scholarly journals Localization in Multiple Nearly-Identical Tuned Vibration Absorbers

2013 ◽  
Vol 2 (3) ◽  
pp. 157 ◽  
Author(s):  
Abdullah Saleh Alsuwaiyan
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Torsional Vibration ◽  
Forced Vibration ◽  
Absolute Magnitude ◽  
Vibration Absorbers ◽  
Steady State Analysis ◽  
Tuned Vibration Absorbers ◽  
Translational Vibration ◽  
The Mathematical Model

The forced vibration of multiple nearly identical translational vibration absorbers is considered. Localization, where the amplitudes of vibration of a group of the absorbers can become relatively large as compared to those of the corresponding perfectly tuned system is investigated. In this work, imperfections amoung the absorbers are allowed and brought into the analysis through the stiffnesses of the absorbers' springs. Steady-state analysis of the mathematical model is used to obtain the results. Results, which focus on translational absorber systems, are found to be consistent with previous results obtained for torsional vibration absorbers. It is found that strengths of the localized responses depend on the levels of imperfections, the relative imperfections among absorbers, and the absorbers' damping. Localization is shown to exist in the undamped multiple nearly-identical vibration absorbers system, or more generally, in the system where the ratio of the level of absorbers' damping to the level of imperfections in the absorbers is small. It is also shown that localized responses can be effectively avoided by introducing some intentional mistuning in the absorbers' stiffnesses. This mistuning should be small in absolute magnitude in order not to reduce the absorbers' performance and should be large when compared to the absorbers' imperfections.

scholarly journals Hybrid Secondary Suspension Systems

2009 ◽  
Vol 16 (5) ◽  
pp. 467-480 ◽  
Author(s):  
Nader Vahdati ◽  
Mehdi Ahmadian
Keyword(s):  
Mathematical Model ◽  
Vibration Absorbers ◽  
Simple Mathematical Model ◽  
System Behavior ◽  
Engine Mounts ◽  
Suspension Systems ◽  
Tuned Vibration Absorbers ◽  
Simulation Results ◽  
Secondary Suspension ◽  
The Mathematical Model

Passive fluid mounts are used in the fixed wing applications as engine mounts. The passive fluid mount is placed in between the engine and the fuselage to reduce the cabin's structure- borne noise and vibration generated by the engine.To investigate the benefits of passive fluid mounts used in conjunction with tuned vibration absorbers (TVA), a simple mathematical model is developed. This mathematical model includes the mathematical model of a passive fluid mount, a TVA, and a spring representing the fuselage structure. The simulation results indicate that when passive fluid mounts are used in conjunction with TVAs, an active suspension system behavior is nearly created.

Steady-State Responses in Systems of Nearly-Identical Torsional Vibration Absorbers

2003 ◽  
Vol 125 (1) ◽  
pp. 80-87 ◽  
Author(s):  
A. S. Alsuwaiyan ◽  
Steven W. Shaw
Keyword(s):  
Steady State ◽  
Torsional Vibration ◽  
Equations Of Motion ◽  
Vibration Absorbers ◽  
Fully Nonlinear Equations ◽  
State Response ◽  
Steady State Responses ◽  
Nonlinear Equations Of Motion ◽  
The Mathematical Model ◽  
State Responses

In this paper we consider the steady-state response of a rotor fitted with a system of nearly identical torsional vibration absorbers. The absorbers are of the centrifugal pendulum type, which provide an effective mean of attenuating torsional vibrations of the rotor at a given order. The model considered employs absorbers that are tuned close to the order of the excitation, with an intentional mistuning that is selected by design, and imperfections among the absorbers which arise from manufacturing, wear, and other effects. It is shown that these systems can experience localized responses in which the response amplitude of one or more absorbers can become relatively large as compared to the response of the corresponding system with identical absorbers. The results are based on an exact steady-state analysis of the mathematical model, and they show that the strength of the localization depends on the average level of absorber mistuning (a design parameter), the magnitude of the relative imperfections among the absorbers, and the absorber damping. It is found that the most desirable situation is one in which the relative imperfections are kept as small as possible, and that this becomes more crucial when the levels of mistuning and damping are very small. The results of the analysis are confirmed by simulations of the fully nonlinear equations of motion of the rotor/absorber system. It is concluded that the presence of localization should be accounted for in absorber designs, since its presence makes the absorbers less effective in terms of vibration reduction and, perhaps more significantly, it can drastically reduce their operating range, since such absorbers typically have limited rattle space.

scholarly journals New “Full-Bridge Buck Inverter–DC Motor” System: Steady-State and Dynamic Analysis and Experimental Validation

Electronics ◽  
2019 ◽  
Vol 8 (11) ◽  
pp. 1216 ◽  
Author(s):  
Eduardo Hernández-Márquez ◽  
Carlos Alejandro Avila-Rea ◽  
José Rafael García-Sánchez ◽  
Ramón Silva-Ortigoza ◽  
Magdalena Marciano-Melchor ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Motor System ◽  
Circuit Simulation ◽  
Dc Motor ◽  
Matlab Simulink ◽  
Duty Cycles ◽  
System Variables ◽  
The Mathematical Model ◽  
Steady State Stability

