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.

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.

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.

Dynamic Characteristics of Tsing Ma Suspension Bridge

1996 ◽  
Vol 1541 (1) ◽  
pp. 43-50 ◽  
Author(s):  
Siu Kui Au ◽  
Neil Mickleborough ◽  
Paul N. Roschke
Keyword(s):  
Analytical Solutions ◽  
Bridge Deck ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Suspension Bridge ◽  
Mode Shapes ◽  
Out Of Plane ◽  
Quantitative Results ◽  
Suspension Cable ◽  
Bending Modes

Numerical simulation was carried out to determine the dynamic properties of the Tsing Ma Suspension Bridge. Both the structure as a whole and individual subcomponents were modeled. Classical analytical solutions for simplified models from the available literature were compared with the results obtained from a finite-element code. Quantitative results for static deflection, natural frequencies, and mode shapes were compared with analytical solutions from linear theory. Out-of-plane modes were shown to be dominant. For in-plane antisymmetric and symmetric bending modes, in which the suspension cable and bridge deck vibrate in the same direction, the natural frequency of the main span of the bridge is determined to be approximately equal to the square root of the sum of the squares of the frequencies of the cable and bridge deck.

Managing Vortex Induced Vibration in Well Jumper Systems

2008 ◽  
Author(s):  
Kenneth Bhalla ◽  
Lixin Gong
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Cross Flow ◽  
Mitigation Measures ◽  
Mode Shapes ◽  
Bottom Current ◽  
Vortex Induced Vibration ◽  
Flow Response ◽  
Out Of Plane ◽  
Lock In

The purpose of this paper is to present a method that has been developed to identify if vortex induced vibration (VIV) occurs in well jumper systems. Moreover, a method has been developed to determine when VIV mitigation measures such as strakes are required. The method involves determining the in-plane and out-of-plane natural frequencies and mode shapes. The natural frequencies are then used, in conjunction with the maximum bottom current expected at a given location to determine if suppression is required. The natural frequency of a jumper system is a function of many variables, e.g. span length, leg height, pipe diameter and thickness, buoyancy placement, buoyancy uplift, buoyancy OD, insulation thickness, and contents of the jumper. The suppression requirement is based upon calculating a lower bound lock-in current speed based upon an assumed velocity bandwidth centered about the lock-in current. The out-of-plane VIV cross-flow response is produced by a current in the plane of the jumper; whereas the in-plane VIV cross-flow response is produced by the out-of-plane current. Typically, the out-of-plane natural frequency is smaller than the in-plane natural frequency. Jumpers with small spans have higher natural frequencies; thus small span jumpers may require no suppression or suppression on the vertical legs. Whereas, larger span jumpers may require no suppression, suppression on the vertical legs or suppression on all the legs. The span of jumper systems (i.e. production, water injection, gas lift/injection ...) may vary in one given field; it has become apparent that not all jumper systems require suppression. This technique has allowed us to recognize when certain legs of a given jumper system may require suppression, thus leading to a jumper design whose safety is not compromised while in the production mode, as well as minimizing downtime and identifying potential savings from probable fatigue failures.

Axisymmetric Vibrations of a Piezoelectric Spherical Shell Submerged in a Compressible Viscous Fluid Medium

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Juxi Hu ◽  
Zhiping Qiu ◽  
Tsung-Chow Su
Keyword(s):  
Viscous Fluid ◽  
Natural Frequencies ◽  
Essential Feature ◽  
Elastic Shell ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Compressible Viscous Fluid ◽  
Previous Theory ◽  
Fluid Medium ◽  
Shell Motion

Axisymmetric vibrations of a hollow piezoelectric sphere submerged in a compressible viscous fluid medium are investigated. The piezoelectric sphere is radially polarized. The differential equations governing the shell motion are obtained by the use of Hamilton’s principle. Based on the classical bending theory of shells, it is shown that all the piezoelectric contributions can be included in the in vacuo natural frequencies and their corresponding mode shapes. As such, the previous theory on elastic shell vibration becomes readily extendable. The flow field, determined by the boundary layer theory, is coupled to the shell motion through no-slip and no-penetrating conditions. It is found that the contribution of the piezoelectric parameters in the thin shell’s free vibration is of small order and is negligible. Natural frequencies and their associated vibration characteristics are numerically obtained and presented for a Polyvinglindene fluoride (PVDF) shell submerged in water. Dynamic responses of a submerged piezoelectric sherical shell, and the associated radiation of sound are investigated. The oscillations are harmonically driven by an axisymmetrically applied electric potential difference across the surface of the shell. The vibrational, fluid loading, and energy flow characteristics are derived and evaluated for a PVDF shell submerged in water. The essential feature of the modal response is determined by various critical frequencies, such as resonant frequencies and vibration-absorbing frequencies. Viscous effect is found noticeable in several cases.

Buckling Loads and Natural Frequencies of Drill Bits and Fluted Cutters

1984 ◽  
Vol 106 (3) ◽  
pp. 196-204 ◽  
Author(s):  
E. B. Magrab ◽  
D. E. Gilsinn
Keyword(s):  
Natural Frequencies ◽  
Twist Angle ◽  
Axial Loading ◽  
Basis Functions ◽  
Mode Shapes ◽  
Euler Beam ◽  
Buckling Loads ◽  
Drill Bits ◽  
Out Of Plane ◽  
Beam Type

