Approximate Analytical Determination of Vibrodiagnostic Parameters of the Presence of a Closing Crack in Bar Elements Under Subharmonic Resonance

The Influence of Amplitude-Dependent Damping on Vibrodiagnostic Parameters of the Presence of a Closing Crack in a Beam Under Subharmonic Resonance

“…In further elaboration on the work [3,4], the present paper summarizes the findings of approximate calculations of vibrodiagnostic parameters of the presence of a closing mode I edge crack in a beam of rectangular cross-section ( Fig. 1) for different boundary conditions and types of harmonic excitation of 1/2-order subharmonic resonance in the first mode of bending vibration under amplitude-dependent damping conditions.…”

“…Calculation Procedure. According to the results obtained in [3,4], in the case of tuned 1/2-order subharmonic resonance in the jth mode of bending vibration the main vibrodiagnostic parameter of the presence of a closing edge crack of depth a in some beam section x x c = is the ratio between the maximum amplitudes of the first (resonant) harmonic A jC 1 and second harmonic A 2S of the beam deflection in any chosen section x 0 : Here, q( ) õ 0 is the ratio of the amplitudes À 2S of the total deflection N of the vibration modes considered and the amplitudes A j 2 of deflection by the resonant jth mode of vibration for a beam, which is assumed, to a certain approximation, to be intact, in a section x 0 under an excitation frequency n w = 2 j :…”

“…It is seen from (1) and (3) that, insofar as the dependence of the decrement on the vibration amplitude and frequency is known, the main task is to determine the damage characteristic (4).…”

“…Calculation Procedure. According to the results obtained in [3,4], in the case of tuned 1/2-order subharmonic resonance in the jth mode of bending vibration the main vibrodiagnostic parameter of the presence of a closing edge crack of depth a in some beam section x x c = is the ratio between the maximum amplitudes of the first (resonant) harmonic A jC …”

“…As mentioned earlier [1][2][3][4], the analysis of interrelation between fatigue crack parameters and vibrations of elastic bodies for the purpose of elaborating effective methods of vibrodiagnostics of fatigue damage still attracts researchers' attention. Significant research efforts are focused on the study of the vibration spectrum of an elastic body with a closing crack under super-and subharmonic resonances.…”