An Analytical Investigation of the Trapeze Effect Acting on a Thin Flexible Ribbon

2014 ◽  
Vol 81 (12) ◽  
Author(s):  
Jérôme F. Sicard ◽  
Jayant Sirohi
Keyword(s):  
Steady State ◽  
Numerical Model ◽  
Stress Field ◽  
Cross Sections ◽  
Natural Frequencies ◽  
Axial Stress ◽  
Analytical Investigation ◽  
Pure Bending ◽  
Torsional Coupling ◽  
Tip Mass

This paper systematically explores the extensional–torsional coupling due to the trapeze effect acting on a thin flexible ribbon subjected to combined tension and torsion. Kinematic relationships as well as expressions for the restoring torque associated with this effect are analytically derived. Additionally, the locus of points about which the cross sections of a twisted ribbon under tension rotate is derived. These points, called torsional centers, are found to be coincident with the centroids of the axial stress field at each station along the ribbon. More generally, it is shown that when a flexible slender member is in tension, combined transverse forces must act at the centroid of the axial stress field to produce pure bending and no twist. As a result, the elastic axis (EA) of the member shifts from the locus of shear centers to the locus of centroids of the axial stress field. A numerical model is developed to investigate the effect of the position of the EA on the prediction of steady-state deformations and natural frequencies of a rotating ribbon with tip mass. By assuming the EA to be the locus of the shear centers, the tip twist is overpredicted by a factor of 2 for small twist angles, and up to 2.5 for large twist deformations. In addition, assuming the EA to be the locus of shear centers results in an error of up to 60% in the predicted natural frequencies at large twist angles.

Theoretical and Experimental Analysis of Coupled Flexural-Torsional Vibrations of Rotating Beams

2018 ◽  
Author(s):  
Mohammad Javad Khodaei ◽  
Amin Mehrvarz ◽  
Nicholas Candelino ◽  
Nader Jalili
Keyword(s):  
Mathematical Modeling ◽  
Steady State ◽  
Piezoelectric Actuator ◽  
Experimental Analysis ◽  
Natural Frequencies ◽  
Unmodeled Dynamics ◽  
Torsional Vibrations ◽  
Rotating Beams ◽  
Tip Mass ◽  
Sensor Mass

In this paper, the flexural-torsional vibrations of a segmented cantilever beam are considered both theoretically and experimentally under steady-state base rotation. While operating in this steady-state, a piezoelectric actuator is used to excite the beam at various test frequencies. Further, through preliminary investigations, it is demonstrated that accelerometer measurements are not suitable for such a testing apparatus, as these sensors add complex unmodeled dynamics and change the natural frequencies of vibration. The resulting unmodeled dynamics appear to be caused by a large initial deflection due to the added sensor mass, contradicting the conventional assumption that the beam is initially undeformed. This initial bending results in a Coriolis acceleration, and consequently produces a substantial deviation from the anticipated tip response. To further investigate the effect of base rotation on flexural vibrations, experiments were performed in the absence of piezoelectric excitation, both with and without the tip mass. For these conditions, the theory uniformly predicts no flexural or torsional vibrations, while the experimental results demonstrate significant vibrations in both cases. These discrepancies illuminate the presence of significant unmodeled dynamics that are neglected in the conventional mathematical modeling, potentially invalidating the classical simplifications when considering rotating beams.

scholarly journals Development of Piezoelectric Harvesters with Integrated Tuning Devices

2018 ◽  
Author(s):  
Alberto Doria ◽  
Cristian Medè ◽  
Giulio Fanti ◽  
Daniele Desideri ◽  
Alvise Maschio ◽  
...  
Keyword(s):  
Numerical Model ◽  
High Frequency ◽  
Natural Frequencies ◽  
Strain Analysis ◽  
Coupled System ◽  
Experimental Results ◽  
Main Resonance ◽  
Modes Of Vibration ◽  
Tip Mass ◽  
Piezoelectric Harvester

The possibility of improving the performance of a piezoelectric harvester by means of novel tuning devices integrated with the harvester’s structure is investigated. Some prototypes of harvesters with tuning devices are developed by mounting cantilever dynamic absorbers on standard harvesters. A mathematical model is used for predicting the natural frequencies of the coupled system. Tests on prototypes are carried out with an impulsive method. Experimental results show that a small tuning device can lower the main resonance frequency of a piezoelectric harvester of the same extent as a larger tip mass and moreover generates at high frequency a second resonance peak. A multi-physics numerical model is developed for predicting the generated power and for performing stress-strain analysis of harvesters equipped with Integrated Tuning Devices (ITDs). The numerical model is validated on the basis of experimental results. Several configurations of ITDs are conceived and studied. Numerical results show that harvesters with ITDs are able to generate relevant power at two frequencies owing to the particular shape of the modes of vibration. The stress in the harvesters with ITDs is smaller than the stress in the harvester with a tip mass tuned to the same frequency.

scholarly journals Thermoelastic analysis of FGM hollow cylinder for variable parameters and temperature distributions using FEM

