Effects of Boundary Flexibility on the Vibration of a Continuum With a Moving Oscillator

2002 ◽  
Vol 124 (4) ◽  
pp. 552-560 ◽  
Author(s):  
Yonghong Chen ◽  
C. A. Tan ◽  
L. A. Bergman
Keyword(s):  
Shear Force ◽  
Equations Of Motion ◽  
Interaction Force ◽  
Dynamic Interaction ◽  
Spatial And Temporal Distributions ◽  
Expansion Series ◽  
Frequency Components ◽  
Elastically Supported ◽  
Moving Oscillator ◽  
The Continuum

In this paper, the problem of an oscillator traversing an elastically supported continuum is studied. The flexibility in the boundaries of the continuum is modeled by linear, transverse springs. The response of the continuum and the dynamic interaction force between the moving oscillator and the continuum are evaluated by an eigenfunction expansion series. To circumvent convergence difficulties associated with the jump in the shear force due to the moving interaction force, an improved series expansion employing the static Green’s function is derived. The coupled governing equations of motion are solved numerically and results are obtained to examine the effects of the boundary flexibility on the response, the dynamic interaction force, the shear force spatial and temporal distributions, as well as the convergence properties of the expansion series. It is found that high order modal terms contribute significantly to the shear force expansion series in the elastically supported model. The presence of large amplitude and high frequency components in the shear force is critical in understanding the cumulative fatigue failure of the structure. A useful and compact formula estimating the value of the support stiffness above which a boundary may be modeled as simply supported is also derived.

Effects of Boundary Flexibility in the Moving Oscillator Problem

2001 ◽  
Author(s):  
Chin An Tan ◽  
Yonghong Chen ◽  
Lawrence A. Bergman
Keyword(s):  
Natural Frequency ◽  
Eigenfunction Expansion ◽  
Transverse Direction ◽  
Interaction Force ◽  
Critical Value ◽  
Significant Implication ◽  
Bernoulli Beam ◽  
Elastically Supported ◽  
Euler Bernoulli Beam ◽  
Moving Oscillator

Abstract In this paper, the problem of an oscillator moving across an elastically supported Euler-Bernoulli beam is examined. The oscillator is modeled by a one-degree-of-freedom sprung mass and the end supports are modeled by linear springs in the transverse direction. Solution for the response of the beam is represented by an eigenfunction expansion series. Numerical results are obtained for the eigenvalues and the response of the elastically supported beam, and the interaction force (force in the oscillator spring). To guide the discussion, a critical value of the support stiffness is determined from the plot of the first natural frequency versus the support stiffness. Effects of the boundary flexibility on the maximum beam response and the maximum interaction force are discussed as a function of the speed and the oscillator frequency. The boundary flexibility is shown to have a significant implication in the design analysis of the moving oscillator problem, especially for shorter span beam structures.

Application of the Mode-Acceleration Technique to the Solution of the Moving Oscillator Problem

1999 ◽  
Author(s):  
Alexander V. Pesterev ◽  
Lawrence A. Bergman
Keyword(s):  
Shear Force ◽  
Series Representation ◽  
Bending Moment ◽  
Static Solution ◽  
Distributed Parameter ◽  
Distributed Parameter System ◽  
Parameter System ◽  
One Dimensional ◽  
Acceleration Technique ◽  
Moving Oscillator

Abstract The problem of calculating the dynamic response of a one-dimensional distributed parameter system excited by an oscillator traversing the system with an arbitrarily varying speed is investigated. An improved series representation for the solution is derived that takes into account the jump in the shear force at the point of the attachment of the oscillator, which makes it possible to efficiently calculate the distributed shear force and, where applicable, bending moment. The improvement is achieved through the introduction of the “quasi-static” solution, an approximation to the desired one, which makes it possible to apply to the moving oscillator problem the “mode-acceleration” technique conventionally used for acceleration of series in problems related to the steady-state vibration of distributed systems. Numerical results illustrating the efficiency of the method are presented.

scholarly journals Physical and Mathematical Fluid Mechanics

Water ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 2199
Author(s):  
Markus Scholle
Keyword(s):  
Fluid Mechanics ◽  
Continuum Hypothesis ◽  
Equations Of Motion ◽  
Local Equilibrium ◽  
Physical Modelling ◽  
Mathematical Methods ◽  
Open Questions ◽  
Software Codes ◽  
The One ◽  
The Continuum

Fluid mechanics has emerged as a basic concept for nearly every field of technology. Despite there being a well-developed mathematical theory and available commercial software codes, the computation of solutions of the governing equations of motion is still challenging, especially due to the nonlinearity involved, and there are still open questions regarding the underlying physics of fluid flow, especially with respect to the continuum hypothesis and thermodynamic local equilibrium. The aim of this Special Issue is to reference recent advances in the field of fluid mechanics both in terms of developing sophisticated mathematical methods for finding solutions of the equations of motion, on the one hand, and on novel approaches to the physical modelling beyond the continuum hypothesis and thermodynamic local equilibrium, on the other.

