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Free Vibration Analysis of Rotating Thin Twisted Plates.
Abstract
Free vibrations of rotating cantilevered thin twisted plates are investigated. First, the exact strain-displacement relationships in large deflections of thin twisted plates are derived and the principle of virtual work for free vibrations of rotating cantilevered thin twisted plates is formulated. Then, a numerical procedure based on the Rayleigh-Ritz method is proposed using algebraic polynomials as assumed displacement functions. The results of the present analysis are compared with those obtained using the finite-element method to verify the usefulness of derived equations. Finally, effects of rotation, setting angle and setting length on frequency parameters are studied for typical thin twisted plates.
... Leissa et al [11] studied cylindrical shells with chamber and twist on the shallow shell theory by Ritz method. Recently Tsuji et al [12] studied rotating thin twisted plates by the Rayleigh Ritz method.Hu and Tsuji [13] studied the rotating thin cylindrical panels with twist on general shell theory. Lo [14] in his analysis simplified the nonlinear problem by assuming the blade to be rigid everywhere except at the root presented the solution in phase plane. ...
... This method is based on a Block lancoz algorithm. Lancoz method has been developed for finding the some or all of the eigen values [12,13] and eigen vectors of large symmetric sparse matrix. For dynamic analysis an unsymmetrical Block Lancoz algorithm may be employed to handle matrices with repeated eigen values, permit dynamic response analysis with multiple simultaneously applied loads/accommodate unsymmetrical damping matrices [14,15] Lancoz method may also be used to reduce order structural models for component synthesis and control applications [16]. ...
The design of optimum marine propeller is one of the most important aspects of naval architecture. With the increase in demands for high operating efficiency, power and low level of noise, vibration reduction the design of propellers became extremely complex. This paper describes the numerical prediction of free vibration characteristics of a B-series propeller using finite element approach as a base line method. The propeller analysis is performed as a single objective function subjected to the constraints imposed by cavitation, material strength and propeller thrust. An important aspect of autonomous underwater vehicle is to evaluate its modal characteristics in terms of its mode shapes and natural frequencies. The effect of stacking sequences, fibre orientation angles are studied and finally an optimum stacking sequence has been determined for optimum characteristics of B-series (B40.7)marine propellers.
... Rao and Gupta, 2001;Surace et al., 1997;Yoo et al., 2001). Plate and shell are more approximate models of blades, but there was a little work done, such as rotating twisted plates by FEM using two different shape functions (Ramamurti and Kielb, 1984), rotating pre-twisted and tapered plates also by FEM of triangular shell elements with three nodes and eighteen degrees of freedom (Sreenivasamurthy and Ramamurti, 1981), shells with camber and twist on shallow shell theory by Ritz method (Leissa et al., 1982), rotating thin twisted plates by the Rayleigh-Ritz procedure (Tsuiji et al., 1995) and twisted cylindrical thin panels on general shell theory (Hu and Tsuiji, 1999), where the effects of parameters of the rotating systems on vibration characteristics were studied. The main purpose in this paper is to develop an numerical analysis method for vibration of a rotating twisted and open conical shell based on the study of non-rotating twisted and open conical shells (Hu et al., submitted for publication). ...
Based on a non-linear strain–displacement relationship of a non-rotating twisted and open conical shell on thin shell theory, a numerical method for free vibration of a rotating twisted and open conical shell is presented by the energy method, where the effect of rotation is considered as initial deformation and initial stress resultants which are obtained by the principle of virtual work for steady deformation due to rotation, then an energy equilibrium of equation for vibration of a twisted and open conical shell with the initial conditions is also given by the principle of virtual work. In the two numerical processes, the Rayleigh–Ritz procedure is used and the two in-plane and a transverse displacement functions are assumed to be algebraic polynomials in two elements. The effects of characteristic parameters with respect to rotation and geometry such as an angular velocity and a radius of rotating disc, a setting angle, a twist angle, curvature and a tapered ratio of cross-section on vibration performance of rotating twisted and open conical shells are studied by the present method.
An investigation of a conventional propeller made from composite materials was conducted in which its vibration characteristics were studied. Optimized designing of a composite propeller was performed for various constrained and unconstrained design objectives. Only symmetric ply stacking sequences were considered. Results show that the ply stacking sequence has an effect on the characteristics of a conventional propeller. Proper stacking sequence of the composite propeller improves its performance as compared to its metallic counterpart. The finite element method is used to calculate the resulting natural frequency and mode shapes of the propeller blades. In the present study the shapes of the propeller blade is modelled as cantilever discretized into various number of hexahedral and pentahedral finite elements. Propeller vibration characteristics are calculated by ply orientation angles, for achieving the desired objectives Ansys and Radiosis solvers are used. From the results it can be made clear that by proper selection of optimum number of layers from 8 to 16 and tailoring the ply orientation angles operational frequencies of composite materials can be further enhanced and can be made much stiffer than metallic one.
This bibliography lists references to papers, conference proceedings and theses/dissertations dealing with finite element vibration analysis of beams, plates and shells that were published in 1994-1998. It contains 361 citations. Also included, as separated subsections, are vibration analysis of composite materials and vibration analysis of structural elements with cracks/contacts.
This bibliography lists references to papers, conference proceedings and theses/dissertations dealing with finite element analysis of rotor dynamics problems that were published in 1994-1998. It contains 319 citations. Also included, as separate subsections, are finite element analyses of rotor elements - discs, shafts, spindles, and blades. Topics dealing with fracture mechanics, contact and stability problems of rotating machinery are also considered in specific sections. The last part of the bibliography presents papers dealing with specific industrial applications.
A non-linear strain–displacement relationship of a pre-twisted conical shell on the general shell theory is utilized, and a method for vibration of a rotating cantilever conical shell with pre-twist is developed by the principle of virtual work and the Rayleigh–Ritz method. Firstly, deformation and stress resultants caused by rotation are analyzed. Secondly, an equilibrium of energy for vibration of a pre-twisted conical shell having the conditions achieved in the first process is given and then an eigenfrequency equation of a rotating cantilever conical shell with pre-twisted is formulated. The effects of parameters such as an angular velocity, a radius of a hub, a setting angle, a twist angle, a subtended angle and a tapered ratio of cross-section on the fundamental vibration are investigated.
Blades are idealized as twisted cylindrical thin panels and the free vibrations of rotating blades are studied in this paper. First the steady deformation due to rotation is studied by using the principle of virtual work for deformation, then considering the initial deformations and the initial stress resultants, the vibration of the panel is analyzed by using the principle of virtual work for free vibration. The numerical procedure for analyzing the free vibrations of rotating twisted cylindrical thin panels is presented by the Rayleigh–Ritz method. The solutions are shown in non-dimensional frequency parameters and compared with the previous results. Finally, the effects of twist angle, center angle, setting angle, rotating speed and radius of rotating disc on the vibrations are investigated.
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