تحلیل فرکانسی تشخیص ترک در تیرها با استفاده از روش ماتریس انتقال

In this paper the frequency analysis of transverse vibration of an Euler-Bernoulli beam with a number of cracks in the longitudinal direction of the beam has been studied. Modelling of connection for both the left and right sides of a cracked element of the beam was performed using a torsional spring. Based on separation of variables technique, a harmonic response for the beam transverse vibration has been considered. Using a general form of mode shape for the beam, the relation between quantities of deflection, slope, bending moment and shear force at both ends of the beam’s element have been obtained employing the transfer matrix method. Then, at the crack location for every cracked element of the beam, the quantities of deflection, slope, bending moment and shear force for both left and right sides of the crack are connected to each other and total transfer matrix in which relate the properties of the end node of the beam to the first one has been extracted. The frequency equations of transverse vibration of the cracked beam with clamped-free and simply support end conditions are obtained and the natural frequencies of the cracked beam has been obtained. The simulation results of frequency analysis for variation of non-dimensional amplitudes of two transmitted sinusoidal waves in longitudinal direction of the beam with different frequencies when impact the crack on the beam in terms of frequency of transmitted waves are presented using diagnosis Fourier transformation method.