Free vibration analysis of rotating thick plates
TL;DR: In this article, a finite element formulation for vibration analysis of rotating thick plates is developed, which combines the Mindlin plate theory with second order strain-displacement assumptions for plate modeling.
About: This article is published in Journal of Sound and Vibration.The article was published on 2009-06-05. It has received 81 citations till now. The article focuses on the topics: Vibration of plates & Plate theory.
Citations
More filters
TL;DR: In this paper, a rotating pretwisted cylindrical shell model with a presetting angle is established to investigate nonlinear dynamic responses of the aero-engine compressor blade.
Abstract: A rotating pretwisted cylindrical shell model with a presetting angle is established to investigate nonlinear dynamic responses of the aero-engine compressor blade. The centrifugal force and the Coriolis force are considered in the model. The aerodynamic pressure is obtained by the first-order piston theory. The strain–displacement relationship is derived by the Green strain tensor. Based on the first-order shear deformation theory and the isotropic constitutive law, nonlinear partial differential governing equations are derived by using the Hamilton principle. Discarding the Coriolis force effect, Galerkin approach is utilized to reduce nonlinear partial differential governing equations into a two-degree-of-freedom nonlinear system. According to nonlinear ordinary differential equations, numerical simulations are performed to explore nonlinear transient dynamic responses of the system under the effect of the single point excitation and nonlinear steady-state dynamic responses of the system under the effect of the uniform distribution excitation. The effects of the excitation parameter, damping coefficient, rotating speed, presetting angle and pretwist angle on nonlinear dynamic responses of the system are fully discussed.
45 citations
TL;DR: In this article, a new dynamic model based on the shell theory is presented to investigate the vibration behavior of a rotating composite laminated blade with a pre-twisted angle, where the effects of the Coriolis and centrifugal forces due to the rotation motion of the blade are considered in the formulation.
45 citations
TL;DR: In this paper, the spectral-Tchebychev (ST) technique is used to solve the integral boundary value problem for rotating structures, including those with complex geometries and mixed boundary conditions.
44 citations
TL;DR: In this article, a two-dimensional spectral-Tchebychev (2D-ST) technique was proposed to predict the dynamics of thick plates having arbitrary geometries under different boundary conditions.
43 citations
TL;DR: In this article, the authors presented an experimental approach to obtain the speed-dependent two-dimensional dynamics of miniature UHS spindles through experimental modal analysis, where a custom-made impact excitation system was used to reproducibly excite the spindle dynamics up to 20 kHz while controlling the impact force.
Abstract: Micromachining dynamics commonly dictate the attainable accuracy and throughput that can be obtained from micromachining operations. The dynamic behavior of miniature ultra-high-speed (UHS) spindles used in micromachining critically affects micromachining dynamics. As such, there is a strong need for effective techniques to characterize the dynamic behavior of miniature UHS spindles. This paper presents a systematic experimental approach to obtain the speed-dependent two-dimensional dynamics of miniature UHS spindles through experimental modal analysis. A miniature cylindrical artifact with 5 mm overhang is attached to (and rotating with) the spindle to enable providing the dynamic excitations to and measuring the resulting motions of the spindle. A custom-made impact excitation system is used to reproducibly excite the spindle dynamics up to 20 kHz while controlling the impact force. The resulting radial motions of the spindle are measured in two mutually perpendicular directions using two independent fiber-optic laser Doppler vibrometers (LDVs). To ensure the mutual orthogonality of the measurements, the two lasers are aligned precisely using an optical procedure. A frequency-domain filtering approach is used to remove the unwanted spindle motion data from the measurements, thereby isolating the dynamic response. The spindle dynamics is then represented in the form of frequency response functions (FRFs). A global curve-fitting technique is applied to identify natural frequencies and damping ratios. The developed approach is demonstrated on a miniature UHS spindle with aerodynamic bearings, and dynamic characteristics are analyzed at different spindle speeds and collet pressures. The spindle speed is shown to have a significant effect on dynamic response, especially at higher spindle speeds, while the collet pressure is observed not to have any significant effect on the spindle dynamics. It is concluded that the presented approach can be used to characterize the dynamics of miniature UHS spindles effectively.
40 citations
References
More filters
4,554 citations
TL;DR: In this paper, a new dynamic modeling method was proposed to derive the equation of motion of a rotating cantilever beam, which can be directly used for the vibration analysis including the coupling effect, which could not be considered in the conventional modelling method.
320 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