In this study, the analytical and experimental free vibration analysis of rectangular cross-section uniform cracked thick beam on two-parameter vibration and noise isolating elastic foundation, considering shear deformation and rotatory inertia is made by the finite element method. The beam element in our study is a recently introduced 4 degrees of freedom thick beam element and has two nodes with two degrees of freedom at each node such as transverse displacements and cross-section rotations. Two kinds of end conditions, i.e. clamped-clamped and clamped-free ends are considered in this study. Axial displacement of the beam is also considered. For axial displacement of the beam, linear finite elements are used. The elastic foundation is idealized as a constant two-parameter model characterized by two moduli, i.e. the Winkler foundation modulus k and the shear foundation modulus kG. In the case kG = 0, this model reduces to the Winkler model, i.e. the elastic foundation is idealized as a constant one-parameter model. The effects of foundation stiffness parameters, partial elastic foundation and crack changing its depth on the natural frequencies of the beam are examined. The effect of partial elastic foundation on the natural frequencies of the beam is examined for only half of the beam length. The crack is in the middle of the beam and only on one side of the beam having a form of open crack. In the analytical analysis, the spring coefficients of the crack are calculated in the computer program and then directly added to the stiffness matrix. The crack model used in this study is mentioned as a linear spring model in the literature. The crack modeled is in the middle of the beam and the related spring constants of rotational and extensional springs, which will be used, are added to the global matrix in the process. In the experimental analysis, steel and hard plastic beam are used as the beam material. Moreover, sponge and glass wool, which are manufactured by Petkim Ltd., are used as the isolating elastic foundation material. The results obtained from the analytical and experimental studies are presented by showing in tables and graphs and their importance in design is discussed. The analytical and experimental results and comparisons show the efficiency and effectiveness of the proposed method.
Free Vibration Analysis of Variable Cross-Section Single-Layered Graphene Nano-Ribbons (SLGNRs) Using Differential Quadrature Method
