Determination of Isospectral Nonuniform Rotating Beams

2012 ◽  
Vol 79 (6) ◽  
Author(s):  
Sandilya Kambampati ◽  
Ranjan Ganguli ◽  
V. Mani
Keyword(s):  
Natural Frequencies ◽  
Rotation Speed ◽  
Rectangular Cross Section ◽  
Rotating Beam ◽  
Element Analysis ◽  
Rotating Beams ◽  
Type Transformation ◽  
The Given ◽  
Nonuniform Beam

In this paper we look for nonuniform rotating beams that are isospectral to a given uniform nonrotating beam. A rotating nonuniform beam is isospectral to the given uniform nonrotating beam if both the beams have the same spectral properties, i.e., both the beams have the same set of natural frequencies under a given boundary condition. The Barcilon-Gottlieb type transformation is proposed that converts the governing equation of a rotating beam to that of a uniform nonrotating beam. We show that there exist rotating beams isospectral to a given uniform nonrotating beam under some special conditions. The boundary conditions we consider are clamped-free and hinged-free with an elastic hinge spring. An upper bound on the rotation speed for which isospectral beams exist is proposed. The mass and stiffness distributions for these nonuniform rotating beams which are isospectral to the given uniform nonrotating beam are obtained. We use these mass and stiffness distributions in a finite element analysis to show that the obtained beams are isospectral to the given uniform nonrotating beam. A numerical example of a beam having a rectangular cross section is presented to show the application of our analysis.

scholarly journals Isospectrals of non-uniform Rayleigh beams with respect to their uniform counterparts

2018 ◽  
Vol 5 (2) ◽  
pp. 171717 ◽  
Author(s):  
Srivatsa Bhat K ◽  
Ranjan Ganguli
Keyword(s):  
Boundary Condition ◽  
Cross Section ◽  
Natural Frequencies ◽  
Rectangular Cross Section ◽  
Beam Equation ◽  
The Finite Element Method ◽  
Rayleigh Beam ◽  
Uniform Beam ◽  
Governing Differential Equation ◽  
The Given

In this paper, we look for non-uniform Rayleigh beams isospectral to a given uniform Rayleigh beam. Isospectral systems are those that have the same spectral properties, i.e. the same free vibration natural frequencies for a given boundary condition. A transformation is proposed that converts the fourth-order governing differential equation of non-uniform Rayleigh beam into a uniform Rayleigh beam. If the coefficients of the transformed equation match with those of the uniform beam equation, then the non-uniform beam is isospectral to the given uniform beam. The boundary-condition configuration should be preserved under this transformation. We present the constraints under which the boundary configurations will remain unchanged. Frequency equivalence of the non-uniform beams and the uniform beam is confirmed by the finite-element method. For the considered cases, examples of beams having a rectangular cross section are presented to show the application of our analysis.

Stiff-String Basis Functions for Vibration Analysis of High Speed Rotating Beams

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
Jagadish Babu Gunda ◽  
Ranjan Ganguli
Keyword(s):  
Finite Element ◽  
High Speed ◽  
Natural Frequencies ◽  
Basis Functions ◽  
Beam Equation ◽  
Rotating Beam ◽  
Rotating Beams ◽  
Centrifugal Stiffening ◽  
Convergence Study ◽  
Stiffening Effect

A new rotating beam finite element is developed in which the basis functions are obtained by the exact solution of the governing static homogenous differential equation of a stiff string, which results from an approximation in the rotating beam equation. These shape functions depend on rotation speed and element position along the beam and account for the centrifugal stiffening effect. Using this new element and the Hermite cubic finite element, a convergence study of natural frequencies is performed, and it is found that the new element converges much more rapidly than the conventional Hermite cubic element for the first two modes at higher rotation speeds. The new element is also applied for uniform and tapered rotating beams to determine the natural frequencies, and the results compare very well with the published results given in the literature.

scholarly journals An Evaluation of Material Properties Using EMA and FEM

2016 ◽  
Vol 24 (39) ◽  
pp. 15-22
Author(s):  
Rastislav Ďuriš ◽  
Eva Labašová
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Structural Dynamics ◽  
Material Properties ◽  
Elasticity Modulus ◽  
Natural Frequencies ◽  
Optimization Methods ◽  
Experimental Measurements ◽  
Element Analysis

Abstract The main goal of the paper is the determination of material properties from experimentally measured natural frequencies. A combination of two approaches to structural dynamics testing was applied: the experimental measurements of natural frequencies were performed by Experimental Modal Analysis (EMA) and the numerical simulations, were carried out by Finite Element Analysis (FEA). The optimization methods were used to determine the values of density and elasticity modulus of a specimen based on the experimental results.

