Nonlinear Vibrations Analysis of Overhead Power Lines: A Beam With Mass–Spring–Damper–Mass Systems

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Mohammad A. Bukhari ◽  
Oumar R. Barry
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Nonlinear Frequency ◽  
Response Curves ◽  
Mass System ◽  
Parametric Studies ◽  
Overhead Power Lines ◽  
Nonlinear Equations Of Motion ◽  
Mass Spring ◽  
Stockbridge Damper

This paper examines the nonlinear vibration of a single conductor with Stockbridge dampers. The conductor is modeled as a simply supported beam and the Stockbridge damper is reduced to a mass–spring–damper–mass system. The nonlinearity of the system stems from the midplane stretching of the conductor and the cubic equivalent stiffness of the Stockbridge damper. The derived nonlinear equations of motion are solved by the method of multiple scales. Explicit expressions are presented for the nonlinear frequency, solvability conditions, and detuning parameter. The present results are validated via comparisons with those in the literature. Parametric studies are conducted to investigate the effect of variable control parameters on the nonlinear frequency and the frequency response curves. The findings are promising and open a horizon for future opportunities to optimize the design of nonlinear absorbers.

On the vibration analysis of power lines with moving dampers

2017 ◽  
Vol 24 (18) ◽  
pp. 4096-4109 ◽  
Author(s):  
MA Bukhari ◽  
O Barry ◽  
E Tanbour
Keyword(s):  
Transmission Lines ◽  
Equations Of Motion ◽  
Power Lines ◽  
Governing Equations ◽  
Wind Force ◽  
Vibration Displacement ◽  
Mass System ◽  
Overhead Transmission Lines ◽  
Parametric Studies ◽  
Mass Spring

This work investigates the performance of a moving damper for overhead transmission lines. The damper or absorber consists of mass-spring-damper-mass system. The absorber is connected to a single conductor subjected to pretension and wind force. The governing equations of motion are obtained using Hamilton’s principle, and numerical analysis is carried out using MATLAB®. The model is validated by comparing the present results to those in the literature. Parametric studies are conducted to investigate the performance of the proposed absorber. The results indicate that a moving absorber can be more effective than a fixed absorber. It is also demonstrated that the vibration displacement decreases with increasing forcing frequency and decreasing absorber speed.

Nonlinear Vibrations of a Beam-Spring-Large Mass System

2017 ◽  
Author(s):  
Mohammad A. Bukhari ◽  
Oumar R. Barry
Keyword(s):  
Natural Frequencies ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Large Mass ◽  
Mode Shapes ◽  
Resonance Excitation ◽  
Response Curves ◽  
Mass System ◽  
Spring System

This paper presents the nonlinear vibration of a simply supported Euler-Bernoulli beam with a mass-spring system subjected to a primary resonance excitation. The nonlinearity is due to the mid-plane stretching and cubic spring stiffness. The equations of motion and the boundary conditions are derived using Hamiltons principle. The nonlinear system of equations are solved using the method of multiple scales. Explicit expressions are obtained for the mode shapes, natural frequencies, nonlinear frequencies, and frequency response curves. The validity of the results is demonstrated via comparison with results in the literature. Exact natural frequencies are obtained for different locations, rotational inertias, and masses.

Study of plate vibrating in fluids having part-through crack at random angles and locations

2021 ◽  
pp. 095440622110127
Author(s):  
Ruqia Ikram ◽  
Asif Israr
Keyword(s):  
Frequency Response ◽  
Multiple Scales ◽  
Peak Amplitude ◽  
Nonlinear Frequency ◽  
Response Curves ◽  
Crack Location ◽  
Cracked Plate ◽  
Nonlinear Frequency Response ◽  
Angle Crack ◽  
Crack Angle

This study presents the vibration characteristics of plate with part-through crack at random angles and locations in fluid. An experimental setup was designed and a series of tests were performed for plates submerged in fluid having cracks at selected angles and locations. However, it was not possible to study these characteristics for all possible crack angles and crack locations throughout the plate dimensions at any fluid level. Therefore, an analytical study is also carried out for plate having horizontal cracks submerged in fluid by adding the influence of crack angle and crack location. The effect of crack angle is incorporated into plate equation by adding bending and twisting moments, and in-plane forces that are applied due to antisymmetric loading, while the influence of crack location is also added in terms of compliance coefficients. Galerkin’s method is applied to get time dependent modal coordinate system. The method of multiple scales is used to find the frequency response and peak amplitude of submerged cracked plate. The analytical model is validated from literature for the horizontally cracked plate submerged in fluid as according to the best of the authors’ knowledge, literature lacks in results for plate with crack at random angle and location in the presence of fluid following validation with experimental results. The combined effect of crack angle, crack location and fluid on the natural frequencies and peak amplitude are investigated in detail. Phenomenon of bending hardening or softening is also observed for different boundary conditions using nonlinear frequency response curves.

