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Elastically restrained Bernoulli-Euler beams applied to rotary machinery modelling
作者姓名:Tiago A.N.Silva  Nuno M.M.Maia
作者单位:ISEL;Polytechnic;Institute;Lisbon;Department;Mechanical;Engineering;Conselheiro;Emídio;Navarro;IDMEC-IST;Technical;University;
基金项目:supported by the Portuguese Foundation for Science and Tech-nology(FCT),under the project POCI 2010 and the PhD grant SFRH/BD/44696/2008
摘    要:Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending,the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams carrying a finite number of concentrated elements along their length.Based on Rayleigh's quotient,an iterative strategy is developed to find the approximated torsional stiffness coefficients,which allows the reconciliation between the theoretical model results and the experimental ones,obtained through impact tests.The mentioned algorithm treats the vibration of continuous beams under a determined set of boundary and continuity conditions, including different torsional stiffness coefficients and the effect of attached concentrated masses and rotational inertias, not only in the energetic terms of the Rayleigh's quotient but also on the mode shapes,considering the shape functions defined in branches.Several loading cases are examined and examples are given to illustrate the validity of the model and accuracy of the obtained natural frequencies.

关 键 词:模型应用  欧拉梁  伯努利  旋转机械  弹性支撑  刚度系数  弹性支承梁  连续性条件

Elastically restrained Bernoulli-Euler beams applied to rotary machinery modelling
Tiago A.N.Silva,Nuno M.M.Maia.Elastically restrained Bernoulli-Euler beams applied to rotary machinery modelling[J].Acta Mechanica Sinica,2011,27(1):56-62.
Authors:Tiago A N Silva  Nuno M M Maia
Institution:(1) 811 Northview Pl., Coquitlam, BC, V3J 3R4, Canada;(2) Condor Rebar Consultants, Inc., 300-1128 Hornby St., Vancouver, BC, V6Z 2L4, Canada
Abstract:Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending, the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams carrying a finite number of concentrated elements along their length. Based on Rayleigh’s quotient, an iterative strategy is developed to find the approximated torsional stiffness coefficients, which allows the reconciliation between the theoretical model results and the experimental ones, obtained through impact tests. The mentioned algorithm treats the vibration of continuous beams under a determined set of boundary and continuity conditions, including different torsional stiffness coefficients and the effect of attached concentrated masses and rotational inertias, not only in the energetic terms of the Rayleigh’s quotient but also on the mode shapes, considering the shape functions defined in branches. Several loading cases are examined and examples are given to illustrate the validity of the model and accuracy of the obtained natural frequencies.
Keywords:Transverse vibration of beams · Elastic supports · Torsional stiffness coefficients
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