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In the present paper, the free and forced vibration of multiple cracked multi span continuous beams made of functionally graded material (FGM) is investigated by the dynamic stiffness method. First, there are constructed dynamic stiffness matrix and nodal load vector of multiple cracked FGM beam element using Timoshenko beam theory and massless double spring model of crack. Then, effect of cracks parameters on free and forced vibration of the FGM continuous beams is examined. The theoretical developments are validated by numerical examples. The obtained results provide an efficient method to analyze free and forced vibration of multiple cracked FGM framed structures and assessment of the behavior of damaged structures.

Mode shapes of multiple cracked beam-like structures made of Functionally Graded Material (FGM) are analyzed by using the dynamic stiffness method. Governing equations in vibration theory of multiple cracked FGM beam are derived on the base of Timoshenko beam theory; power law variation of material; coupled spring model of crack and taking into account the actual position of neutral axis. A general solution of vibration in frequency domain is obtained and used for constructing dynamic stiffness matrix of the multiple cracked FGM Timoshenko beam element that provides an efficient method for modal analysis of multiple cracked FGM frame structures. The theoretical development is illustrated by numerical analysis of crack-induced change in mode shapes of multi-span continuous FGM beam.

This paper presents crack identification in multiple cracked beams made of functionally graded material (FGM) by using stationary wavelet transform (SWT) of mode shapes and taking into account influence of Gaussian noise. Mode shapes are obtained from multiple cracked FGM beam element and spring model of cracks. The theoretical development was illustrated and validated by numerical examples. The investigated results show that crack identification method by using SWT of mode shapes is efficient and realizable.

In this paper, an integrated procedure is proposed to identify cracks in a portal framed structure made of functionally graded material (FGM) using stationary wavelet transform (SWT) and neural network (NN). Material properties of the structure vary along the thickness of beam elements by the power law of volumn distribution. Cracks are assumed to be open and are modeled by double massless springs with stiffness calculated from their depth. The dynamic stiffness method (DSM) is developed to calculate the mode shapes of a cracked frame structure based on shape functions obtained as a general solution of vibration in multiple cracked FGM Timoshenko beams. The SWT of mode shapes is examined for localization of potential cracks in the frame structure and utilized as the input data of NN for crack depth identification. The integrated procedure proposed is shown to be very effective for accurately assessing crack locations and depths in FGM structures, even with noisy measured mode shapes and a limited amount of measured data.