A mathematical model of a new “full-bridge Buck inverter–DC motor” system is developed and experimentally validated. First, using circuit theory and the mathematical model of a DC motor, the dynamic behavior of the system under study is deduced. Later, the steady-state, stability, controllability, and flatness properties of the deduced model are described. The flatness property, associated with the mathematical model, is then exploited so that all system variables and the input can be differentially parameterized in terms of the flat output, which is determined by the angular velocity. Then, when a desired trajectory is proposed for the flat output, the input signal is calculated offline and is introduced into the system. In consequence, the validation of the mathematical model for constant and time-varying duty cycles is possible. Such a validation of this mathematical model is tackled from two directions: (1) by circuit simulation through the SimPowerSystems toolbox of Matlab-Simulink and (2) via a prototype of the system built by using Matlab-Simulink and a DS1104 board. The good similarities between the circuit simulation and the experimental results allow satisfactorily validating the mathematical model.

The Effect of Leakage on Railroad Brake Pipe Steady State Behavior

1988 ◽  
Vol 110 (3) ◽  
pp. 329-335 ◽  
Author(s):  
K. Abdol-Hamid ◽  
D. E. Limbert ◽  
G. A. Chapman
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Transmission Lines ◽  
Computation Time ◽  
State Behavior ◽  
Implicit Finite Difference Scheme ◽  
Inlet Flow Rate ◽  
Model Equations ◽  
The Mathematical Model ◽  
Steady State Behavior

A mathematical model for pneumatic transmission lines containing leakage is developed. This model is used to show the effect of leakage size and distribution on the steady state behavior of the brake pipe on a train brake system. The model equations are solved using the implicit finite difference scheme without neglecting any terms. The model is presented in a nonlinear continuous network form, consisting of N sections. Each of the network sections represents one car and may contain one leakage. A computer program was developed to solve the model equations. This program is capable of simulating a train with cars of various lengths and takes a minimum amount of computation time as compared with previous methods. Through analysis and experimentation, the authors have demonstrated that pressure gradient and inlet flow rate are very sensitive to leakage locations as compared with leakage size. The results, generated by the mathematical model, are compared with the experimental data of two different brake pipe set-ups having different dimensions.

Optimization of Torsional Dynamic Properties of Hydraulic Excavator Slewing Transmission Mechanism

2012 ◽  
Vol 538-541 ◽  
pp. 2536-2542
Author(s):  
Zhao Jun Li ◽  
Yu Ling Zhang ◽  
Tao Mao ◽  
Xu Juan Yang
Keyword(s):  
Mathematical Model ◽  
Torsional Vibration ◽  
Dynamic Properties ◽  
Optimization Theory ◽  
Moment Of Inertia ◽  
Transmission Mechanism ◽  
Hydraulic Excavator ◽  
Vibration Equation ◽  
Working Device ◽  
The Mathematical Model

A hydraulic excavator is taken as the object to study. Considering the characteristics of slewing transmission mechanism of hydraulic excavator, the torsional vibration equation is established by the finite element method. According to the torsional vibration equation, the effects of the equivalent moment of inertia of working device on the torsional dynamic properties of slewing transmission mechanism are analyzed. Using the optimization theory, the mathematical model is built, which is by means of the equivalent moment of inertia of working device as objective function and by means of the position parameters of the working device as design variables. Based on the mathematical model, the optimization of torsional dynamic properties of slewing transmission mechanism is studied. Finally, a numerical example is presented.

scholarly journals Mass transfer during electrodeposition of metals at a periodically changing rate

1999 ◽  
Vol 64 (5-6) ◽  
pp. 317-340 ◽  
Author(s):  
Miodrag Maksimovic ◽  
Konstantin Popov
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Steady State ◽  
Layer 4 ◽  
Millisecond Range ◽  
The Mathematical Model ◽  
Pulsating Current ◽  
Pulsating Overpotential ◽  
Changing Rate ◽  
Electrodeposition Of Metals

1. Introduction 2. Mass transfer in the steady state periodic condition 2.1. Reversing current 2.2. Pulsating current 2.3. Alternating current superimposed on direct current 3. The influence of the charge and discharge of the electrical double layer 4. The validity of the mathematical model 4.1. Reversing current in the millisecond range 4.2. Reversing current in the second range 4.3. Pulsating current 4.4. Pulsating overpotential 5. Conclusion

scholarly journals On the global attractors in one mathematical model of antiviral immunity

2020 ◽  
Author(s):  
Alexei Tsygvintsev
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Immune System ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Antiviral Immunity ◽  
Global Attractors ◽  
Viral Pathogens ◽  
Basic Reproductive Ratio ◽  
The Mathematical Model

AbstractWe consider the mathematical model introduced by Batholdy et al. [1] describing the interaction between viral pathogens and immune system. We prove the global asymptotic stability of the infection steady-state if the basic reproductive ratio R0 is greater than unity. That solves the conjecture announced in [7].

Sign in / Sign up

Export Citation Format

Share Document