Influence Of Crack Depth And attached Masses On Beam natural Frequencies

摘要

A mathematical model describing the lateral free vibration of a clamped-clamped cracked beam carrying concentrated masses is derived. The masses are assumed small relative to the beam mass; also, the beam is assumed continuous with uniformly distributed properties. The attached masses are modelled as point masses with negligible rotary inertia, and the crack is simulated by a torsional spring. The Lagrangian dynamics, in conjunction with the assumed mode method are used in deriving the equation of motion. The effect of the locations of the attached masses and depth of the crack on the system frequency change is investigated along with the interaction between the attached masses and the crack depth. This interaction appears as a nonlinear coupling term in the natural frequency equation of the system. It is found that the coupling term may be used as an indicator of the error in relating system frequency change to crack only. Verification is carried out using three-dimensional finite element analysis.