Approximate Linear Theories for the Dynamics of Slack Cables Supporting a Discrete Mass

1991 ◽  
Author(s):  
S.-P. Cheng ◽  
N. C. Perkins
Keyword(s):  
Three Dimensional ◽  
Small Mass ◽  
Mode Shapes ◽  
Mass Model ◽  
Free Response ◽  
Eigen Solutions ◽  
Technical Interest ◽  
Spatially Varying ◽  
Discrete Mass ◽  
Natural Frequency Spectrum

Abstract A continuum model is presented that describes the three-dimensional response of an elastic cable that supports a single attached mass. Two asymptotic forms of this model are analyzed for the free, linear response of slack suspensions having small equilibrium curvature (sag) and level supports. The first model, which is valid for relatively small attached masses, assumes that the cable stretches quasi-statically and results in uniform dynamic cable tension. The quasi-static stretching assumption is partially relaxed in the second model which accounts for spatially varying dynamic tension in an approximate manner. The eigen-solutions associated with free response are compared for the two models. Results indicate that the “small mass model” provides excellent approximations to the natural frequency spectrum and vibration mode shapes for most cables and modes of technical interest. A simple criterion is presented which governs the range of validity of the small mass model.

FLUTTER CALCULATION BASED ON GVT-RESULTS AND THEORETICAL MASS MODEL

Aviation ◽  
2009 ◽  
Vol 13 (4) ◽  
pp. 122-129 ◽  
Author(s):  
Wojciech Chajec
Keyword(s):  
Mass Distribution ◽  
Normal Modes ◽  
Ground Vibration ◽  
Small Mass ◽  
Mode Shapes ◽  
Mass Model ◽  
Stiffness Properties ◽  
Theoretical Mass ◽  
Vibration Tests ◽  
Calculation Software

Ground vibration tests (GVT) are a typical source of data for flutter prediction. In this paper, a simple, lowcost method to calculate flutter is presented. In this method, measured frequencies, mode shapes of an airplane are used and, additionally, the theoretical mass model of it. If the theoretical mass model is used, it is possible to calculate generalized masses of modes and cross mass couplings between them. The mass couplings of normal modes should be zero. Orthogonalization is correction of the mode shapes to lead the couplings to zero. The possible orthogonalization methods are presented in chapter 2. Based on eigenmodes of airplane configuration during GVT, it is possible to determine the eigenmodes of the same free airplane after a relatively small mass change, i.e. for another mass distribution that was not investigated by GVT. In the procedure presented in chapter 3, it is assumed that geometric and stiffness properties do not change. The methodology was used in the own flutter calculation software that is useful for flutter prediction of light airplanes and sailplanes. Santrauka Dažnuminiai bandymai žemėje yra tipinis informacijos šaltinis flaterio skaičiavimui. Šiame straipsnyje pateikiamas paprastas ir pigus flaterio skaičiavimo metodas. Šiame metode naudojamos lėktuvo išmatuotų dažnuminių modų formos ir teorinis lėktuvo masių modelis. Naudojant teorinį masių modelį galima apskaičiuoti apibendrintas modų mases ir masių ryšius tarp jų. Normalinių modų masių ryšys turi būti lygus nuliui. Ortogonalizavimu koreguojamos modų formos, siekiant ryšius sumažinti iki nulio. Galimi ortogonalizavimo metodai pateikti antrame skyriuje. Remiantis lėktuvo laisvųjų svyravimo modomis, gautomis dažnuminių bandymų žemėje metu, galima nustatyti kitokio masių pasiskirstymo įtaką laisvųjų svyravimų modoms. Procedūroje, pateiktoje trečiame skyriuje, manoma, kad geometrinės ir standumo savybės nesikeičia. Ši metodologija buvo panaudota savoje programinėje įrangoje flateriui skaičiuoti, kurią galima naudoti lengvų lėktuvų ir sklandytuvų flaterio skaičiavimui.

