Vibration Modes of Centrifugally Stiffened Beams
01 Mar 1982-Journal of Applied Mechanics (American Society of Mechanical Engineers)-Vol. 49, Iss: 1, pp 197-202
TL;DR: In this paper, the exact frequencies and mode shapes for rotating beams in which both the flexural rigidity and the mass distribution vary linearly were solved using the Frobenius method.
Abstract: The method of Frobenius is used to solve for the exact frequencies and mode shapes for rotating beams in which both the flexural rigidity and the mass distribution vary linearly. Results are tabulated for a variety of situations including uniform and tapered beams, with root offset and tip mass, and for both hinged root and fixed root boundary conditions. The results obtained for the case of the uniform cantilever beam are compared with other solutions, and the results of a conventional finite-element code.
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TL;DR: The status and some recent developments in computational modeling of flexible multibody systems are summarized in this article, where a number of aspects of flexible multi-body dynamics including: modeling of the flexible components, constraint modeling, solution techniques, control strategies, coupled problems, design, and experimental studies.
Abstract: The status and some recent developments in computational modeling of flexible multibody systems are summarized. Discussion focuses on a number of aspects of flexible multibody dynamics including: modeling of the flexible components, constraint modeling, solution techniques, control strategies, coupled problems, design, and experimental studies. The characteristics of the three types of reference frames used in modeling flexible multibody systems, namely, floating frame, corotational frame, and inertial frame, are compared. Future directions of research are identified. These include new applications such as micro- and nano-mechanical systems; techniques and strategies for increasing the fidelity and computational efficiency of the models; and tools that can improve the design process of flexible multibody systems. This review article cites 877 references. @DOI: 10.1115/1.1590354#
360 citations
TL;DR: In this article, the free vibration of rotating beams is analyzed by means of a finite-element method of variable order, where the displacement is assumed to be analytic within an element and thus can be approximated to any degree of accuracy desired by a complete power series.
Abstract: The free vibration of rotating beams is analyzed by means of a finite-element method of variable order. This method entails displacement functions that are a complete power series of a variable number of terms. The terms are arranged so that the generalized coordinates are composed of displacements and slopes at the element extremities and, additionally, displacements at certain points within the element. The displacement is assumed to be analytic within an element and thus can be approximated to any degree of accuracy desired by a complete power series. Numerical results are presented for uniform beams with zero and nonzero hub radii, tapered beams, and a nonuniform beam with discontinuities. Since the present method reduces to a conventional beam finite-element method for a cubic displacement function, the results are compared and found to be superior to the conventional results in terms of accuracy for a given number of degrees of freedom. Indeed, essentially exact eigenvalues and eigenvectors are obtained with this technique, which is far more rapidly convergent than other approaches in the literature.
232 citations
TL;DR: In this article, a finite element analysis for a rotating cantilever beam is presented based on a dynamic modelling method using the stretch deformation instead of the conventional axial deformation, three linear partial differential equations are derived from Hamilton's principle.
198 citations
TL;DR: In this article, the dynamic stiffness matrix of a uniform rotating Bernoulli-Euler beam is derived using the Frobenius method of solution in power series, which includes the presence of an axial force at the outboard end of the beam in addition to the usual centrifugal force arising from the rotational motion.
188 citations
TL;DR: In this paper, a spectral finite element method (SFEM) is proposed to develop a low-degree-of-freedom model for dynamic analysis of rotating tapered beams, which exploits semi-analytical progressive wave solutions of the governing partial differential equations.
Abstract: A spectral finite element method (SFEM) is proposed to develop a low-degree-of-freedom model for dynamic analysis of rotating tapered beams. The method exploits semi-analytical progressive wave solutions of the governing partial differential equations. Only one single spectral finite element is needed to obtain any modal frequency or mode shape, which is as accurate or better than other approaches reported in the literature for straight or uniformly tapered beams. The minimum number of such spectral finite elements corresponds to the number of substructures, that is, beam sections with different uniform tapers, in a rotating beam to capture the complete system dynamic characteristics. The element assembly procedure is accomplished in the same fashion as the conventional finite element approach. Results are for a number of examples such as a straight beam and beams with uniform taper or compound tapers. Overall, for a rotating blade system, our SFEM provides highly accurate predictions for any modal frequency using a single element or very few elements corresponding to the number of uniform taper changes in the blade system. Nomenclature EI (x) = beam bending flexural stiffness EI 0 = reference beam bending flexural stiffness L = beam length M(x) = beam bending moment m(x) = beam mass per unit length m0 = reference beam mass per unit length R =o ffset length between beam and rotating hub T (x) = beam axial force due to centrifugal stiffening V (x) = beam shear force W(x) = beam bending mode shape function w(x, t) = beam transverse displacement α = beam mass per unit length constant βi = beam bending flexural stiffness constant, i = 1, 4 η = nondimensional axial force µ = nondimensional natural frequency � = beam rotation speed ω =e xcitation frequency
151 citations