Rotating shafts have a vast application in various industries especially in the aerospace industry such as engines, compressors and turbines. The researchers have performed considerable efforts on the rotating shafts’ dynamic behavior because of their sensitivity to the rotor specifications and different parameters such as supports. In this paper by employing a pipe elbow element, an especial finite element formulation is derived to investigate dynamic behavior of rotating shaft in the presence of support clearance. The proposed element consists of four nodes with twenty-four degrees of freedom, which also accounts for the shear and gyroscopic effects. Within a finite element analysis framework, the focus of the paper is proposing a formulation to account for the dynamic behavior of a rotating shaft with much less number of elements. The element is implemented in a finite element code and then is used to model and analyze some rotating shaft examples. In order to verify the developed formulation, results are compared with those obtained from other schemes reported in the literature.

This paper deals with free vibrations of the axially functionally graded (AFG) horseshoe arch. The modulus of elasticity and the mass density of AFG material of arch are chosen as a univariate quadratic function. The differential equations with the boundary conditions that govern the free vibration of such arch are derived and numerically solved to calculate natural frequencies and mode shapes. Natural frequencies of this study agree well with those of the finite element ADINA. Parametric studies of the geometrical and mechanical properties of the arch on frequencies and mode shapes are performed and extensively discussed.

In this paper, free vibrations of the tapered shear deformable column are studied. The column is clamped at the bottom and is free or hinged or clamped at the top. The column has a tapered cross-section, square and circular, under the condition of constant volume. The axial compressive load is acted to the top. The differential equations of such column were derived, in which the effects of the rotary inertia and shear deformation were included. For computing natural frequencies with mode shapes, the differential equations were solved numerically. The effects of column parameters of the frequencies and mode shapes were performed, and its results were extensively discussed.

In this paper, the first and second stage compressor blades of a gas turbine were studied by the experimental and numerical modal analyses. At first, the geometric models of these blades were generated by the 3D scanner and then the mode shapes and the natural frequencies of each blade were extracted by a series of numerical modal analyses. The numerical results were compared with the data obtained from the experimental modal analysis and the validity and accuracy of the developed numerical models were confirmed. Unlike most studies that use fixed-free boundary condition for performing a modal analysis, this objective was pursued by applying a free-free boundary condition. This study also investigated the effect of using wax or glue for mounting the accelerometer on the blade by assessing the FRF curves obtained from the modal tests in the frequency range of 0-10000 Hz. The sensitivity of the test results to applying free-free boundary condition, the number of accelerometers and their positions were investigated by defining three modal test configurations. The results obtained by these test configurations were compared with the results of numerical analyses and finally, the best configuration for the modal test of the studied compressor blade was determined.

In the present world stiffeners are widely used to fulfill the requirement of high stiffness. Stiffened plates are used in most of the mechanical structures. In this paper free vibration analysis of eccentric and concentric stiffened isotropic plate with central stiffener and double stiffener has been studied and effect of various parameters such as boundary conditions, aspect ratio on non-dimensional frequency parameter of plate are investigated. Comparison of non-dimensional frequency parameter for eccentric and concentric isotropic stiffened plate with effect of number of stiffener at different mode shapes, aspect ratios and boundary conditions is studied using ANSYS parametric design language (APDL) code. A ten nodded element (SOLID 187) from ANSYS element library is used for the discretization of proposed stiffened isotropic plate. Convergence study of developed model with respect to the number of modes has been done and results are compared from the related available published literature. Non dimensional frequencies are higher for fully clamped boundary condition for eccentric and concentric stiffened isotropic plate in comparison to other boundary condition. It is also seen that non dimensional frequencies are increases in a moderate value for eccentric and concentric isotopic plate with double stiffener in comparison to the central stiffener.

This paper presents a numerical analysis of free vibration of thin circular and annular plate using finite element method. The first five natural frequencies are presented for uniform annular plates of various inner-to-outer radius ratios, with nine possible combinations of free, clamped and simply supported boundary conditions at the inner and outer edges of plates. The accuracy of the method is established by comparing the results available in the literature. Results show that natural frequency parameter increases as the inner-to-outer radius ratio increases except in case of free boundary condition, for which it decreases with the inner-to-outer radius ratio. This result provides benchmark values that can be used to validate result obtained by other approximate approaches such as finite difference method, differential quadrature method and boundary element method.

In this paper, an analytical method is proposed for calculation of natural frequencies of a delaminated composite beam from both free and constrained mode frequencies. In previous studies, the frequencies of a delaminated composite beam were computed with assumption of occurring open or close delamination during the vibration. According to this assumption, two separated modes, i.e., “free mode” and “constrained mode”, are occurred in vibration of the delaminated beam. In fact, a delamination may breathe (open and close) during the vibration and the assumptions of the free or constrained mode models are not completely correct in the whole of the vibration period. For this reason, a new formulation is proposed for calculation of natural frequencies based on the breathing of delamination. The obtained results are compared with various theoretical and experimental results available in the literature. Thus, the effects of location and size of delamination can be investigated on the natural frequencies of delaminated beams.