Dynamic Modeling of the Double-Nut Planetary Roller Screw Mechanism Considering Elastic Deformations

2021 ◽  
Author(s):  
Xiaojun Fu ◽  
Geng Liu ◽  
Xin Li ◽  
Ma Shangjun ◽  
Qiao Guan
Keyword(s):  
External Force ◽  
Load Distribution ◽  
Equations Of Motion ◽  
Great Influence ◽  
Compressive Force ◽  
Mass System ◽  
Elastic Deformations ◽  
Roller Screw ◽  
Screw Mechanism ◽  
Nonlinear Equations Of Motion

Abstract With the rising application of double-nut Planetary Roller Screw Mechanism (PRSM) into industry, increasing comprehensive studies are required to identify the interactions among motion, forces and deformations of the mechanism. A dynamic model of the double-nut PRSM with considering elastic deformations is proposed in this paper. As preloads, inertial forces and elastic deformations have a great influence on the load distribution among threads, the double-nut PRSM is discretized into a spring-mass system. An adjacency matrix is introduced, which relates the elastic displacements of nodes and the deformations of elements in the spring-mass system. Then, the compressive force acting on the spacer is derived and the equations of load distribution are given. Considering both the equilibrium of forces and the compatibility of deformations, nonlinear equations of motion for the double-nut PRSM are developed. The effectiveness of the proposed model is verified by comparing dynamic characteristics and the load distribution among threads with those from the previously published models. Then, the dynamic analysis of a double-nut PRSM is carried out, when the rotational speed of the screw and the external force acting on the nut #2 are changed periodically. The results show that if the external force is increased, the preload of the nut #1 is decreased and that of the nut #2 is increased. Although the nominal radii of rollers are the same, the maximum contact force acting on the roller #2 is much larger than that of the roller #1.

Load Transfer Control for a Gantry Crane with Arbitrary Delay Constraints

2002 ◽  
Vol 8 (2) ◽  
pp. 135-158 ◽  
Author(s):  
Paolo Dadone ◽  
Hugh F. Vanlandingham
Keyword(s):  
Load Transfer ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Gantry Crane ◽  
Phase Plane Analysis ◽  
Plane Analysis ◽  
Nonlinear Approach ◽  
Linearized Model ◽  
Nonlinear Equations Of Motion ◽  
Quadratic And Cubic Nonlinearities

This paper describes a method to move the load of a gantry crane to a desired position in the presence of known, but arbitrary, motion-inversion delays as well as cart acceleration constraints. The method idea is based on a phase-plane analysis of the linearized model. In order to limit residual pendulation at the goal position, the method is extended to account for quadratic and cubic nonlinearities. The method of multiple scales is used to determine an approximate solution to the nonlinear equations of motion, thus providing a more accurate measure of the frequency of the oscillations. The nonlinear approach is very successful in limiting residual oscillations to very small values (less than 1 degree of amplitude), offering a reduction, with respect to the linear case, of as much as two orders of magnitude. Finally, this method offers a rationale for the future development of a controller for suppression of load oscillations in ship-mounted cranes in the presence of arbitrary delays.

scholarly journals Nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermo loading based on a novel HSDT

2021 ◽  
Author(s):  
Reza Mohammadi
Keyword(s):  
Nonlinear Vibration ◽  
Frequency Ratio ◽  
Vibration Analysis ◽  
Multiple Scales ◽  
Numerical Technique ◽  
Perturbation Technique ◽  
Equations Of Motion ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
Nonlinear Frequency

Abstract In this paper, the nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermo loading based on a novel HSDT is studied. Nonlocal elasticity theory is applied to consider the small scale effect. The nonlinear equations of motion are derived using Hamilton’s principle. First, a Galerkin-based numerical technique is applied to reduce the nonlinear governing equation into a set of Duffing-type time-dependent differential equations. Afterward, the analytical solutions are derived based on the method of multiple scales (MMS) and perturbation technique. All of the mechanical properties of the beam are temperature dependent. The impacts of the several variables are investigated on the nonlinear frequency ratio of the nanobeams. The results illustrate that when maximum deflection is smaller/ greater than 0.2, its impact on the nonlinear frequency ratio will decrease/increase.

