Dynamic Analysis of an Elevator Traveling Cable Using a Singularity-Free Beam Formulation

2017 ◽  
Vol 84 (4) ◽  
Author(s):  
W. Fan ◽  
W. D. Zhu
Keyword(s):  
Dynamic Analysis ◽  
Multibody Dynamics ◽  
Natural Frequencies ◽  
Vertical Motion ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Out Of Plane ◽  
Forced Responses ◽  
Free Beam ◽  
Good Agreement

A round elevator traveling cable is modeled using a singularity-free beam formulation. Equilibria of the traveling cable with different elevator car positions are studied. Natural frequencies and the corresponding mode shapes of the traveling cable are calculated and they are in excellent agreement with those calculated by abaqus. In-plane natural frequencies of the traveling cable do not change much with the car position compared with its out-of-plane ones. Dynamic responses of the traveling cable are calculated and they are in good agreement with those from commercial multibody dynamics software recurdyn. Effects of vertical motion of the car on free responses of the traveling cable and those of in-plane and out-of-plane building sways on forced responses are investigated.

Dynamic Analysis of an Elevator Traveling Cable Using a Singularity-Free Beam Formulation

2017 ◽  
Author(s):  
W. Fan ◽  
W. D. Zhu
Keyword(s):  
Natural Frequencies ◽  
Vertical Motion ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Normal Strain ◽  
Euler Parameters ◽  
Current Formulation ◽  
Out Of Plane ◽  
Forced Responses ◽  
Free Beam

An elevator traveling cable is modeled using a singularity-free beam formulation and its static and dynamic behaviors are analyzed. The beam is assumed to be an extensible Euler-Bernoulli beam, and the configuration of the beam is described by Euler parameters, which can resolve the singularity problem of Euler angles, and the normal strain of the centroid line of the beam. The position of the centroid line of the beam is integrated from its slope. Governing equations of the beam and constraint equations are derived using Lagrange’s equations for systems with constraints. The current formulation is used to calculate the equilibrium and dynamic responses of an elevator traveling cable with arbitrarily moving ends. Equilibria of a traveling cable with different elevator car positions are calculated. Natural frequencies and corresponding mode shapes of the traveling cable are calculated and they are in excellent agreement with those calculated by ABAQUS. In-plane natural frequencies of the traveling cable do not change much with the car position compared with its out-of-plane ones. Dynamic responses of the traveling cable are calculated using the current formulation and compared with those from commercial multibody dynamics software RecurDyn, and they are in good agreement with each other. Free responses of the traveling cable due to vertical motion of the car and forced responses with inplane and out-of-plane building sways are simulated, and their effects on dynamic responses of the traveling cable are investigated. While the vertical motion of the car can affect the in-plane lateral response of the traveling cable, it has almost no effect on its out-of-plane response. Building sways can affect both lateral and out-of-plane responses of the traveling cable, but they have little effect on its vertical response.

Tire Vibrations

1977 ◽  
Vol 5 (4) ◽  
pp. 202-225 ◽  
Author(s):  
G. R. Potts ◽  
C. A. Bell ◽  
L. T. Charek ◽  
T. K. Roy
Keyword(s):  
Natural Frequencies ◽  
Standing Waves ◽  
Resonant Mode ◽  
Mode Shapes ◽  
Resonant Vibrations ◽  
Resonant Frequencies ◽  
Radial Tire ◽  
Analysis Techniques ◽  
Thin Ring ◽  
Good Agreement

Abstract Natural frequencies and vibrating motions are determined in terms of the material and geometric properties of a radial tire modeled as a thin ring on an elastic foundation. Experimental checks of resonant frequencies show good agreement. Forced vibration solutions obtained are shown to consist of a superposition of resonant vibrations, each rotating around the tire at a rate depending on the mode number and the tire rotational speed. Theoretical rolling speeds that are upper bounds at which standing waves occur are determined and checked experimentally. Digital Fourier transform, transfer function, and modal analysis techniques used to determine the resonant mode shapes of a radial tire reveal that antiresonances are the primary transmitters of vibration to the tire axle.

Dynamic model for high-speed rotors based on their experimental characterization

2017 ◽  
Vol 2 (4) ◽  
pp. 25
Author(s):  
L. A. Montoya ◽  
E. E. Rodríguez ◽  
H. J. Zúñiga ◽  
I. Mejía
Keyword(s):  
Dynamic Model ◽  
High Speed ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Experimental Characterization ◽  
Rotating Systems ◽  
Computing Performance ◽  
The Impact ◽  
Stiffness Distribution ◽  
Good Agreement

