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Resonance of second order in vibrations of a beam containing a transverse crack

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The article deals with the resonance of n-th order in forced transverse vibrations of a beam containing a crack situated perpendicularly to the middle line of the beam over its entire width and having a certain depth. The Ostrogradsky — Hamilton and Ritz methods are used to construct a system of ordinary nonlinear differential equations describing the dynamic behavior of a cracking beam. By the method of averaging a system of differential equations with slow variables is constructed for determining the amplitude and phase characteristics in subharmonic resonance of second order. A formula is obtained correlating the parameter of crack depth with the second harmonic of the forced periodic vibration process. The results of modeling on a PC are presented.

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Translated from Problemy Prochnosti, No. 3, pp. 56–63, March, 1995.

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Plakhtienko, N.P., Yasinskii, S.A. Resonance of second order in vibrations of a beam containing a transverse crack. Strength Mater 27, 146–152 (1995).

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  • Differential Equation
  • Dynamic Behavior
  • Nonlinear Differential Equation
  • Slow Variable
  • Transverse Vibration