The application of vibration characteristics to damage modelling and identification in plate structures

Damage modelling is essential in the preliminary design of structures. Moreover, the identification of damage using numerical methods can make maintenance more efficient and economical. Also, applying damage detection procedures at an early stage can prevent catastrophic structure failures. For this project, vibration parameters (natural frequencies and mode shapes) are used to identify the location and severity of damage in classical thin plates. A delaminated composite plate is introduced in a comparative study, for which natural frequencies are obtained using an exact strip model to verify the proposed detection method. Next, the direct problem of calculating the relative change in natural frequencies of an isotropic simple supported plate due to a predefined single arbitrary crack with random direction, location, depth and length is mainly addressed, giving a comprehensive understanding of the relationship between the location and severity of the crack and the free vibration natural frequencies and mode shapes. This study is highly pertinent, and a hybrid model is proposed which couples exact strip analysis for the undamaged part and finite element analysis for the damaged part. In the finite element part, a crack is modelled as a rotational spring stiffness giving additional degrees of freedom to the stiffness matrix. The finite element and exact strip dynamic stiffness matrices are assembled into a global dynamic stiffness matrix, coupled using Lagrangian Multipliers to equate the displacements at the boundaries of the two parts. Applying an efficient bandwidth method for Gaussian elimination, the resulting transcendental eigenvalue problem is solved by a simplified form of the Wittrick-Williams algorithm for the first six natural frequencies. For the inverse problem, chosen natural frequencies are calculated accurately for both undamaged and damaged cases. The changes in natural frequencies are normalised to isolate the effect of damage location and severity individually. The same normalisation procedure is applied to measured natural frequencies. Point estimates of the damage location are obtained for noise free measurements, while an interval estimate is given by noisy measurements. A relevant severity range is then estimated. Mode shapes are monitored by an automatic sign method for correctly tracking the propagation of damage