Rotating systems components such as rotors, have dynamic characteristics that are of great importance to understand because they may cause failure of turbomachinery. Therefore, it is required to study a dynamic model to predict some vibration characteristics, in this case, the natural frequencies and mode shapes (both of free vibration) of a centrifugal compressor shaft. The peculiarity of the dynamic model proposed is that using frequency and displacements values obtained experimentally, it is possible to calculate the mass and stiffness distribution of the shaft, and then use these values to estimate the theoretical modal parameters. The natural frequencies and mode shapes of the shaft were obtained with experimental modal analysis by using the impact test. The results predicted by the model are in good agreement with the experimental test. The model is also flexible with other geometries and has a great time and computing performance, which can be evaluated with respect to other commercial software in the future.

scholarly journals Out-of-Plane Vibration of Curved Uniform and Tapered Beams with Additional Mass

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Hamdi Alper Özyiğit ◽  
Mehmet Yetmez ◽  
Utku Uzun
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Variable Cross ◽  
Additional Mass ◽  
Inertia Effects ◽  
Tapered Beam ◽  
Out Of Plane ◽  
Good Agreement

As there is a gap in literature about out-of-plane vibrations of curved and variable cross-sectioned beams, the aim of this study is to analyze the free out-of-plane vibrations of curved beams which are symmetrically and nonsymmetrically tapered. Out-of-plane free vibration of curved uniform and tapered beams with additional mass is also investigated. Finite element method is used for all analyses. Curvature type is assumed to be circular. For the different boundary conditions, natural frequencies of both symmetrical and unsymmetrical tapered beams are given together with that of uniform tapered beam. Bending, torsional, and rotary inertia effects are considered with respect to no-shear effect. Variations of natural frequencies with additional mass and the mass location are examined. Results are given in tabular form. It is concluded that (i) for the uniform tapered beam there is a good agreement between the results of this study and that of literature and (ii) for the symmetrical curved tapered beam there is also a good agreement between the results of this study and that of a finite element model by using MSC.Marc. Results of out-of-plane free vibration of symmetrically tapered beams for specified boundary conditions are addressed.

Fluid Added Mass Effect in the Modal Response of a Pump-Turbine Impeller

2009 ◽  
Author(s):  
Eduard Egusquiza ◽  
Carme Valero ◽  
Quanwei Liang ◽  
Miguel Coussirat ◽  
Ulrich Seidel
Keyword(s):  
Natural Frequencies ◽  
Experimental Tests ◽  
Mass Effect ◽  
Added Mass ◽  
Mode Shapes ◽  
Pump Turbine ◽  
Modal Response ◽  
Surrounding Fluid ◽  
Turbine Impeller ◽  
Good Agreement

In this paper, the reduction in the natural frequencies of a pump-turbine impeller prototype when submerged in water has been investigated. The impeller, with a diameter of 2.870m belongs to a pump-turbine unit with a power of around 100MW. To analyze the influence of the added mass, both experimental tests and numerical simulations have been carried out. The experiment has been performed in air and in water. From the frequency response functions the modal characteristics such as natural frequencies and mode shapes have been obtained. A numerical simulation using FEM (Finite Elements Model) was done using the same boundary conditions as in the experiment (impeller in air and surrounded by a mass of water). The modal behaviour has also been calculated. The numerical results were compared with the available experimental results. The comparison shows a good agreement in the natural frequency values both in air and in water. The reduction in frequency due to the added mass effect of surrounding fluid has been calculated. The physics of this phenomenon due to the fluid structure interaction has been investigated from the analysis of the mode-shapes.

Vibrations of an Intermediately Supported U-Bend Tube

1975 ◽  
Vol 97 (1) ◽  
pp. 23-32 ◽  
Author(s):  
L. S. S. Lee
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Experimental Tests ◽  
Bending Stiffness ◽  
Stiffness Ratio ◽  
Plane Vibration ◽  
Straight Beam ◽  
Out Of Plane ◽  
Straight Segments ◽  
Good Agreement

Vibrations of an intermediately supported U-bend tube fall into two independent classes as an incomplete ring of single span does, namely, the in-plane vibration and the coupled twist-bending out-of-plane vibration. Natural frequencies may be expressed in terms of a coefficient p which depends on the stiffness ratio k, the ratio of lengths of spans, and the supporting conditions. The effect of the torsional flexibility of a curved bar acts to release the bending stiffness of a straight beam and hence decrease the natural frequency. Some conclusions for an incomplete ring of single span may not be equally well applicable to the U-tube case due to the effects of intermediate supports and the presence of the supporting straight segments. Results of the analytical predictions and the experimental tests of an intermediately supported U-tube are in good agreement.

Vibrational characteristics of an earth dam

1966 ◽  
Vol 56 (6) ◽  
pp. 1207-1226
Author(s):  
W. O. Keightley
Keyword(s):  
Theoretical Analysis ◽  
Natural Frequencies ◽  
Forced Vibrations ◽  
Earth Dam ◽  
Mode Shapes ◽  
Modal Damping ◽  
Vibrational Characteristics ◽  
Good Agreement ◽  
Lower Frequencies

Abstract An earth dam was excited into vibrations, in the upstream-downstream direction, by four rotating eccentric-mass vibration generators which were operated on the crest. Natural frequencies, mode shapes, and equivalent viscous modal damping constants of the dam were revealed by the forced vibrations. A theoretical analysis of the dam, based on consideration of shearing deformations only, shows moderately good agreement with the behavior which was observed at the lower frequencies.

