Another second order beam vibration theory: Explicit bending warping flexibility and restraint

1990 ◽  
Vol 137 (1) ◽  
pp. 43-51 ◽  
Author(s):  
M.S. Ewing
Keyword(s):  
Second Order ◽  
Beam Vibration ◽  
Vibration Theory

Lateral Vibration of a Consistent Continuous Beam With a Crack

1997 ◽  
Author(s):  
Thomas G. Chondros ◽  
Andrew D. Dimarogonas ◽  
Jonathan Yao
Keyword(s):  
Displacement Field ◽  
Edge Crack ◽  
Fatigue Cracks ◽  
Lateral Vibration ◽  
Single Edge ◽  
Cracked Beam ◽  
Beam Vibration ◽  
Vibration Theory ◽  
Lateral Vibrations ◽  
Double Edge

Abstract A continuous cracked beam vibration theory is developed for the lateral vibration of cracked Euler-Bernoulli beams with single-edge or double-edge cracks. The Hu-Washizu-Barr variational formulation was used to develop the differential equation and the boundary conditions of the cracked beam as an one-dimensional continuum. The displacement field about the crack was used to modify the stress and displacement field throughout the bar. The crack was modelled as a continuous flexibility using the displacement field in the vicinity of the crack, found with fracture mechanics methods. The results of three independent evaluations of the lowest natural frequency of lateral vibrations for beams with a single-edge crack are presented: the continuous cracked beam vibration theory developed here, the lumped crack beam vibration analysis, and an asymptotic solution. Experimental results from aluminum beams with fatigue cracks are very close to the values predicted. A steel beam with a double-edge crack was also investigated with the above mentioned methods, and results compared well with experimental data.

A CONTINUOUS CRACKED BEAM VIBRATION THEORY

1998 ◽  
Vol 215 (1) ◽  
pp. 17-34 ◽  
Author(s):  
T.G. Chondros ◽  
A.D. Dimarogonas ◽  
J. Yao
Keyword(s):  
Cracked Beam ◽  
Beam Vibration ◽  
Vibration Theory

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

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