Study on Vibration Characteristics of Multi-Beam Structures with Stick and Slip at Joints
Source abstract
Abstract
Stick–slip phenomena may manifest at the joints during cyclic vibrations in beam structures connected by some forms of joint. This work incorporates the sticking–slip effect of joint connections into the dynamic analysis framework of multi-beam structures through changes in friction forces. The system characteristic equation is solved using the incremental harmonic balance method, the vibration characteristics of the connected structure are explored through the dynamic response, and the accuracy of the model established in this paper is verified through experiments. The equivalent stiffness and damping changes of a connecting beam under different connection states are investigated for the first time. The research indicates that the “tracking” phenomenon, induced by abrupt damping and resonance frequency variations due to low contact pressure and a low friction coefficient, leads to a relatively stable vibration response amplitude across an extended frequency range. This results in the gradual attenuation of resonance peaks within the frequency response curve, giving rise to a defined resonance frequency range. As connection stiffness diminishes, the system demonstrates characteristics of internal resonance. In addition, the influence characteristics of external excitation and connection joint position on the vibration response of multi-beam structures are also explored. This model provides an effective method for studying the vibration problems of complex beam frame structures.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Structural Load-Bearing Analysis · Engineering Structural Analysis Methods · Structural Engineering and Vibration Analysis
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
College of Engineering, Ocean University of China, Qingdao 266100, China
Funding
Fundamental Research funds for the Central Universities · National Natural Science Foundation of China
References (55)
Show source-provided references
1. Dynamics of transversely vibrating beams using four engineering theories10.1006/jsvi.1999.2257 ↗
2. Timoshenko, S. (1983). History of Strength of Materials: With a Brief Account of the History of Theory of Elasticity and Theory of Structures, Courier Corporation.
3. On the transverse vibrations of bars of uniform cross-section10.1080/14786442208633855 ↗
4. Strutt, J.W., and Rayleigh, J.W.S. (1877). The Theory of Sound, Macmillan.
5. The second frequency spectrum of Timoshenko beams10.1016/S0022-460X(77)80118-1 ↗
6. Free vibration analysis of stepped beams by using Adomian decomposition method
7. Nonlocal longitudinal, flapwise, and chordwise vibrations of rotary doubly coaxial/non-coaxial nanobeams as nanomotors10.1016/j.ijmecsci.2019.105291 ↗
8. Free vibration analysis of a rotating single edge cracked axially functionally graded beam for flap-wise and chord-wise modes10.1016/j.engstruct.2021.112564 ↗
9. Dynamic stiffness formulation and free vibration analysis of centrifugally stiffened Timoshenko beams10.1006/jsvi.2001.3716 ↗
10. Shu, C. (2012). Differential Quadrature and Its Application in Engineering, Springer Science & Business Media.
11. Effect of tapering on natural frequencies of rotating beams10.1155/2007/865109 ↗
12. Modeling the dynamics of mechanical joints10.1016/j.ymssp.2011.01.010 ↗
13. Overview of mechanical modeling methods for bolted connections
14. A distributed-element model for hysteresis and its steady-state dynamic response10.1115/1.3625199 ↗
15. On a class of models for the yielding behavior of continuous and composite systems10.1115/1.3607751 ↗
16. Dynamic Properties of Machine Bolted Joints Summary10.4028/www.scientific.net/AMM.423-426.1594 ↗
17. Fundamental consequences of a new intrinsic time measure: Plasticity as a limit of the endochronic theory
18. Bouc, R. (1967, January 5–9). Forced vibrations of mechanical systems with hysteresis. Proceedings of the Fourth Conference on Nonlinear Oscillations, Prague, Czech Republic.