In-Plane Vibration Modes of Arbitrarily Thick Disks

1997 ◽  
Author(s):  
Kevin I. Tzou ◽  
Jonathan A. Wickert ◽  
Adnan Akay
Keyword(s):  
Natural Frequencies ◽  
Arbitrary Dimension ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Three Dimensional Model ◽  
Bending Vibration ◽  
Annular Disk ◽  
Out Of Plane ◽  
Plane Bending

Abstract The three-dimensional vibration of an arbitrarily thick annular disk is investigated for two classes of boundary conditions: all surfaces traction-free, and all free except for the clamped inner radius. These two models represent limiting cases of such common engineering components as automotive and aircraft disk brakes, for which existing models focus on out-of-plane bending vibration. For a disk of significant thickness, vibration modes in which motion occurs within the disk’s equilibrium plane can play a substantial role in setting its dynamic response. Laboratory experiments demonstrate that in-plane modes exist at frequencies comparable to those of out-of-plane bending even for thickness-to-diameter ratios as small as 10−1. The equations for three-dimensional motion are discretized through the Ritz technique, yielding natural frequencies and mode shapes for coupled axial, radial, and circumferential deformations. This treatment is applicable to “disks” of arbitrary dimension, and encompasses classical models for plates, bars, cylinders, rings, and shells. The solutions so obtained converge in the limiting cases to the values expected from the classical theories, and to ones that account for shear deformation and rotary inertia. The three-dimensional model demonstrates that for geometries within the technologically-important range, the natural frequencies of certain in- and out-of-plane modes can be close to one another, or even identically repeated.

scholarly journals A space structural mechanics model of silicene

2020 ◽  
Vol 234 (1-2) ◽  
pp. 3-10
Author(s):  
Mohsen Motamedi
Keyword(s):  
Natural Frequencies ◽  
Strain Curve ◽  
Structural Mechanics ◽  
Dynamics Simulation ◽  
Mode Shapes ◽  
Two Dimensional ◽  
Stress Strain Curve ◽  
Beam Elements ◽  
Mechanics Model ◽  
Good Agreement

The two-dimensional nanostructures such as graphene, silicene, germanene, and stanene have attracted a lot of attention in recent years. Many studies have been done on graphene, but other two-dimensional structures have not yet been studied extensively. In this work, a molecular dynamics simulation of silicene was done and stress–strain curve of silicene was obtained. Then, the mechanical properties of silicene were investigated using the proposed structural molecular mechanics method. First, using the relations governing the force field and the Lifson–Wershel potential function and structural mechanics relations, the coefficients for the BEAM elements was determined, and a structural mechanics model for silicene was proposed. Then, a silicene sheet with 65 Å × 65 Å was modeled, and Young’s modulus of silicene was obtained. In addition, the natural frequencies and mode shapes of silicene were calculated using finite element method. The results are in good agreement with reports by other papers.

Development of an Analytical Model for Beams With Two Dimples in Opposing Direction

2017 ◽  
Author(s):  
Mofareh Ghazwani ◽  
Kyle Myers ◽  
Koorosh Naghshineh
Keyword(s):  
Differential Equations ◽  
Opposite Direction ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Modal Strain Energy ◽  
Noise And Vibration ◽  
Various Boundary Conditions ◽  
Strategic Approach ◽  
Value Model ◽  
Good Agreement

Structures such as beams and plates can produce unwanted noise and vibration. An emerging technique can reduce noise and vibration without any additional weight or cost. This method focuses on creating two dimples in the same and opposite direction on a beam’s surface where the effect of dimples on its natural frequencies is the problem of interest. The change in the natural frequency between both cases have a different trend. The strategic approach to calculate natural frequencies is as follows: first, a boundary value model (BVM) is developed for a beam with two dimples and subject to various boundary conditions using Hamilton’s Variational Principle. Differential equations describing the motion of each segment are presented. Beam natural frequencies and mode shapes are obtained using a numerical solution of the differential equations. A finite element method (FEM) is used to model the dimpled beam and verify the natural frequencies of the BVM. Both methods are also validated experimentally. The experimental results show a good agreement with the BVM and FEM results. A fixed-fixed beam with two dimples in the same and opposite direction is considered as an example in order to compute its natural frequencies and mode shapes. The effect of dimple locations and angles on the natural frequencies are investigated. The natural frequencies of each case represent a greater sensitivity to change in dimple angle for dimples placed at high modal strain energy regions of a uniform beam.

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