Effects Of Hub Radius Research Articles

Effect of Hub Radius on Rotational Stability of Functionally Graded Timoshenko Beams

This work is concerned to examine the rotational stability of functionally graded cantilever Timoshenko beams. Power law with various indices as well as exponential law were used to find out the effect of hub radius parameter on the stability of both functionally graded ordinary (FGO) beam. Floquet’s theory was used to establish the stability boundaries. The governing equation of motion was followed by Hamilton’s principle and solved by Finite element method. Dependence of Bulk modulus on thickness of beam was studied using both power law and exponential distribution. The influence of hub radius parameter was found to be enhancing the stability of FGO beams. It has further been confirmed that the effect of hub radius with exponential distribution of constituent phases renders better stability compared to power law distribution of the phases in the functionally graded material(FGM).

Semi-active nonlinear vibration control of a functionally graded material rotating beam with uncertainties, using a frequency estimator

A novel semi-active controller with adaptable parameters is developed to suppress the forced-vibration of a functionally graded material Timoshenko rotating beam with unknown parameters. The control algorithm is provided with a frequency estimator in order to identify the unknown frequency of the external excitations. The simplicity of the adaptive algorithm and efficient performance through a wide range of frequencies, are the advantages of the presented controller. Consecutive calculations allow the control parameters to be adjusted when the excitation frequency changes abruptly. The effects of hub radius, transverse shear deformation, and rotary inertia and tip masses are taken into account and the finite element method is utilized to discretize the dynamic model. The results demonstrate that the control algorithm is able to reduce the nonlinear vibration of the rotating beam at different nodes along its length when the frequency of the excitations changes. The controller is also effective when the rotational speed of the hub changes gradually over time.

Free vibration analysis of a rotating non-uniform functionally graded beam

In this paper, free vibration characteristics of a rotating double tapered functionally graded beam is investigated. Material properties of the beam vary continuously through thickness direction according to the power-law distribution of the volume fraction of the constituents. The governing differential equations of motion are derived using the Hamilton's principle and solved utilizing an efficient and semi-analytical technique called the Differential Transform Method (DTM). Several important aspects such as taper ratios, rotational speed, hub radius, as well as the material volume fraction index which have impacts on natural frequencies of such beams are investigated and discussed in detail. Numerical results are tabulated in several tables and figures. In order to demonstrate the validity and accuracy of the current analysis, some of present results are compared with previous results in the literature and an excellent agreement is observed. It is showed that the natural frequencies of an FG rotating double tapered beam can be obtained with high accuracy by using DTM. It is also observed that nondimensional rotational speed, height taper ratio, power-law exponent significantly affect the natural frequencies of the FG double tapered beam while the effects of hub radius and breadth taper ratio are negligible.

VIBRATION ANALYSIS OF A ROTATING TAPERED COMPOSITE BEAM WITH TIP MASS

In this study, free vibration responses of a rotating tapered composite beam with tip mass are investigated. The energy expressions for the kinetic and potential energies of a rotating composite beam with tip mass have been formulated. The energy expressions are then applied in Lagrange’s equations to develop the equation of motion of a composite beam with tip mass. The stiffness and mass matrices for a standard composite beam element with two end nodes with two degrees of freedom at each node are derived. Various parametric studies are performed to investigate the effect of tip mass and the rotational speed on the variation of natural frequencies of the composite beam. The investigations are also done to study the effect of hub radius on the natural frequencies. It is shown that the addition of tip mass increases the stiffness of the structure and consequently increases the natural frequencies.

Effect of Tapering on Natural Frequencies of Rotating Beams

The problem of free vibration of a rotating tapered beam is investigated by developing explicit expressions for the mass, elastic and centrifugal stiffness matrices in terms of the taper ratios. This investigation takes into account the effect of tapering in two planes, the effect of hub radius as well as the stiffening effect of rotation. The equations of motion are derived; the associated generalized eigenvalue problem is defined in conjunction with a suitable Lagrangian form and solved for a wide range of parameter changes. The effect of tapering on the natural frequencies of the beam is examined with all parameter changes present. Results are compared with those available in literature and are found to be in excellent agreement.

The Effect of Hub Radius on the Flow Due to a Rotating Disk

The Effect of Hub Radius on the Flow Due to a Rotating Disk

Free vibration characteristics of rotating Timoshenko beams

The in-plane and out-of-plane free vibrations of a rotating Timoshenko beam are analyzed by means of a finite element technique. The beam is discretized into a number of simple elements with four degrees of freedom each. The governing equations for the free vibrations of the rotating beam are derived from Hamilton's principle. The effects of hub radius, setting angle, shear deformation and rotary inertia are incorporated into a finite element model for determining the bending frequencies of the rotating beam. Numerical results for uniform cantilever beams with and without the hub radius are given for various values of the rotational speed, and are compared with the available results. It is shown that the present technique offers an accurate and effective method for solving the free vibration problems of rotating beams.

Effect of Hub Radius on the Vibrations of a Uniform Bar

Abstract Methods are discussed for obtaining upper and lower bounds on the frequencies of a uniform beam, rotating at a constant speed about an axis at one end, and vibrating transversely to the plane of rotation. Previous results are extended to include the case of a nonzero hub radius. Bounds on the first two frequencies are given for several ratios of hub radius to beam length. These show that the frequencies depend almost linearly on the hub radius for various rotational speeds.