Dynamic Stability Analysis of Viscoelastic Beam under the Follower Forces

2011 ◽  
Vol 413 ◽  
pp. 283-288
Author(s):  
Rui Hua Zhuo ◽  
Shu Wang Yan ◽  
Lei Yu Zhang
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Stability Analysis ◽  
Power Series ◽  
Dynamic Stability ◽  
Vibration Frequency ◽  
Time Domain ◽  
Differential Operators ◽  
Viscoelastic Beam ◽  
Follower Forces

The unification differential equation of buckling and motion of viscoelastic beam subjected to the uniformly distributed follower forces in time domain was established by differential operators including extension viscosity, shearing viscosity and moment of inertia. According to the unification differential equation, dynamic stability of three-parameter model of viscoelastic beams subjected to follower forces with clamped-free supported boundary condition was firstly analyzed by power series. The relations of the follower force versus vibration frequency and decay coefficient were obtained, so was the effect of viscous coefficient on the critical load of beams.

scholarly journals Implicit Subspace Iteration to Improve the Stability Analysis in Grinding Processes

2020 ◽  
Vol 10 (22) ◽  
pp. 8203 ◽  
Author(s):  
Jorge Alvarez ◽  
Mikel Zatarain ◽  
David Barrenetxea ◽  
Jose Ignacio Marquinez ◽  
Borja Izquierdo
Keyword(s):  
Stability Analysis ◽  
Dynamic Stability ◽  
Time Domain ◽  
Grinding Processes ◽  
Subspace Iteration ◽  
Efficient Calculation ◽  
Chatter Vibrations ◽  
Stability Maps ◽  
Iteration Methods ◽  
The Stability

An alternative method is devised for calculating dynamic stability maps in cylindrical and centerless infeed grinding processes. The method is based on the application of the Floquet theorem by repeated time integrations. Without the need of building the transition matrix, this is the most efficient calculation in terms of computation effort compared to previously presented time-domain stability analysis methods (semi-discretization or time-domain simulations). In the analyzed cases, subspace iteration has been up to 130 times faster. One of the advantages of these time-domain methods to the detriment of frequency domain ones is that they can analyze the stability of regenerative chatter with the application of variable workpiece speed, a well-known technique to avoid chatter vibrations in grinding processes so the optimal combination of amplitude and frequency can be selected. Subspace iteration methods also deal with this analysis, providing an efficient solution between 27 and 47 times faster than the abovementioned methods. Validation of this method has been carried out by comparing its accuracy with previous published methods such as semi-discretization, frequency and time-domain simulations, obtaining good correlation in the results of the dynamic stability maps and the instability reduction ratio maps due to the application of variable speed.

Numerical Analysis of Dynamic Stability of Elastic Truss Structures

1998 ◽  
Vol 13 (2) ◽  
pp. 75-81 ◽  
Author(s):  
Qi-Lin Zhang ◽  
Udo Peil
Keyword(s):  
Stability Analysis ◽  
Numerical Analysis ◽  
Dynamic Stability ◽  
Time Domain ◽  
Truss Structures ◽  
Equilibrium Equations ◽  
Numerical Examples ◽  
Motion Trajectories ◽  
Dynamic Excitations ◽  
Energy Increment

In this paper the concept of energy increment map is presented for stability judgement of elastic truss structures under arbitrary dynamic excitations. The modified member theory is adopted to establish the equilibrium equations of the structures. The motion trajectories of structures are numerically solved in time domain and the corresponding stability states are studied according to the energy increment map. Numerical examples show that the method of this paper can lead to satisfactory results in dynamic stability analysis of elastic truss structures.

scholarly journals Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Jamilu Abubakar ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

scholarly journals Frequency-Dependent FDTD Algorithm Using Newmark’s Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Bing Wei ◽  
Le Cao ◽  
Fei Wang ◽  
Qian Yang
Keyword(s):  
Differential Equation ◽  
Electric Field ◽  
Field Intensity ◽  
Time Domain ◽  
Difference Method ◽  
Electric Field Intensity ◽  
Polarization Vector ◽  
Solution Stability ◽  
Central Difference ◽  
Central Difference Method

According to the characteristics of the polarizability in frequency domain of three common models of dispersive media, the relation between the polarization vector and electric field intensity is converted into a time domain differential equation of second order with the polarization vector by using the conversion from frequency to time domain. Newmarkβγdifference method is employed to solve this equation. The electric field intensity to polarizability recursion is derived, and the electric flux to electric field intensity recursion is obtained by constitutive relation. Then FDTD iterative computation in time domain of electric and magnetic field components in dispersive medium is completed. By analyzing the solution stability of the above differential equation using central difference method, it is proved that this method has more advantages in the selection of time step. Theoretical analyses and numerical results demonstrate that this method is a general algorithm and it has advantages of higher accuracy and stability over the algorithms based on central difference method.

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