Vibration Analysis of Cracked Structures as a Roving Body Passes a Crack Using the Rayleigh-Ritz Method

Abstract

The natural frequencies of a cracked plate with a roving mass were computed using the Rayleigh-Ritz Method for various sets of boundary condition. The obtained frequencies exhibit a sudden shift as a roving body crosses a crack. If the crack is only partial and continuity of translation is maintained, then the frequency shift occurs only when the body possesses a rotary inertia. If the crack is a complete one (through thickness) which permits differential translation to occur on either side of the crack, a particle having mass only (translatory inertia) is sufficient to cause a sudden shift. There is no need for a rotary inertia. This is potentially useful in detecting cracks in structures, as it is possible to track the changes in the natural frequencies of a structure as a test body such as a vehicle on a bridge moves and identify points where sudden frequency changes occur.

A Review on Vibration-Based Damage Detection Methods for Civil Structures

“…Based on this, they also presented an explicit closed-form solution of the governing equation of a multicracked Euler-Bernoulli beam carrying a roving body. Similarly, Ilanko et al [34] ana-Figure 5. The application of auxiliary mass: (a) the experimental set-up in [30] and (b) the experimental set-up in [32].…”

“…Based on this, they also presented an explicit closed-form solution of the governing equation of a multi-cracked Euler-Bernoulli beam carrying a roving body. Similarly, Ilanko et al [34] analyzed the frequency changes as a roving body passed a crack on a plate using the Rayleigh-Ritz Method for various boundary conditions. A sudden frequency shift was obtained as the roving body with rotary inertia crossed a partial crack or with translational inertia only when crossing a complete (through-thickness) crack.…”

“…This can be a simplified model for crack detection in a bridge, which is to identify points where sudden frequency shifts occur as a vehicle moves on the bridge; thus, the crack locations can be obtained. Experimental verification is needed to examine the feasibility of the method in [33,34]. Massless rotational springs were used to model the crack, and the evaluation of crack severity (i.e., spring stiffness) remains a challenge.…”

“…For unique identification of damage location, there are a few promising ways to include the spatial information of damage in frequency responses. For example, an auxiliary mass with or without rotary inertia can be attached to the structure [20][21][22][23][24]30,[32][33][34]. In this case, the mass acts as a probe, and the spatial information of damage is contained in the curve of frequency versus mass location.…”

“…For example, a stationary roving mass is utilized to enhance the effect of a crack on the dynamics of a cracked beam and provide additional spatial information about the crack [19,30]. A roving mass with or without rotary inertia has been used for crack detection in beams, plates, and cylindrical shells [20,21,33,34] without any knowledge of the theoretical model and irrespective of the crack severity. However, its practical application is yet to be explored.…”