Parametric Vibrations in Discs: Point-Wise and Distributed Loads, Including Rotating Friction

1995 ◽  
Author(s):  
H. Ouyang ◽  
S. N. Chan ◽  
J. E. Mottershead ◽  
M. I. Friswell ◽  
M. P. Cartmell
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Transverse Load ◽  
Transverse Mass ◽  
Follower Load ◽  
Parametric Resonances ◽  
Spring System ◽  
Multiple Scales Analysis ◽  
Mass Spring ◽  
Rotating Load

Abstract This paper is concerned with the parametric resonances in a stationary annular disc when excited by a rotating load system. Two forms of the load system are considered. In the first, the load consists of a discrete transverse mass-spring-damper system and a frictional follower load. Secondly, a distributed mass-spring system (without friction) is studied. In both cases the transverse load is rotated at a uniform speed around the disc. Equations of motion are developed for the two cases, and the results of a multiple scales analysis are presented. The disc is found to exhibit many parametric resonances at subcritical speeds when friction is present.

Development of Seated Human Model With Uncertain Parameters and Estimation of the Ride Comfort

2018 ◽  
Author(s):  
Jong-Jin Bae ◽  
Namcheol Kang
Keyword(s):  
Ride Comfort ◽  
Probability Distributions ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Human Model ◽  
Whole Body ◽  
Mode Shapes ◽  
Comfort Index ◽  
Parametric Studies ◽  
Nonlinear Equations Of Motion

This study deals with the biodynamic responses of the 5-degree-of-freedom mathematical human model to whole-body vibrations in a vehicle. The nonlinear equations of motion of the human model were derived, and the spring constants and damping coefficients were extracted from the experimental data in the literature using optimization process. The natural frequencies and mode shapes were also calculated using linearized human model. In order to examine the effects of the variations of the human parameters, the parametric studies with respect to the stiffness values were performed. The mode veering phenomenon was observed between fourth and fifth mode of the linearized human model. In addition, the frequency responses of the nonlinear 5-degree-of-freedom model were also obtained, and the frequency shift and jump phenomena were observed. Furthermore, the estimation of the ride comfort was performed using CarSim and Matlab/Simulink with several road profiles according to ISO classification. Besides, we also calculated the ride comfort index using BS 6841 standard. In order to calculate the statistical responses of human model, the Monte-Carlo simulation applied to the nonlinear human model having uncertain stiffness assuming Gaussian distribution. These stochastic approaches enable the proposed human model to estimate probability distributions of the ride comfort index.

Dynamic Stability of a Spinning Timoshenko Beam Subjected to a Moving Mass-Spring-Damper Unit

2010 ◽  
Author(s):  
T. H. Young ◽  
M. S. Chen
Keyword(s):  
Dynamic Stability ◽  
Timoshenko Beam ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Axial Direction ◽  
Longitudinal Axis ◽  
Moving Mass ◽  
The Stability ◽  
The Galerkin Method ◽  
Mass Spring

This paper investigates the dynamic stability of a finite Timoshenko beam spinning along its longitudinal axis and subjected to a moving mass-spring-damper (MSD) unit traveling in the axial direction. The mass of the moving MSD unit makes contact with the beam all the time during traveling. Due to the moving MSD unit, the beam is acted upon by a periodic, parametric excitation. In this work, the equations of motion of the beam are first discretized by the Galerkin method. The discretized equations of motion are then partially uncoupled by the modal analysis procedure suitable for gyroscopic systems. Finally the method of multiple scales is used to obtain the stability boundaries of the beam. Numerical results show that if the displacement of the MSD unit is equal to only one of the two transverse displacements of the beam, very large unstable regions may appear at main resonances.

scholarly journals Nonlinear Response of Cantilever Beams to Combination and Subcombination Resonances

1998 ◽  
Vol 5 (5-6) ◽  
pp. 277-288 ◽  
Author(s):  
Ali H. Nayfeh ◽  
Haider N. Arafat
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Nonlinear Ordinary Differential Equations ◽  
Response Curves ◽  
First Order ◽  
Aspect Ratios

The nonlinear planar response of cantilever metallic beams to combination parametric and external subcombination resonances is investigated, taking into account the effects of cubic geometric and inertia nonlinearities. The beams considered here are assumed to have large length-to-width aspect ratios and thin rectangular cross sections. Hence, the effects of shear deformations and rotatory inertia are neglected. For the case of combination parametric resonance, a two-mode Galerkin discretization along with Hamilton’s extended principle is used to obtain two second-order nonlinear ordinary-differential equations of motion and associated boundary conditions. Then, the method of multiple scales is applied to obtain a set of four first-order nonlinear ordinary-differential equations governing the modulation of the amplitudes and phases of the two excited modes. For the case of subcombination resonance, the method of multiple scales is applied directly to the Lagrangian and virtual-work term. Then using Hamilton’s extended principle, we obtain a set of four first-order nonlinear ordinary-differential equations governing the amplitudes and phases of the two excited modes. In both cases, the modulation equations are used to generate frequency- and force-response curves. We found that the trivial solution exhibits a jump as it undergoes a subcritical pitchfork bifurcation. Similarly, the nontrivial solutions also exhibit jumps as they undergo saddle-node bifurcations.

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