Vibration of an Eccentrically Clamped Annular Plate

1993 ◽  
Author(s):  
Jung-Ge Tseng ◽  
Jonathan A. Wickert
Keyword(s):  
Data Storage ◽  
Natural Frequencies ◽  
Annular Plate ◽  
Outer Edge ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Laboratory Measurements ◽  
Free Response ◽  
Amplitude Vibration ◽  
Natural Frequency Spectrum

Abstract Small amplitude vibration of an eccentric annular plate, which is free along its outer edge and clamped along the interior, is investigated through experimental and analytical methods. A disk with this geometry, or a stacked array in which the clamping and symmetry axes of each disk are nominally coincident, is common in data storage and brake systems applications. In the present case, the geometric imperfections on the boundary can have important implications for the disk’s dynamic response. Changes that occur in the natural frequency spectrum, the mode shapes, and the free response under eccentric mounting are studied through laboratory measurements and an approximate discrete model of the plate. The natural frequencies and modes are found through global discretization of the Kamke quotient for a classical thin plate. For the axisymmetric geometry, the natural frequencies of the “sine” and “cosine” vibration modes for a specified number of nodal diameters are repeated. With increasing eccentricity, on the other hand, each pair of repeated frequencies splits at a rate that depends on the number of nodal diameters. Over a range of clamping and eccentricity ratios, the model’s predictions are compared to the measured results.

Vibration of an Eccentrically Clamped Annular Plate

1994 ◽  
Vol 116 (2) ◽  
pp. 155-160 ◽  
Author(s):  
J.-G. Tseng ◽  
J. A. Wickert
Keyword(s):  
Data Storage ◽  
Natural Frequencies ◽  
Annular Plate ◽  
Outer Edge ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Laboratory Measurements ◽  
Free Response ◽  
Amplitude Vibration ◽  
Natural Frequency Spectrum

Small amplitude vibration of an eccentric annular plate, which is free along its outer edge and clamped along the interior, is investigated through experimental and analytical methods. A disk with this geometry, or a stacked array in which the clamping and symmetry axes of each disk are nominally coincident, is common in data storage and brake systems applications. In the present case, the geometric imperfections on the boundary can have important implications for the disk’s dynamic response. Changes that occur in the natural frequency spectrum, the mode shapes, and the free response under eccentric mounting are studied through laboratory measurements and an approximate discrete model of the plate. The natural frequencies and modes are found through global discretization of the Kamke quotient for a classical thin plate. For the axisymmetric geometry, the natural frequencies of the “sine” and “cosine” vibration modes for a specified number of nodal diameters are repeated. With increasing eccentricity, on the other hand, each pair of repeated frequencies splits at a rate that depends on the number of nodal diameters. Over a range of clamping and eccentricity ratios, the model’s predictions are compared to the measured results.

scholarly journals Identification of Mode Shapes of a Composite Cylinder Using Convolutional Neural Networks

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 2801
Author(s):  
Bartosz Miller ◽  
Leonard Ziemiański
Keyword(s):  
Neural Networks ◽  
Convolutional Neural Networks ◽  
Composite Structures ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Identification Algorithm ◽  
Material Degradation ◽  
Local Material ◽  
Noisy Input ◽  
Shape Vector

The aim of the following paper is to discuss a newly developed approach for the identification of vibration mode shapes of multilayer composite structures. To overcome the limitations of the approaches based on image analysis (two-dimensional structures, high spatial resolution of mode shapes description), convolutional neural networks (CNNs) are applied to create a three-dimensional mode shapes identification algorithm with a significantly reduced number of mode shape vector coordinates. The CNN-based procedure is accurate, effective, and robust to noisy input data. The appearance of local damage is not an obstacle. The change of the material and the occurrence of local material degradation do not affect the accuracy of the method. Moreover, the application of the proposed identification method allows identifying the material degradation occurrence.

