A finite element method for free vibration analysis of generally laminated composite plateswith central crack and clamped edges have been studied using ANSYS 5.4 program. The fiber-reinforced composite materials are ideal for structural applications where highstrength-to-weight and stiffness-to-weight ratios are required, where structures must safelywork during its service life. But damages initiate a breakdown period on the structures.Cracks are among the most encountered damage types in the structures. The non-dimensionalfundamental frequency of vibration decreases with presence of cracks because, therigidity of cracked plate decreases. The natural frequency of plates depends on size andshape of the cracks, the effect of number of layers is found to be insignificant beyond fourlayers and the change of fiber orientation increasing the fundamental frequency of vibration.The results obtained have been compared with the available published literature with goodagreement results
Free vibration analysis of a cracked cantilever beam with two types of additional substructure attachment is investigated using ANSYS program. The cantilever beam is used as a master structure with single substructure attachment in various locations (as 1-DOF mass attachment and 1-DOF mass-spring attachment) with influence of crack in different location and depths. The results for the changes of the natural frequencies of a cracked beam are compared with the results produced by Vahit et al [1]. So the same geometrical properties have been studied. In additional work a cracked beam carrying two types of substructure attachment are compared with the results of the beam without a crack and with multi crack depth. In all calculations the beam has a uniform cross-section and the crack was modeled by reduction in the modulus of the beam. The reducing effects of the cracked beam on the natural frequencies had been more apparent with the substructure attached to the beam in different situations. The effect of mass-spring substructure is larger than the effect of the attachment when modeled as mass substructure for the same mass, with 17% for the first natural frequency and 2% for the second and third natural frequencies. The results can be used to identify cracks in simple beam structure; cracks have a clearer decreasing impact on the natural frequencies.
In this research a simply supported beam is used as a master structure with unknown number of attachments (fuzzy substructure) which is modeled as a system of 1-DOF attachments. Two types of attachments models were studied, namely 1-DOF mass attachment model and 1-DOF mass-spring attachment model. It is shown that the effect of attachments on the master structure natural frequencies when modeled as (mass-spring substructure) is larger than that when modeled as (mass substructure) for the same attachment mass. Engineering Statistics and normal distribution were used to find the values of the attachments to be added to the simply supported beam to improve the dynamical properties of the master structure and to find the best distribution of the attachment. The results also show that the distribution of the additional substructure can produce a great change in the natural frequencies so that the proposed statistical approach can be used to find the best distribution of attachments and number, value and location of the additional substructure .