Conditions for the planes of symmetry of an elastically supported rigid body

2009 ◽  
Vol 223 (8) ◽  
pp. 1755-1766 ◽  
Author(s):  
S J Jang ◽  
Y J Choi
Keyword(s):  
Rigid Body ◽  
Eigenvalue Problems ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Mass Matrices ◽  
Out Of Plane ◽  
Modes Of Vibration ◽  
Compliance Matrices ◽  
Special Points ◽  
Elastically Supported

Introducing the planes of symmetry into an oscillating rigid body suspended by springs simplifies the complexity of the equations of motion and decouples the modes of vibration into in-plane and out-of-plane modes. There have been some research results from the investigation into the conditions for planes of symmetry in which prior conditions for the simplification of the equations of motion are required. In this article, the conditions for the planes of symmetry that do not need prior conditions for simplification are presented. The conditions are derived from direct expansions of eigenvalue problems for stiffness and mass matrices that are expressed in terms of in-plane and out-of-plane modes and the orthogonality condition with respect to the mass matrix. Two special points, the planar couple point and the perpendicular translation point are identified, where the expressions for stiffness and compliance matrices can be greatly simplified. The simplified expressions are utilized to obtain the analytical expressions for the axes of vibration of a vibration system with planes of symmetry.

Passive Control of Vibration of Elastically Supported Beams Subjected to Moving Loads

2005 ◽  
Author(s):  
D. Younesian ◽  
E. Esmailzadeh ◽  
M. H. Kargarnovin
Keyword(s):  
High Speed ◽  
Passive Control ◽  
Vibration Suppression ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Compressive Force ◽  
Moving Loads ◽  
Axial Compressive Force ◽  
Before And After ◽  
Elastically Supported

Vibration suppression of elastically supported beams subjected to moving loads is investigated in this work. For a Timoshenko beam with an arbitrary number of elastic supports, subjected to a constant axial compressive force, and having a tuned mass damper (TMD) installed at the mid-span, the equations of motion are derived and using the Galerkin approach the solution is sought. The optimum values of the frequency and damping ratio are determined both analytically and numerically and presented as some design curves directly applicable in the TMD design for bridge structures. To show the efficiency of the designed TMD, computer simulation for two real bridges, subjected to a S.K.S Japanese high-speed train, is carried out and the results obtained are compared for before and after the installation of the TMD system.

scholarly journals Forced Vibration of Delaminated Timoshenko Beams under the Action of Moving Oscillatory Mass

2013 ◽  
Vol 20 (1) ◽  
pp. 79-96 ◽  
Author(s):  
M.H. Kargarnovin ◽  
M.T. Ahmadian ◽  
R.A. Jafari-Talookolaei
Keyword(s):  
Dynamic Response ◽  
Forced Vibration ◽  
Equations Of Motion ◽  
Mode Shapes ◽  
Solution Technique ◽  
Timoshenko Beams ◽  
Modal Expansion ◽  
Forced Vibration Analysis ◽  
First Time ◽  
Moving Oscillator

This paper presents the dynamic response of a delaminated composite beam under the action of a moving oscillating mass. In this analysis the Poisson's effect is considered for the first time. Moreover, the effects of rotary inertia and shear deformation are incorporated. In our modeling linear springs are used between delaminated surfaces to simulate the dynamic interaction between sub-beams. To solve the governing differential equations of motion using modal expansion series, eigen-solution technique is used to obtain the natural frequencies and their corresponding mode shapes necessary for forced vibration analysis. The obtained results for the free and forced vibrations of beams are verified against reported similar results in the literatures. Moreover, the maximum dynamic response of such beam is compared with an intact beam. The effects of different parameters such as the velocity of oscillating mass, different ply configuration and the delamination length, its depth and spanwise location on the dynamic response of the beam are studied. In addition, the effects of delamination parameters on the oscillator critical speed are investigated. Furthermore, different conditions under which the detachment of moving oscillator from the beam will initiate are investigated.

