FREQUENCY AND MODE SHAPE-ANALYSIS OF RESTRAINED BEAM-TYPE STRUCTURE WITH 2 INTERMEDIATE CRACKS MASS FOR VIBRATION DIAGNOSIS

A mathematical model to study the influence on the system vibration modes of one or two cracks in a uniform prismatic beam elastically restrained against rotation and translation at both ends and carrying lumped masses with rotary inertia, is presented. Parametric studies are carried out for the effect of stiffness of elastic constraints, the location and magnitude of cracks, concentrated masses and their rotary inertia, for the 10 combinations of the well known four classical end conditions, on the natural frequency parameters and mode shapes of the system. A system frequency equation is derived in a discrete matrix form. Good agreement is found between the results obtained using the model presented and those of previous investigators. The typical frequency charts of the present study may be useful to engineering design and non-destructive testing analysts as a tool for diagnosis and detection of cracks in engineering applications.