First-order optimal linear and nonlinear detuning of centrifugal pendulum vibration absorbers

2015 ◽  
Vol 335 ◽  
pp. 34-54 ◽  
Author(s):  
J. Mayet ◽  
H. Ulbrich
Keyword(s):  
Vibration Absorbers ◽  
First Order ◽  
Centrifugal Pendulum Vibration Absorbers ◽  
Optimal Linear ◽  
Linear And Nonlinear

scholarly journals Lagrangian Representations for Linear and Nonlinear Transport

2017 ◽  
Vol 63 (3) ◽  
pp. 418-436
Author(s):  
Stefano Bianchini ◽  
Paolo Bonicatto ◽  
Elio Marconi
Keyword(s):  
Conservation Laws ◽  
Continuity Equation ◽  
Space Dimension ◽  
Nonlinear Transport ◽  
Scalar Conservation Laws ◽  
First Order ◽  
Entropy Dissipation ◽  
Linear And Nonlinear ◽  
Scalar Conservation ◽  
The One

In this note we present a unifying approach for two classes of first order partial differential equations: we introduce the notion of Lagrangian representation in the settings of continuity equation and scalar conservation laws. This yields, on the one hand, the uniqueness of weak solutions to transport equation driven by a two dimensional BV nearly incompressible vector field. On the other hand, it is proved that the entropy dissipation measure for scalar conservation laws in one space dimension is concentrated on countably many Lipschitz curves.

Design of Pendulum Absorbers for Transverse Vibration Attenuation of Rotating Beams

1997 ◽  
Author(s):  
Yenkai Wang ◽  
Steven W. Shaw ◽  
Chang-Po Chao
Keyword(s):  
Transverse Vibration ◽  
Design Strategy ◽  
Simplified Model ◽  
Vibration Absorbers ◽  
Rotating Beam ◽  
External Excitation ◽  
Rotating Beams ◽  
Transverse Vibrations ◽  
Vibration Attenuation ◽  
Centrifugal Pendulum Vibration Absorbers

Abstract This paper considers the placement, sizing and tuning of centrifugal pendulum vibration absorbers for the reduction of transverse vibrations in rotating beams. A simplified model describing the linearized dynamics of a rotating beam with external excitation and attached absorbers is used for the analysis. A design strategy is offered wherein individual absorbers are designed to reduce vibration amplitudes and stress levels caused by troublesome resonances. It is shown that this procedure offers significant reduction in vibratory stresses, even in the case of excitations composed of multiple harmonics.

Performance of a Non Linear Dynamic Vibration Absorbers

2014 ◽  
Vol 31 (3) ◽  
pp. 345-353 ◽  
Author(s):  
F. Djemal ◽  
F. Chaari ◽  
J.-L. Dion ◽  
F. Renaud ◽  
I. Tawfiq ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Wide Band ◽  
Experimental Investigations ◽  
Vibration Absorbers ◽  
Dynamic Phenomenon ◽  
Jump Phenomenon ◽  
Cubic Nonlinearity ◽  
Linear Dynamic ◽  
Dynamic Vibration Absorbers ◽  
Linear And Nonlinear

AbstractThe most common method of vibration control is the use of the dynamic absorbers. Two types of absorbers can be found: Linear and nonlinear. The use of linear absorbers allows reducing vibration but only at the resonance frequency, whereas nonlinear absorbers attenuate vibration on a wide band of frequency. In this paper, a nonlinear two degrees of freedom (DOF) model is developed. A cubic nonlinearity induced by a gap is considered. The objective of the paper is to characterize nonlinear vibration of the system by applying explicit formulation (EF). An experimental study is performed to validate the numerical results. The jump phenomenon is the principal nonlinear dynamic phenomenon observed on both numerical and experimental investigations.

Energy-Based Approach for Controller Design of Overhead Cranes: A Comparative Study

2013 ◽  
Vol 365-366 ◽  
pp. 784-787 ◽  
Author(s):  
Nguyen Quang Hoang ◽  
Soon Geul Lee
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Asymptotically Stable ◽  
Overhead Crane ◽  
Overhead Cranes ◽  
Swing Angle ◽  
Optimal Linear ◽  
Linear And Nonlinear ◽  
Invariance Theorem ◽  
Lyapunov Technique

In this paper, five controllers including linear and nonlinear ones for an underactuated overhead crane are derived based on the passivity of the system. The total energy of the system and its square are used in Lyapunov candidate function to design controllers. The equilibrium point of the closed loop is proven to be asymptotically stable by the Lyapunov technique and LaSalle invariance theorem. In addition, the optimal linear controller is also combined to force the swing angle to converge fast to zero by reaching destination of the trolley. Numerical simulations are carried out to evaluate the controllers.

scholarly journals Lie symmetry analysis for the solution of first-order linear and nonlinear fractional differential equations

2018 ◽  
Vol 7 (2) ◽  
pp. 37 ◽  
Author(s):  
Mousa Ilie ◽  
Jafar Biazar ◽  
Zainab Ayati
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lie Symmetry ◽  
Order Linear ◽  
Nonlinear Fractional Differential Equations ◽  
First Order ◽  
Fractional Equations ◽  
Fractional Differential ◽  
Linear And Nonlinear ◽  
Fractional Equation

Obtaining analytical or numerical solution of fractional differential equations is one of the troublesome and challenging issues among mathematicians and engineers, specifically in recent years. The purpose of this paper is to solve linear and nonlinear fractional differential equations such as first order linear fractional equation, Bernoulli, and Riccati fractional equations by using Lie Symmetry method, based on conformable fractional derivative. For each equation, some numerical examples are presented to illustrate the proposed approach.  

An Efficient Numerical Simulation for Solving Dynamical Systems With Uncertainty

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
Ali Ahmadian ◽  
Soheil Salahshour ◽  
Chee Seng Chan ◽  
Dumitur Baleanu
Keyword(s):  
Dynamical Systems ◽  
Stability And Convergence ◽  
Uncertain Parameters ◽  
Crucial Issue ◽  
Computational Costs ◽  
First Order ◽  
Wide Range ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Fuzzy Dynamical Systems

In a wide range of real-world physical and dynamical systems, precise defining of the uncertain parameters in their mathematical models is a crucial issue. It is well known that the usage of fuzzy differential equations (FDEs) is a way to exhibit these possibilistic uncertainties. In this research, a fast and accurate type of Runge–Kutta (RK) methods is generalized that are for solving first-order fuzzy dynamical systems. An interesting feature of the structure of this technique is that the data from previous steps are exploited that reduce substantially the computational costs. The major novelty of this research is that we provide the conditions of the stability and convergence of the method in the fuzzy area, which significantly completes the previous findings in the literature. The experimental results demonstrate the robustness of our technique by solving linear and nonlinear uncertain dynamical systems.

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