 April 2019
Abstract
In the first part of the article (see «Robotics and Technical Cybernetics». 2019. No. 1, Vol. 7) quadrature models with lumped parameters were presented to simulate extended flexible beams (LPM models G2, G3, Q6), and their theory was given. In this second part of the article, consideration of properties of these models is continued, and their further comparison with other known models of flexible beams is given. Models are tested on some important mechanical problems. Examples of their practical application in numerical simulations are also given. Proposed models can serve as specific rigid finite elements for computer simulation of dynamics of various robotic and mechanical structures with flexible links.
Key words
Simulation of distributed flexibility, discretization of Euler-Bernoulli beam, lumped parameter models, Gauss quadrature, dynamics of flexible multi-body systems, rigid finite elements.
DOI
https://doi.org/10.31776/RTCJ.7206
Bibliographic description
Leontev, V. (2019). Quadrature lumped parameter models for flexible long links of manipulators. Part II. Tests and application. Robotics and Technical Cybernetics, 7(2), pp.125-135.
UDC identifier:
519.876.5
References
28. Leontev, V. (2019). Quadrature lumped parameter models for long flexible links of ma-nipulators. Part I. Design of the models. Robotics and Technical Cybernetics, 7(1), pp.34-45. (in Russ.).
29. Rabotnov, Y. (1988). Mekhanika Deformiruemogo Tverdogo Tela [Deformable Solid Mechanics]. Moscow: Nauka Publ., p.712. (in Russ.).
30. Timoshenko, S., Young, D. and Weaver, W. (1985). Kolebaniya v Inzhenernom Dele [Vibration problems in Engineering]. Moscow: Mashinostroenie Publ., p.472. (in Russ.).
31. Leontev, V. (2017). Mnogofunktsional'naya komp'yuternaya programma rascheta kine-matiki, statiki, a takzhe resheniya pryamykh, obratnykh i smeshannykh zadach dinamiki otkrytoi mnogozvennoi tsepi tverdykh tel (programma MP-ДИН) [Multifunctional software application for calculation of kinematics, statics and for solving of direct, inverse and mixed kinematic problems for open multilink chain of solid bodies]. 2016663291. (in Russ.).
32. Pisarenko, G., Yakovlev, A. and Matveev, V. (1988). Spravochnik po Soprotivleniyu Materialov [Performance of Construction Materials References]. Kiev: Naukova Dumka Publ., p.736. (in Russ.).
33. Serensen, S. et al. (1962). Spravochnik Mashinostroitelya. Tom 3 [Book of References for Mechanic Engineer. Volume 3]. Moscow: Mashgiz Publ., p.654. (in Russ.).
34. Yudin, V. (1980). Analiz kolebanii strely manipulyatora [Oscillation analysis of manipulator lift arm]. Prikladnaya Mekhanika, 16(10), pp.108-115. (in Russ.).
35. Fung, T. (2003). Numerical dissipation in time-step integration algorithms for structural dynamic analysis. Progress in Structural Engineering and Materials, 5(3), pp.167-180.
36. Hairer, E. and Wanner, G. (1996). Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. Berlin [etc.]: Springer-Verlag.
37. Har, J. and Tamma, K. (2012). Advances in Computational Dynamics of Particles, Materials and Structures. Hoboken: John Wiley & Sons.
38. Leontiev, V. (2007). Extension of LMS formulations for L-stable optimal integration meth-ods with U0–V0 overshoot properties in structural dynamics: the level-symmetric (LS) integration methods. International Journal for Numerical Methods in Engineering, 71(13), pp.1598-1632.
39. Leontyev, V. (2010). Direct time integration algorithm with controllable numerical dissipa-tion for structural dynamics: Two-step Lambda method. Applied Numerical Mathematics, 60(3), pp.277-292.
40. Rzhanitsyn, A. (1982). Stroitel'naya Mekhanika: Uchebnoe Posobie dlya Vuzov [Structural Engineering: Textbook for Institutes of Higher Education]. Moscow: Vysshaya Shkola Publ., p.400. (in Russ.).
