INFLUENCE OF CRACK DEPTH AND ATTACHED MASSES ON BEAM NATURAL FREQUENCIES

S.A.M. AL-Said∗ and A.A. AL-Qaisia∗∗

References

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  12. [12] B.S. Haisty & W.T. Springer, A general beam element foruse in damage assessment of complex structures, Journal ofVibration, Acoustics, Stress, and Reliability in Design, 110,1988, 389–394.NomenclatureA Cross sectional area of the beama Crack depthB Beam widthD Crack depth ratio (D = a/H)E Modulus of elasticity of the beamH Half depth of the beamI Area moment of inertia for the beam crosssectionKB Beam cross section radius of gyrationKBB = KB/LBLB Total length of the beammB Beam massmAi Attached massMBAi Mass ratio = mAi/mBNA Number of attached massesNM Number of assumed modesqi i-th generalized coordinatet TimeT Kinetic energyU Potential energyV Transverse deflectionVAi Attached mass transverse movementX Distance along x axisXAi Attached mass locationXcr Crack locationη = X/LBηAi = XAi/LBηcr = Xcr/LBβ0 Non-dimensional frequency for intact beamwithout attached massβMD Non-dimensional frequency for cracked beamwith attached massβ = ωρA L4BEIβD Non-dimensional frequency for cracked beamwithout attached massβM Non-dimensional frequency for intact beamwith attached massΔβMD =βMD − β0β0ΔβM =βM − β0β0ΔβD =βD − β0β0(ΔβD)li =βMD − βMβ0Δβco = ΔβMD − ΔβD − ΔβMΘcr Crack flexibilityτ = β = ωρA L4BEI∗( )ddτ•( )ddt( )ddη

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