The buckling loads, natural frequencies and mode shapes of twist-drill bits and certain fluted cutters under a variety of combinations of twist angle, cross-section geometry, and axial loading have been obtained. The drill bit is modelled as a twisted Euler beam under axial loading that is clamped at both ends. The governing system of differential equations is solved by the Galerkin procedure. Explicit forms for the basis functions used to generate the Galerkin coefficients are presented in general form in an appendix. They may be used for obtaining numerical results for that class of problems which use the Rayleigh-Ritz-Galerkin methods with beam-type functions as the basis functions. The representative set of modes obtained exhibit a complex out-of-plane twisting-type motion that suggests a possible explanation for the out-of-roundness of certain drilled holes.

scholarly journals Nonlinear Dynamic Modeling and Analysis of an L-Shaped Multi-Beam Jointed Structure with Tip Mass

Materials ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7279
Author(s):  
Jin Wei ◽  
Tao Yu ◽  
Dongping Jin ◽  
Mei Liu ◽  
Dengqing Cao ◽  
...  
Keyword(s):  
Differential Equations ◽  
Nonlinear Dynamic ◽  
Natural Frequencies ◽  
Great Influence ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Nonlinear Odes ◽  
Global Mode ◽  
Orthogonality Relations ◽  
Tip Mass

A dynamic model of an L-shaped multi-beam joint structure is presented to investigate the nonlinear dynamic behavior of the system. Firstly, the nonlinear partial differential equations (PDEs) of motion for the beams, the governing equations of the tip mass, and their matching conditions and boundary conditions are obtained. The natural frequencies and the global mode shapes of the linearized model of the system are determined, and the orthogonality relations of the global mode shapes are established. Then, the global mode shapes and their orthogonality relations are used to derive a set of nonlinear ordinary differential equations (ODEs) that govern the motion of the L-shaped multi-beam jointed structure. The accuracy of the model is verified by the comparison of the natural frequencies solved by the frequency equation and the ANSYS. Based on the nonlinear ODEs obtained in this model, the dynamic responses are worked out to investigate the effect of the tip mass and the joint on the nonlinear dynamic characteristic of the system. The results show that the inertia of the tip mass and the nonlinear stiffness of the joints have a great influence on the nonlinear response of the system.

scholarly journals Damage Evaluation of Free-Free Beam Based on Vibration Testing

2020 ◽  
Vol 1 (2) ◽  
pp. 142-152 ◽  
Author(s):  
Duong Huong Nguyen ◽  
Long Viet Ho ◽  
Thanh Bui-Tien ◽  
Guido De Roeck ◽  
Magd Abdel Wahab
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Numerical Models ◽  
Element Model ◽  
3D Models ◽  
Mode Shapes ◽  
Structure Damage ◽  
Modal Properties ◽  
Vibration Responses ◽  
Free Beam

Damage can be detected by vibration responses of a structure. Damage changes the modal properties such as natural frequencies, mode shapes, and damping ratios. Natural frequency is one of the most frequently used damage indicators. In this paper, the natural frequency is used to monitor damage in a free-free beam. The modal properties of the intact free-free beam are identified based on a setup of 15 accelerometers. A finite element model is used to model the free-free beam. Three models are considered: beam (1D), shell (2D), and solid (3D). The numerical models are updated based on the first five bending natural frequencies. The free-free beam is damaged by a rectangle cut. The experiment is re-setup and the model properties of the damaged beam are re-identified. The cuttings are modeled in the numerical simulations. The first five numerical bending natural frequencies of the damaged beam are compared with the experimental ones. The results showed that the 1D beam element model has the highest errors, while the 2D and 3D models have approximately the same results. Therefore, the 2D representation can be used to model the damaged beam for fast computation.

Vibrations of Suspended Cables

1983 ◽  
Vol 50 (3) ◽  
pp. 687-689
Author(s):  
J. G. Gale ◽  
C. E. Smith
Keyword(s):  
Natural Frequencies ◽  
Analytical Investigation ◽  
Plane Motion ◽  
Mode Shapes ◽  
Arc Length ◽  
Power Series Solutions ◽  
Out Of Plane ◽  
Independent Variable ◽  
Suspended Cables ◽  
Frequency Ratios

An analytical investigation of the small, normal-mode motions of a homogeneous, inextensible, perfectly flexible cable suspended in a gravitational field was made. With cable arc length as the independent variable, the differential equations that govern the mode shapes have irrational coefficients. A transformation of the independent position variable yields equations that have polynominal coefficients, which then lend themselves to power series solutions. Natural frequencies of oscillation and corresponding mode shapes are determined from these solutions. Figures showing the natural frequency ratios for a variety of cable support geometries are presented for both in-plane and out-of-plane motion.

scholarly journals Influence of Excitation on Dynamic System Identification for a Multi-Span Reinforced Concrete Bridge

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
M. Alwash ◽  
B. F. Sparling ◽  
L. D. Wegner
Keyword(s):  
Reinforced Concrete ◽  
Natural Frequencies ◽  
Harmonic Excitation ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Concrete Bridge ◽  
Random Loading ◽  
Reinforced Concrete Bridge ◽  
Random Forcing ◽  
Vehicle Loading

In vibration-based damage detection, changes to structural modal properties are tracked over time in order to infer the current state of damage or deterioration. As such, the ability to obtain reliable estimates of modal parameters, particularly natural frequencies and mode shapes, is of critical importance. In the present study, the influence of the dynamic excitation source on the accuracy and statistical uncertainty of modal property estimates for a three span reinforced concrete bridge was investigated experimentally and numerically. Comparisons were made between the dynamic responses due to vehicle loading, harmonic and random forcing, impact, and environmental excitation. It was demonstrated that natural frequencies and mode shapes extracted from the free vibration response following vehicle and random loading events were of higher quality than corresponding values determined during the forcing phase of those events. Harmonic excitation at resonant frequencies and impact were also found to produce statistically reliable results.

Sign in / Sign up

Export Citation Format

Share Document