Matrix Solution for the Vibration of Nonuniform Beams

1950 ◽  
Vol 17 (3) ◽  
pp. 337-339
Author(s):  
W. T. Thomson
Keyword(s):  
Matrix Method ◽  
Natural Frequencies ◽  
Matrix Solution ◽  
Tabular Method ◽  
Nonuniform Beam

Abstract A matrix method for the determination of natural frequencies of any nonuniform beam is presented. It accomplishes the same task as that of Myklestad’s tabular method with the added advantage of simplicity of formulation. Included is a procedure for the case where the nonuniform beam is represented by a series of uniform sections.

Structural Analysis of a Tracking Photovoltaic System with a Pedestal Solar Tracker

2014 ◽  
Vol 493 ◽  
pp. 361-366
Author(s):  
Chih Kuang Lin ◽  
Chen Yu Dai
Keyword(s):  
Solar Radiation ◽  
Structural Integrity ◽  
Natural Frequencies ◽  
Elevation Angle ◽  
Photovoltaic System ◽  
Structural Deformation ◽  
Pv System ◽  
Element Analysis ◽  
Solar Tracker ◽  
The Given

The structural integrity and deformation-induced misalignment of solar radiation for a tracking photovoltaic (PV) system under self-weight is investigated using a finite element analysis (FEA) approach. Gravity is applied to calculate the stress distribution and structural deformation. Misalignment of solar radiation induced by structural deformation is also calculated. Moreover, to avoid damages caused by resonance, natural frequencies of vibration for the given tracking PV system are also determined. Strain changes are measured experimentally at two selected locations in the given solar tracker during field operation for comparison with the simulation results. A reasonable agreement between the simulations and experimental measurements is found such that the constructed FEA model is validated to be effective in assessment of the structural integrity for PV systems under self-weight. No structural failure is predicted for all components in the given solar tracker under the given loading condition according to the von Mises failure criterion. An agreement in the trend of variation of misalignment and resultant displacement of PV modules is found. Considering the effect of self-weight only, the maximum misalignment of solar radiation is of 0.275o at elevation angle of 45o when rotating the solar tracker from 0o to 75o. It is expected that such a misalignment value will not cause a significant degradation of power generation for a PV system. The range of natural frequencies of the first six vibration modes for the given PV system is from 3.85 Hz to 11.4 Hz.

Determination of the Eccentricity of a Rotor by Impulse Excitation Technique of Vibration

2015 ◽  
Vol 801 ◽  
pp. 176-181 ◽  
Author(s):  
Ion Crâştiu ◽  
Liviu Bereteu ◽  
Dorin Simoiu
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Center Of Mass ◽  
Modal Parameters ◽  
Element Analysis ◽  
Impulse Excitation ◽  
Vibration Responses ◽  
Plane Flexure ◽  
Development And Validation

The aim of this paper is the development and validation of an impulse excitation technique to determine static imbalance of a rotor. The experimental measurement of the vibroacustic response is carried out by using a condenser microphone. In determining the center of mass three measurements are needed: one in plane flexure, and other out of the plane flexure, to which is added a measurement for a balanced rotor. By the means of Finite Element Method (FEM), the natural frequencies and shape modes of two rotor specimens are determined. The analysis is carried out in balanced condition as well as unbalanced one, after artificially induced imbalance. The vibration responses of the specimens, in free-free conditions, are carried out using algorithms based on Fast Fourier Transform (FFT). To validate the results of the modal parameters estimated using Finite Element Analysis (FEA) these are compared with experimental ones.

