Calculation of Angular Natural Frequency of Massive Beams with Concentrated Mass Loads.End Load,Uniform section,Undamped Free Vibration,Clamped-Free,Mode:1

Calculation of Angular Natural Frequency of Massive Beams with Concentrated Mass Loads.End Load,Uniform section,Undamped Free Vibration,Clamped-Free,Mode:1

1Length of Beam:lm-
2Mass per unit length of beam:u kg/m-
3Mass of Load:m kg-
4Young's modules:E *10^5 N/mm^21*10^9(N/m^2)=0.01*10^5(N/mm^2)
5Area moment of inertia of beam cross section:I cm^41(mm^4)=0.0001(cm^4)
6Graph Plot Input Data: , Figure:
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Keyword・Reference・Remarks・History

LaTex

Keyword

Angular Natural Frequency,Clamped-Free,Massive Beams,Concentrated Mass Loads,Uniform section,Undamped Free Vibration,Mode:1

Reference

[1]:Cyril M.Harris・Charles E.Crede:『SHOCK AND VIBRATION HANDBOOK IN THREE VOLUMES』,McGraw-Hill,pp.1-10~1-16,1961.
[2]:社団法人土木学会:『構造力学公式集 昭和61年版』,pp.217-218,1986.

Remarks

・E:young's modules
・I:Area moment of inertia of beam cross section
・l:Length of beam
・u:Mass per unit length of beam
・m:Mass of Load
・Caution:When mass of load(m) is small than the mass that is about 1.26% of mass of beam(u*l), calculated angular natural frequency will be larger than one which is calculated without concentrated mass.
・Making Equation Image is powered by CODECOGS

History

・2010/10/15:Upload

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