19. Method for random vibration of hysteretic systems10.1061/JMCEA3.0002106 ↗
20. Finite element analysis and modelling of structure with bolted joints10.1016/j.apm.2006.03.020 ↗
21. Bolt loosening at rotating joint interface and its influence on rotor dynamics10.1016/j.engfailanal.2015.11.002 ↗
22. A note on vibrations of generally restrained beams10.1016/0022-460X(89)90069-2 ↗
23. Vibration of beams with generally restrained boundary conditions using Fourier series10.1006/jsvi.2001.3615 ↗
24. Vibrations of Timoshenko beams with elastically restrained ends10.1016/0022-460X(84)90508-X ↗
25. Random vibration of uniform beams with varying boundary conditions by the dynamic-edge-effect method10.1016/0045-7825(94)00708-U ↗
26. Green’s functions of the forced vibration of Timoshenko beams with damping effect10.1016/j.jsv.2013.11.007 ↗
27. Free vibrations of beams with general boundary conditions10.1006/jsvi.2000.3150 ↗
28. The fundamental modal response of elastically connected parallel Timoshenko beams10.1016/j.jsv.2022.116920 ↗
29. Analysis of natural vibration characteristics of continuous multi-span beams with concentrated mass under arbitrary boundary conditions
30. Free vibration of connected double-beam system with general boundary conditions by a modified Fourier–Ritz method10.1007/s00419-017-1339-5 ↗
31. An exact fourier series method for the vibration analysis of multispan beam systems
32. Shake Table response of a dual system with inline friction damper10.1016/j.engstruct.2023.115776 ↗
33. Numerical and experimental investigations on dynamic behaviors of a bolted joint rotor system with pedestal looseness10.1016/j.jsv.2023.118036 ↗
34. Nonlinear response of a beam under distributed moving contact load10.1016/j.cnsns.2004.08.002 ↗
35. Friction-induced vibration for an aircraft brake system-Part 1: Experimental approach and stability analysis10.1016/j.ijmecsci.2005.12.002 ↗
36. Analysis of nonlinear frequency mixing in Timoshenko beams with a breathing crack using wavelet spectral finite element method10.1016/j.jsv.2020.115532 ↗
37. Nonlinear vibration analysis of a generally restrained double-beam structure coupled via an elastic connector of cubic nonlinearity10.1007/s11071-022-07410-w ↗
38. On the efficacy of friction damping in the presence of nonlinear modal interactions10.1016/j.jsv.2016.01.039 ↗
39. Analytical vibration modelling and solution of bars with frictional clamps10.1016/j.jsv.2024.118307 ↗
40. Nonlinear response analysis of bolted joined cylindrical-cylindrical shell with general boundary condition10.1016/j.jsv.2018.12.003 ↗
41. Stability analysis of reduced rotor pedestal looseness fault model10.1007/s11071-015-2264-1 ↗
42. Nonlinear dynamic behavior of a dual-rotor bearing system with coupling misalignment and rubbing faults
43. Casini, P., and Vestroni, F. (2022). Mitigation of Structural Vibrations of MDOF Oscillators by Modal Coupling Due to Hysteretic Dampers. Appl. Sci., 12.10.3390/app121910079 ↗
44. Application of quasi-static modal analysis to a finite element model and experimental correlation10.1016/j.jsv.2020.115376 ↗
45. A lever-type nonlinear energy sink10.1016/j.jsv.2018.08.058 ↗
46. Vibration energy flow transmission in systems with Coulomb friction10.1016/j.ijmecsci.2021.106932 ↗
47. Alberto, J., and Fuentes, A. (2023). On the Influence of Piecewise Defined Contact Geometries on Friction Dampers, KIT Scientific Publishing.
48. Response of a mass-spring system subject to Coulomb damping and harmonic base excitation10.1016/j.ijsolstr.2020.02.037 ↗
49. Displacement transmissibility of a Coulomb friction oscillator subject to joined base-wall motion10.1007/s11071-019-04983-x ↗
50. Experimental investigation of a single-degree-of-freedom system with Coulomb friction10.1007/s11071-019-05443-2 ↗
51. Multi-degree-of-freedom systems with a Coulomb friction contact: Analytical boundaries of motion regimes10.1007/s11071-021-06278-6 ↗
52. Micro/macro-slip damping in beams with frictional contact interface10.1016/j.jsv.2012.05.026 ↗
53. Numerical analysis for the stick-slip vibration of a transversely moving beam in contact with a frictional wall10.1016/j.jsv.2017.12.037 ↗
54. Stick-slip vibration of a cantilever beam subjected to harmonic base excitation10.1007/s11071-018-4164-7 ↗
55. Reduced-order modeling of bladed disks with friction ring dampers10.1115/1.4036952 ↗