|
|
Forced Vibration Calculation of the Eccentric Stepped Beam-Foundation System |
WANG Jian1, 2 ZHANG Zhen-guo1, 2 REN Long-long1, 2 HUA Hong-xing1, 2 |
1. Institute of Vibration, Shock and Noise, Shanghai Jiao Tong University, Shanghai 200240;
2. State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240 |
|
|
Abstract The vibrations in vertical and longitudinal directions will couple if mass eccentricities are considered in the beam, a theoretical/experimental method focus on the vibration of eccentric stepped beam-complicated flexible foundation system is proposed combining the receptance coupling and modified transfer matrix method. The method is validated via the comparison to the results obtained by the FEM. The influence on the response of the system caused by eccentricity is investigated. Eccentricity can hardly affect the vertical response of the system, while it can induce displacement in longitudinal direction even the beam is under vertical excitation. The longitudinal vibration is introduced by the form of eθ, therefore, the associated longitudinal displacement is proportional to eccentricity and its characteristic frequencies are consistent with that of the vertical displacement.
|
Received: 13 June 2016
Published: 15 November 2017
|
|
|
|
[1] LIN H Y. Dynamic analysis of a multi-span uniform beam carrying a number of various concentrated elements[J]. Journal of Sound and Vibration, 2008, 309(1): 262-275.
[2] 崔灿, 蒋晗, 李映辉. 变截面梁横向振动特性半解析法[J]. 振动与冲击, 2012, 31(14): 85-88.
CUI Can, JIANG Han, LI Ying-hui. Semi-analytical method for calculating vibration characteristics of variable cross-section beam[J]. Journal of vibration and shock, 2012, 31(14): 85-88.
[3] ZHANG Z, CHEN F, ZHANG Z, et al. Vibration analysis of non-uniform Timoshenko beams coupled with flexible attachments and multiple discontinuities[J]. International Journal of Mechanical Sciences, 2014, 80: 131-143.
[4] CAO M S, XU W, SU Z, et al. Local coordinate systems-based method to analyze high-order modes of n-step Timoshenko beam[J]. Journal of Vibration and Control, 2015: 1077546315573919.
[5] 王剑, 张振果, 华宏星. 考虑质量偏心 Timoshenko 梁的弯-纵耦合固有振动特性研究[J]. 振动与冲击, 2015, 34(19): 8-12.
WANG Jian, ZHANG Zhenguo, HUA Hongxing. Flexural-longitudinal coupled natural vibration characteristics of a Timoshenko beam considering mass eccentricity[J]. Journal of Vibration and Shock, 2015, 34(19): 8-12.
[6] JUNGER M C, FEIT D. Sosund, structures, and their interaction[M]. Cambridge: MIT press, 1986.
[7] CARESTA M, KESSISSOGLOU N J. Acoustic signature of a submarine hull under harmonic excitation[J]. Applied acoustics, 2010, 71(1): 17-31.
[8] HAROLD D N. Rotordynamic Modeling and Analysis Procedures: A Review[J]. JSME International Journal Series C Mechanical Systems, Machine Elements and Manufacturing, 1998, 41(1): 1-12.
[9] BONELLO P, BRENNAN M J. Modelling the dynamic behaviour of a supercritical rotor on a flexible foundation using the mechanical impedance technique[J]. Journal of sound and vibration, 2001, 239(3): 445-466.
[10] HONG J, SHAPOSHNIKOV K, ZHANG D, et al. Theoretical modeling for a rotor-bearing-foundation system and its dynamic characteristics analysis[C]//Proceedings of the 9th IFToMM International Conference on Rotor Dynamics. Springer International Publishing, 2015: 2199-2214.
[11] WANG Z, LUND J W. Calculations of Long Rotors With Many Bearings on a Flexible Foundation[C]//Third International Conference on Vibration in Rotating Machinery. 1984: 11-13.
[12] ZHANG Z, HUANG X, ZHANG Z, et al. On the transverse vibration of Timoshenko double-beam systems coupled with various discontinuities[J]. International Journal of Mechanical Sciences, 2014, 89: 222-241.
[13] RAO S S, YAP F F. Mechanical vibrations[M]. New York: Addison-Wesley, 1995.
[14] COWPER G R. The shear coefficient in Timoshenko’s beam theory[J]. Journal of applied mechanics, 1966, 33(2): 335-340.
[15] LEISSA A W. Vibration of shells[M]. New York: Acoustical Society of America, 1993.
|
|
|
|