Free Vibrations of Thick, Complete Conical Shells of Revolution From a Three-Dimensional Theory

2005 ◽  
Vol 72 (5) ◽  
pp. 797-800 ◽  
Author(s):  
Jae-Hoon Kang ◽  
Arthur W. Leissa
Keyword(s):  
Ritz Method ◽  
Three Dimensional ◽  
Axial Direction ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Shells Of Revolution ◽  
Dimensional Theory ◽  
Conical Shells ◽  
Cylindrical Coordinate

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution in which the bottom edges are normal to the midsurface of the shells based upon the circular cylindrical coordinate system using the Ritz method. Comparisons are made between the frequencies and the corresponding mode shapes of the conical shells from the authors' former analysis with bottom edges parallel to the axial direction and the present analysis with the edges normal to shell midsurfaces.

scholarly journals Comparison of Two Numerical Algorithms for Computing the Effects of Mistuning of Fan Flutter

2016 ◽  
Author(s):  
L. Salles ◽  
M. Vahdati
Keyword(s):  
Numerical Models ◽  
Three Dimensional ◽  
Numerical Algorithms ◽  
Mode Shapes ◽  
Minimal Amount ◽  
Aeroelastic System ◽  
Cpu Time ◽  
Influence Coefficients ◽  
Non Linear ◽  
The Time Domain

The aim of this paper is to study the effects of mistuning on fan flutter and to compare the prediction of two numerical models of different fidelity. The high fidelity model used here is a three-dimensional, whole assembly, time-accurate, viscous, finite-volume compressible flow solver. The Code used for this purpose is AU3D, written in Imperial College and validated for flutter computations over many years. To the best knowledge of authors, this is the first time such computations have been attempted. This is due to the fact that, such non-linear aeroelastic computations with mistuning require large amount of CPU time and cannot be performed routinely and consequently, faster (low fidelity) models are required for this task. Therefore, the second model used here is the aeroelastic fundamental mistuning model (FMM) and it based on an eigenvalue analysis of the linearized modal aeroelastic system with the aerodynamic matrix calculated from the aerodynamic influence coefficients. The influence coefficients required for this algorithm are obtained from the time domain non-linear Code by shaking one blade in the datum (tuned) frequency and mode. Once the influence coefficients have been obtained, the computations of aero damping require minimal amount of CPU time and many different mistuning patterns can be studied. The objectives of this work are to: 1. Compare the results between the two models and establish the capabilities/limitations of aeroelastic FMM, 2. Check if the introduction of mistuning would bring the experimental and computed flutter boundaries closer, 3. Establish a relationship between mistuning and damping. A rig wide-chord fan blade, typical of modern civil designs, was used as the benchmark geometry for this study. All the flutter analyses carried out in this paper are with frequency mistuning, but the possible consequences of mistuned mode shapes are briefly discussed at the end of this paper. Only the first family of modes (1F, first flap) is considered in this work. For the frequency mistuning analysis, the 1F frequency is varied around the annulus but the 1F mode shapes remain the same for all the blades. For the mode shape mistuning computations, an FE analysis of the whole assembly different mass blades is performed. The results of this work clearly show the importance of mistuning on flutter. It also demonstrates that when using rig test data for aeroelastic validation of CFD codes, the amount mistuning present must be known. Finally, it should be noted that the aim of this paper is the study of mistuning and not steady/unsteady validation of a CFD code and therefore minimal aerodynamic data are presented.

Experimental and Numerical Modal Analysis of Composite Laminated Shells

2019 ◽  
Vol 161 (A1) ◽  
Keyword(s):  
Heat Dissipation ◽  
Mass Matrix ◽  
Experimental Studies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Radius Of Curvature ◽  
Lumped Mass ◽  
Auxiliary Equipment ◽  
Mass Model ◽  
Laminated Shells

The presence of cut outs at different positions of laminated shell component in marine and aeronautical structures facilitate heat dissipation, undertaking maintenance, fitting auxiliary equipment, access ports for mechanical and electrical systems, damage inspection and also influences the dynamic behaviour of the structures. The aim of the present study is to establish a comprehensive perspective of dynamic behavior of laminated deep shells (length to radius of curvature ratio less than one) with cut-out by experiments and numerical simulation. The glass epoxy laminated composite shell has been prepared in the laboratory by resin infusion. The experimental free vibration analysis is carried out on laminated shells with and without cut-out. The mass matrix is developed by considering rotary inertia in a lumped mass model in the numerical modeling. The results obtained from numerical and experimental studies are compared for verification and the consistency between mode shapes is established by applying modal assurance criteria.

