scholarly journals Nonlinear Dynamical Analysis on Four Semi-Active Dynamic Vibration Absorbers with Time Delay

2013 ◽  
Vol 20 (4) ◽  
pp. 649-663 ◽  
Author(s):  
Yongjun Shen ◽  
Mehdi Ahmadian
Keyword(s):  
Time Delay ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Dynamical Analysis ◽  
Control Procedure ◽  
Vibration Absorbers ◽  
Nonlinear Dynamical ◽  
Dynamic Vibration ◽  
Approximate Analytical Solutions ◽  
Dynamic Vibration Absorbers

In this paper four semi-active dynamic vibration absorbers (DVAs) are analytically studied, where the time delay induced by measurement and execution in control procedure is included in the system. The first-order approximate analytical solutions of the four semi-active DVAs are established by the averaging method, based on the illustrated phase difference of the motion parameters. The comparisons between the analytical and the numerical solutions are carried out, which verify the correctness and satisfactory precision of the approximate analytical solutions. Then the effects of the time delay on the dynamical responses are analyzed, and it is found that the stability conditions for the steady-state responses of the primary systems are all periodic functions of time delay, with the same period as the excitation one. At last the effects of time delay on control performance are discussed.

Analytical Solutions of a First-Order Quadratic Nonlinear System With Parametrical and Periodical Excitation

2016 ◽  
Author(s):  
Guopeng Zhou ◽  
Albert C. J. Luo ◽  
Naiding Zhou ◽  
Feng Liang
Keyword(s):  
Dynamical System ◽  
Analytical Solutions ◽  
Harmonic Balance ◽  
Numerical Solutions ◽  
Excitation Frequency ◽  
Nonlinear Dynamical System ◽  
Harmonic Balance Method ◽  
Nonlinear Dynamical ◽  
Approximate Analytical Solutions ◽  
Generalized Harmonic Balance Method

In this paper, a quadratic nonlinear dynamical system with two periodic excitation forces is discussed. Analytical period-1 motions of such dynamical system are obtained by using generalized harmonic balance method. Stability analysis is carried out via eigenvalues analysis. To verify approximate analytical solutions, numerical simulations are completed to compare analytic and numerical solutions of the dynamical system, the approximate precision is guaranteed with appropriate harmonic balance terms. More harmonic terms should be employed to guarantee good approximation of periodic motions if excitation frequency is small. Furthermore, infinite harmonic balance terms must be introduced for chaotic systems.

Structural Optimization of Cantilever Mechanical Elements

1986 ◽  
Vol 108 (4) ◽  
pp. 427-433 ◽  
Author(s):  
Eugene I. Rivin
Keyword(s):  
Structural Optimization ◽  
Natural Frequencies ◽  
Superior Performance ◽  
Vibration Absorbers ◽  
Stability Margins ◽  
Dynamic Vibration ◽  
Robot Arms ◽  
Limited Effectiveness ◽  
Mass Ratios ◽  
Dynamic Vibration Absorbers

Naturally limited stiffness of cantilever elements due to lack of constraint from other structural components, together with low structural damping, causes intensive and slow-decaying transient vibrations as well as low stability margins for self-excited vibrations. In cases of dimensional limitations (e.g., boring bars), such common antivibration means as dynamic vibration absorbers have limited effectiveness due to low mass ratios. This paper describes novel concepts of structural optimization of cantilever components by using combinations of rigid and light materials for their design. Two examples are given: tool holders (boring bars) and robot arms. Optimized boring bars demonstrate substantially increased natural frequencies, together with the possibility of greatly enhanced mass ratios for dynamic vibration absorbers. Machining tests with combination boring bars have been performed in comparison with conventional boring bars showing superior performance of the former. Computer optimization of combination-type robot arms has shown a potential of 10–60 percent reduction in tip-of-arm deflection, together with a commensurate reduction of driving torque for a given acceleration, and a higher natural frequencies (i.e., shorter transients). Optimization has been performed for various ratios of bending and joint compliance and various payloads.

Dynamic Vibration Absorber Optimal Design With Emphasis on Complete Machine Dynamics Modelling

2008 ◽  
Author(s):  
Bohdan M. Diveyev ◽  
Zinovij A. Stotsko
Keyword(s):  
Optimal Design ◽  
Vibration Absorber ◽  
Vibration Absorbers ◽  
Rotating Machines ◽  
Dynamic Vibration Absorber ◽  
New Methods ◽  
Dynamic Vibration ◽  
Methods Development ◽  
Dynamic Vibration Absorbers ◽  
Dynamics Modelling

The main aim of this paper is improved dynamic vibration absorbers design with taking into account complex rotating machines dynamic The is considered for the complex vibroexitated constructions. Methods of decomposition and the numerical schemes synthesis are considered on the basis of new methods of modal methods. Development of of complicated machines and buildings in view of their interaction with system of dynamic vibration absorbers is under discussion.

scholarly journals Perturbation Solutions For Magnetohydrodynamics (Mhd) Flow of in a Non-Newtonian Fluid Between Concentric Cylinders

2019 ◽  
Vol 24 (1) ◽  
pp. 199-211
Author(s):  
M. Yürüsoy ◽  
Ö.F. Güler
Keyword(s):  
Analytical Solutions ◽  
Numerical Solutions ◽  
Variable Viscosity ◽  
Perturbation Technique ◽  
Equations Of Motion ◽  
Mhd Flow ◽  
Model Space ◽  
Viscosity Model ◽  
Concentric Cylinders ◽  
Approximate Analytical Solutions

Abstract The steady-state magnetohydrodynamics (MHD) flow of a third-grade fluid with a variable viscosity parameter between concentric cylinders (annular pipe) with heat transfer is examined. The temperature of annular pipes is assumed to be higher than the temperature of the fluid. Three types of viscosity models were used, i.e., the constant viscosity model, space dependent viscosity model and the Reynolds viscosity model which is dependent on temperature in an exponential manner. Approximate analytical solutions are presented by using the perturbation technique. The variation of velocity and temperature profile in the fluid is analytically calculated. In addition, equations of motion are solved numerically. The numerical solutions obtained are compared with analytical solutions. Thus, the validity intervals of the analytical solutions are determined.

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