Dynamics of Structures with Distributed Gyroscopes: Modal Discretization Versus Spatial Discretization
Source abstract
Abstract
In this study, two discretization numerical methods, modal discretization and spatial discretization methods, were proposed and compared when applied to the gyroscopic structures. If the distributed gyroscopes are attached, the general numerical methods should be modified to derive the natural frequencies and complex modes due to the gyroscopic effect. The modal discretization method can be used for cases where the modal functions of the base structure can be expressed in explicit forms, while the spatial discretization method can be used in irregular structures without modal functions, but cost more computational time. The convergence and efficiency of both modal and spatial discretization techniques are illustrated by an example of a beam with uniformly distributed gyroscopes. The investigation of this paper may provide useful techniques to study structures with distributed inertial components.
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Research context
OpenAlex topics: Vibration and Dynamic Analysis · Dynamics and Control of Mechanical Systems · Magnetic Bearings and Levitation Dynamics
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Affiliations
Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China
School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
Funding
National Natural Science Foundation of China
References (34)
Show source-provided references
1. Control of Beams and Chains through Distributed Gyroscopes10.2514/1.29250 ↗
2. Optimal-Control of Large Space Structures Using Distributed Gyricity10.2514/3.20467 ↗
3. Controllability and Observability of Gyroelastic Vehicles10.2514/3.20728 ↗
4. Stability of gyroelastic beams10.2514/3.13223 ↗
5. Dynamics of Gyroelastic Continua10.1115/1.3167634 ↗
6. Modal parameter analysis of gyroelastic continua10.1115/1.3171881 ↗
7. Dynamics and vibration suppression of space structures with control moment gyroscopes10.1016/j.actaastro.2013.11.032 ↗
8. Dynamics and Modal Analysis of Gyroelastic Body with Variable Speed Control Moment Gyroscopes10.1115/1.4033438 ↗
9. Singularity and steering logic for control moment gyros on flexible space structures10.1016/j.actaastro.2017.04.030 ↗
10. Nonlinear isolation of transverse vibration of pre-pressure beams10.1016/j.jsv.2018.11.028 ↗
11. Dynamics of 3D Timoshenko gyroelastic beams with large attitude changes for the gyros10.1016/j.actaastro.2015.09.012 ↗
12. Modal analysis of a continuous gyroscopic second-order system with nonlinear constraints10.1016/j.jsv.2009.10.004 ↗
13. Nonlinear vibration isolation for fluid-conveying pipes using quasi-zero stiffness characteristics10.1016/j.ymssp.2018.11.057 ↗
14. Free and forced nonlinear vibration of a transporting belt with pulley support ends10.1007/s11071-018-4179-0 ↗
15. Dynamics of a beam with both axial moving and spinning motion: An example of bi-gyroscopic continua10.1016/j.euromechsol.2018.01.006 ↗
16. Carta, G., Jones, I.S., Movchan, N.V., Movchan, A.B., and Nieves, M.J. (2017). Gyro-elastic beams for the vibration reduction of long flexural systems. Proc. R. Soc. A: Math. Phys. Eng. Sci., 473.10.1098/rspa.2017.0136 ↗
17. Eigenvalue sensitivity and veering in gyroscopic systems with application to high-speed planetary gears10.1016/j.euromechsol.2017.09.003 ↗
18. Dynamic Mass of a Reaction Wheel Including Gyroscopic Effects: An Experimental Approach10.2514/1.J055398 ↗
19. On the definition of the natural frequency of oscillations in nonlinear large rotation problems10.1016/j.jsv.2010.02.015 ↗
20. Nonlinear breathing vibrations of eccentric rotating composite laminated circular cylindrical shell subjected to temperature, rotating speed and external excitations10.1016/j.ymssp.2019.02.061 ↗
21. Acar, C., and Shkel, A. (2009). MEMS Vibratory Gyroscopes: Structural Approaches to Improve Robustness, Springer.10.1007/978-0-387-09536-3 ↗
22. Theoretical investigation of indium phosphide buried ring resonators for new angular velocity sensors
23. Dell’Olio, F., Tatoli, T., Ciminelli, C., and Armenise, M.N. (2014). Recent advances in miniaturized optical gyroscopes. J. Eur. Opt. Soc. Rapid Publ., 9.10.2971/jeos.2014.14013 ↗
24. Formulation of a three-node traveling triangular plate element subjected to gyroscopic and in-plane forces10.1016/S0045-7949(02)00291-2 ↗
25. Analytical modeling of asymmetric multi-segment rotor—Bearing systems with Timoshenko beam model including gyroscopic moments10.1016/j.compstruc.2014.08.001 ↗
26. Modal Characteristics of Rotors Using a Conical Shaft Finite-Element10.1016/0045-7825(94)90191-0 ↗
27. Modal characteristics of cracked rotors using a conical shaft finite element10.1016/S0045-7825(97)00345-9 ↗
28. Alsaffar, Y., Sassi, S., and Baz, A. (2018). Band Gap Characteristics of Nonrotating Passive Periodic Drill String. J. Vib. Acoust., 140.10.1115/1.4037851 ↗
29. Band gap characteristics of periodic gyroscopic systems10.1016/j.jsv.2018.07.015 ↗
30. A Finite Rotating Shaft Element Using Timoshenko Beam Theory
31. Shape functions of three-dimensional Timoshenko beam element10.1006/jsvi.2002.5122 ↗
32. Natural frequency veering in planetary gears10.1081/SME-100107620 ↗
33. Veering phenomena in systems with gyroscopic coupling10.1115/1.1940666 ↗
34. Vibration Modes and Natural Frequency Veering in Three-Dimensional, Cyclically Symmetric Centrifugal Pendulum Vibration Absorber Systems10.1115/1.4025678 ↗