Natural Frequencies of Pre-Twisted Airfoil Blades

2017 ◽  
Author(s):  
Neeraj Kavan Chakshu ◽  
Sunil K. Sinha
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Free Boundary ◽  
Cross Section ◽  
Cross Sections ◽  
Natural Frequencies ◽  
Rectangular Cross Section ◽  
Element Analysis ◽  
Free Boundary Conditions ◽  
Airfoil Blades

In this paper, the natural frequencies of pre-twisted cantilever blades of various angles of twist having different airfoil cross sections in the NACA 6 series have been determined. The main objectives of this paper are to replicate the results previously published for the similar types of blades but with the assumption of a uniform rectangular cross-section and to compare it with the results obtained for blades with more refined airfoil cross-sections. Cantilevered type clamped-free boundary conditions have been used in this paper for all blades. The comparison of the natural frequencies among different airfoils of the same NACA series has also been described in the paper in order to find out if any parameter of the airfoil such as camber, maximum thickness etc have any significant role in changing the frequencies of the beam. Commonly used commercial codes for finite element analysis have been used to determine these results.

Finite Element Analysis of a Thin Walled Composite Wing by Including Warping Effects

2010 ◽  
Author(s):  
Ozge Ozdemir Ozgumus ◽  
Seher Durmaz ◽  
Metin Orhan Kaya
Keyword(s):  
Finite Element ◽  
Composite Beam ◽  
Natural Frequencies ◽  
Rectangular Cross Section ◽  
Element Analysis ◽  
Thin Walled ◽  
Ply Orientation ◽  
Finite Element Formulations ◽  
Good Agreement ◽  
Composite Wing

The purpose of the present paper is to develop a finite element code to model a thin-walled composite beam. The beam is modeled as a thin-walled composite beam with a single-cell, rectangular cross-section featuring both CAS and CUS lay-up configurations. Analytical and finite element formulations of the flapwise bending, chordwise bending and torsional displacements of the beam are derived. Effect of the ply orientation on the natural frequencies is investigated and it is noticed that the obtained results are in good agreement with the ones in open literature.

Rotating Beams and Nonrotating Beams With Shared Eigenpair

2009 ◽  
Vol 76 (5) ◽  
Author(s):  
Ananth Kumar ◽  
Ranjan Ganguli
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Cantilever Beam ◽  
Mass Distribution ◽  
Mode Shapes ◽  
Flexural Stiffness ◽  
Rotating Beam ◽  
Element Analysis ◽  
Rotating Beams ◽  
The Finite Element Analysis

In this paper, we look for rotating beams whose eigenpair (frequency and mode-shape) is the same as that of uniform nonrotating beams for a particular mode. It is found that, for any given mode, there exist flexural stiffness functions (FSFs) for which the jth mode eigenpair of a rotating beam, with uniform mass distribution, is identical to that of a corresponding nonrotating uniform beam with the same length and mass distribution. By putting the derived FSF in the finite element analysis of a rotating cantilever beam, the frequencies and mode-shapes of a nonrotating cantilever beam are obtained. For the first mode, a physically feasible equivalent rotating beam exists, but for higher modes, the flexural stiffness has internal singularities. Strategies for addressing the singularities in the FSF for finite element analysis are provided. The proposed functions can be used as test-functions for rotating beam codes and for targeted destiffening of rotating beams.

Rotation Effects on Vibration of Structures Seen From a Rotating Beam Simply Supported off the Rotation Axis

2005 ◽  
Vol 128 (3) ◽  
pp. 328-337 ◽  
Author(s):  
J. Kim
Keyword(s):  
Coriolis Force ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Rotation Axis ◽  
Slenderness Ratio ◽  
Rotating Beam ◽  
Simply Supported ◽  
Axis Of Rotation ◽  
Vibration Responses ◽  
Practical Implications

In rotating beams, the Coriolis force acts through the mass and rotary inertias of the beam. A rotating beam simply supported off the axis of rotation is used as an example to study effects of this Coriolis force on vibration of structures. By adopting such a simple model, mass- and rotary inertia-induced terms in the free vibration responses can be obtained in separate, closed forms. The effect of each of these terms on vibration characteristics of the rotating beam is discussed in relation to parameters such as nonrotating natural frequencies, the rotation speed, and the slenderness ratio. Practical implications of these results in analyses of rotating structures of other types are discussed, for example estimating the significance of rotary inertias in relation to the slenderness ratio and the rotation speed.

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