2020 ◽  
Vol 9 (1) ◽  
pp. 256-264
Author(s):  
Dinkar Sharma ◽  
Ramandeep Kaur
Keyword(s):  
Stress Field ◽  
Hollow Cylinder ◽  
Numerical Study ◽  
Axial Stress ◽  
Circumferential Stress ◽  
Functionally Graded ◽  
Gradient Index ◽  
Variable Parameters ◽  
Graded Material ◽  
Governing Differential Equation

AbstractThis paper presents, numerical study of stress field in functionally graded material (FGM) hollow cylinder by using finite element method (FEM). The FGM cylinder is subjected to internal pressure and uniform heat generation. Thermoelastic material properties of FGM cylinder are assumed to vary along radius of cylinder as an exponential function of radius. The governing differential equation is solved numerically by FEM for isotropic and anistropic hollow cylinder. Additionally, the effect of material gradient index (β) on normalized radial stresses, normalized circumferential stress and normalized axial stress are evaluated and shown graphically. The behaviour of stress versus normalized radius of cylinder is plotted for different values of Poisson’s ratio and temperature. The graphical results shown that stress field in FGM cylinder is influenced by some of above mentioned parameters.

scholarly journals Analytical investigation of high-velocity impact on hybrid unidirectional/woven composite panels

2016 ◽  
Vol 30 (4) ◽  
pp. 545-563 ◽  
Author(s):  
H Shanazari ◽  
GH Liaghat ◽  
H Hadavinia ◽  
A Aboutorabi
Keyword(s):  
Cross Sections ◽  
Shear Failure ◽  
Failure Criteria ◽  
Analytical Investigation ◽  
Woven Fabrics ◽  
Body Armor ◽  
Ballistic Performance ◽  
Nonwoven Fabrics ◽  
Ballistic Protection ◽  
Maximum Tensile Strain

In addition to fiber properties, the fabric structure plays an important role in determining ballistic performance of composite body armor textile. Textile structures used in ballistic protection are woven fabrics, unidirectional (UD) fabric structures, and nonwoven fabrics. In this article, an analytical model based on wave propagation and energy balance between the projectile and the target is developed to analyze hybrid fabric panels for ballistic protection. The hybrid panel consists of two types of structure: woven fabrics as the front layers and UD material as the rear layers. The model considers different cross sections of surface of the target in the woven and UD fabric of the hybrid panel. Also the model takes into account possible shear failure by using shear strength together with maximum tensile strain as the failure criteria. Reflections of deformation waves at interface between the layers and also the crimp of the yarn are modeled in the woven part of the hybrid panel. The results show greater efficiency of woven fibers in front layers (more shear resistance) and UD yarns in the rear layers (more tensile resistance), leading to better ballistic performance. Also modeling the yarn crimp results in more trauma at the backface of the panel producing data closer to the experimental results. It was found that there is an optimum ratio of woven to UD materials in the hybrid ballistic panel.

Steady-State Unbalance Response of Continuous Rotors on Anisotropic Supports

1993 ◽  
Author(s):  
Graziano Curti ◽  
Francesco A. Raffa ◽  
Furio Vatta
Keyword(s):  
Steady State ◽  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Analytical Investigation ◽  
Dynamic Stiffness Matrix ◽  
Rotor Systems ◽  
Beam Elements ◽  
Unbalance Response ◽  
Constant Coefficients ◽  
Linearized Model

Abstract An analytical investigation of the steady-state unbalance response of axisymmetric rotor systems with anisotropic, flexible and damped bearings is presented. According to the exact approach of the dynamic stiffness method, the rotor is modelled by means of continuous beam elements. In this work, the expression of the 8 × 8 dynamic stiffness matrix of a rotating Timoshenko beam is derived and it is shown that it is related, by means of a simple law, to the previously published 4 × 4 dynamic stiffness matrix, which holds for the isotropic bearings case. The effects of concentrated disks and bearings are included into the formulation; in particular, each bearing is described by eight constant coefficients, according to the well-known linearized model of the bearing forces. The unbalance response of a typical rotor system taken from the literature is analyzed. A comparison is presented with the finite element results reported by other authors.

Forced Harmonic Response of Grouped Blade Systems: Part II—Application

1996 ◽  
Vol 118 (1) ◽  
pp. 137-145 ◽  
Author(s):  
L. F. Wagner ◽  
J. H. Griffin
Keyword(s):  
Numerical Model ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Turbine Blades ◽  
Modal Identification ◽  
Harmonic Response ◽  
Model Based ◽  
Grouped Blades ◽  
Flexible Disk ◽  
Symmetric Structures

The vibration of grouped blades on a flexible disk should, for purposes of economy and clarity of modal identification, be analyzed using procedures developed for cyclically symmetric structures. In this paper, a numerical model, based on the theory of cyclically symmetric structures, is applied to the vibration analysis, and in particular, the harmonic response, of a flexible disk supporting a number of groups, or packets, of turbine blades. Results are presented to show variations in the modal participation factors as a function of such parameters as disk flexibility, blade density, and the total number of assembled groups. It is also shown that many characteristics of the system spectra of natural frequencies are strongly dependent on the number of blade groups.

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