Finite Element Analysis of Embedded Parts with Big-Diameter Reinforcing Bar under Shear Force

2010 ◽  
Vol 452-453 ◽  
pp. 509-512
Author(s):  
Yao Guo Zhu ◽  
Qing Xiang Wang
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Shear Force ◽  
Three Dimensional ◽  
Interaction Force ◽  
Internal Force ◽  
Shear Capacity ◽  
System Response ◽  
Element Analysis ◽  
Reinforcing Bar

Nowadays embedded parts which connect steel members with concrete structures have frequently emerged in civil engineering; however the existing design code for embedded parts cannot satisfy the increasing demand of engineering as it was derived from limited experiments. In the paper, a finite element study on embedded parts with big-diameter reinforcing bars under shear force is conducted. The aim of the study was to fully investigate the mechanical performances of embedded parts under shear force using a three-dimensional finite element analysis with the help of a commercial software ANSYS. Cross-section internal force of anchor bar, embedded part deformation, interaction force between anchor bar and concrete, and friction force were investigated in order to well know the system response. The results show that the shear capacity of embedded part obtained from finite element analysis is conservative.

Effects of Tip Mass and Interaction Force on Nonlinear Behavior of Force Modulation FM-AFM Cantilever

2016 ◽  
Vol 33 (2) ◽  
pp. 257-268 ◽  
Author(s):  
K. E. Torkanpouri ◽  
H. Zohoor ◽  
M. H. Korayem
Keyword(s):  
Frequency Shift ◽  
Nonlinear Model ◽  
Equations Of Motion ◽  
Nonlinear Behavior ◽  
Interaction Force ◽  
Beam Model ◽  
Frequency Shifts ◽  
Excitation Mode ◽  
Force Modulation ◽  
Tip Mass

AbstractInfluences of the tip mass, excitation mode of Frequency Modulated Atomic Force Microscope (FM-AFM) on the resonance frequency shift in force modulation (FM) mode are studied. Governing equations of motion are determined based on Timoshenko beam model with concentrated end mass. Approach point and base amplitude are set such that the FM-AFM remains just in FM mode. Either the linearized and nonlinear Derjaguin-Muller-Toporov (DMT) model are investigated. Then frequency shifts are determined for various interaction force regimes. It is showed the effect of tip mass on frequency shift is significant even for small tips. Nonlinear model shows lower frequency shifts in comparison with linearized model. It is showed that the amplitude of response is increased by increasing the tip mass and order of base excitation. Deviation of frequency shift between linearized and nonlinear solution are studied. It is declared that the error between linearized and nonlinear model is complicated. A deviation index is used for explaining behavior of error while tip mass and excitation mode are changed. It is showed, this index predicts the trend of error in all excitation modes and force cases. Behavior of system is linearizing by increasing the order of excitation, generally.

Dynamic Interaction Analysis of Maglev-Guideway System Based on a 3D Full Vehicle Model

2017 ◽  
Vol 17 (01) ◽  
pp. 1750006 ◽  
Author(s):  
Dong-Ju Min ◽  
Myung-Rag Jung ◽  
Moon-Young Kim ◽  
Jong-Won Kwark
Keyword(s):  
Dynamic Equilibrium ◽  
Interaction Analysis ◽  
Equations Of Motion ◽  
Dynamic Interaction ◽  
Surface Irregularity ◽  
Superposition Method ◽  
Vehicle Model ◽  
Equilibrium Equations ◽  
Coupled Equations ◽  
Maglev Vehicle

The purpose of this paper is to develop a detailed 3D maglev vehicle and guideway model and investigate the dynamic response characteristics of the coupled system. For this, the maglev vehicle is modeled as one cabin and four bogies having eight electromagnetics, four sensors, and four secondary suspensions based on the Urban Transit Maglev (UTM) system in Korea. The 3D dynamic equilibrium equations of the cabin and bogies are derived by considering the actively controlled electromagnetic forces. Also, the equations of motion for the guideway are derived using the modal superposition method for vertical, lateral, and torsional modes. The resulting coupled equations of motion are then solved using a predictor–corrector iterative algorithm. Finally, through the numerical simulation of the developed system, the responses using the 3D maglev vehicle model are compared with those obtained by the corresponding 2D model. The effects of surface irregularity on the dynamic interaction behaviors are then evaluated for increasing vehicle speeds. Particularly, the 3D resonance conditions of the guideway girder and the maglev vehicle are presented considering the resonance conditions due to equidistant moving loads. In addition, some resonance phenomena are rigorously explored, including the lateral resonance by a series of vehicles running on a girder.

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