Split Vibration Modes in Acoustically-Coupled Disk Stacks

1995 ◽  
Author(s):  
Jung-Ge Tseng ◽  
Jonathan Wickert
Keyword(s):  
Natural Frequencies ◽  
Three Dimensional ◽  
System Level ◽  
Thin Plates ◽  
Mode Shapes ◽  
Design Parameters ◽  
Phase System ◽  
Acoustic Coupling ◽  
Annular Plates ◽  
Vibration Model

Abstract Vibration of an array of stacked annular plates, in which adjacent plates couple weakly through an acoustic layer, is investigated through experimental and theoretical methods. Such acoustic coupling manifests itself through split natural frequencies, beating in the time responses of adjacent or separated plates, and system-level modes in which plates in the array vibrate in- or out-of-phase at closely-spaced frequencies. Laboratory measurements, including a technique in which the frequency response function of all in-phase modes but no out-of-phase modes, or visa versa, is measured, demonstrate the contribution of coupling to the natural frequency spectrum, and identify the combinations of design parameters for which it is important. For the lower modes of primary interest here, the natural frequencies of the out-of-phase system modes decrease as the air layer becomes thinner, while those of the in-phase mode remain sensibly constant at the in vacuo values. A vibration model comprising N classical thin plates that couple through the three-dimensional acoustic fields established in the annular cavities between plates is developed, and its results are compared with measurements of the natural frequencies and mode shapes.

A Vibrational Mode Analysis of Free Finite-Length Thick Cylinders Using the Finite Element Method

1998 ◽  
Vol 120 (2) ◽  
pp. 371-377 ◽  
Author(s):  
Huan Wang ◽  
Keith Williams ◽  
Wei Guan
Keyword(s):  
Finite Length ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Mode Analysis ◽  
Mode Shapes ◽  
Vibrational Modes ◽  
The Finite Element Method ◽  
Cylinder Length ◽  
Radial Thickness ◽  
Thick Cylinder

Based on their three-dimensional mode shapes, the vibrational modes of free finite length thick cylinders can be classified into 6 categories, consisting of pure radial, radial motion with radial shearing, extensional, circumferential, axial bending, and global modes. This classification, together with the numbers of both the circumferential and the longitudinal nodes, is sufficient to identify each mode of a finite length thick cylinder. The mode classification was verified experimentally by measurements on a thick cylinder. According to the displacement distribution ratio in the radial, tangential and longitudinal directions, the effect of varying cylinder length on the vibrational modes is such that all the modes can be broadly categorized as either pure radial modes, or non pure radial modes. The natural frequencies and mode shapes of the former are dependent upon only the radial dimensions of the models, while the natural frequencies and mode shapes of the latter are dependent upon both the axial length and radial thickness.

scholarly journals Frequency spectrum of the human head–neck to mechanical vibrations

2017 ◽  
Vol 37 (3) ◽  
pp. 611-618 ◽  
Author(s):  
Bin Yang ◽  
Zheng Shi ◽  
Qun Wang ◽  
Feng Xiao ◽  
Tong-Tong Gu ◽  
...  
Keyword(s):  
Finite Element ◽  
Frequency Spectrum ◽  
Mechanical Vibration ◽  
Three Dimensional ◽  
Human Head ◽  
Element Model ◽  
Mode Shapes ◽  
Joint Disorder ◽  
Biomechanical Responses ◽  
Head Neck

This study is based on a real finite element human head–neck model and concentrates on its numerical vibration characteristic. Frequency spectrum and mode shapes of the finite element model of human head–neck under mechanical vibration have been calculated. These vibration characteristics are in good agreement with the previous studies. The simulated fundamental frequency of 35.25 Hz is fairly similar to the published documents, and rarely reported modal responses such as “mastication” and flipping of nasal lateral cartilages modes, however, are introduced by our three-dimensional modal analysis. These additional modes may be of interest to surgeons or clinicians who are specialized in temporomandibular or rhinoplasty joint disorder. Modal validation in terms of modal shapes proposes a necessity for elaborate modeling to identify each individual part’s extra frequencies. Furthermore, it also studies the influence of damping on resonant frequencies and biomechanical responses. It is discovered that damping has an inverse proportionality between damping effect on natural frequency and that on biomechanical responses.

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