Dynamic Characteristics Analysis of Flexible Mechanism Using Three Parameters Damping Model

Volume 2 ◽  
2004 ◽  
Author(s):  
Hongzhao Liu ◽  
Baixi Liu ◽  
Daning Yuan
Keyword(s):  
Differential Equations ◽  
Dynamic Characteristics ◽  
Virtual Work ◽  
Dynamic Equations ◽  
Linkage Mechanism ◽  
Varying Coefficients ◽  
Characteristics Analysis ◽  
Time Varying Coefficients ◽  
Stiffness And Damping ◽  
Damping Model

In this paper, a practical structural damping model for the dynamic analysis of damping alloy is presented. The differential equations of the beam element with three parameters representing stiffness and damping characteristics are deduced through the three parameters constitution and the virtual work principle. By means of the Kineto-Elastodynamic theory, the established element dynamic equations are assembled into the system dynamic equations of flexible linkage mechanism. In order to solve the high order differential equations with time-varying coefficients, a closed form numerical algorithm is constructed. Lastly, an example of a four-bar elastic linkage mechanism is given to show the effectiveness of the proposed method in studying dynamic characteristics of structure containing damping alloy components.

Five Parameters Structural Damping Constitution and Its Application

Volume 2 ◽  
2004 ◽  
Author(s):  
Baixi Liu ◽  
Hongzhao Liu ◽  
Daning Yuan
Keyword(s):  
Finite Element ◽  
Differential Equations ◽  
Dynamic Equations ◽  
State Space Method ◽  
Structural Damping ◽  
Linkage Mechanism ◽  
Experiment Data ◽  
Viscoelastic Theory ◽  
Damping Model ◽  
Space Method

In this paper, the five parameters model of viscoelastic theory is introduced as the constitutive equation for damping alloy. Based on the experiment data, the five parameters are fitted by using an optimization algorithm. The finite element dynamic equations are derived through the established five parameters constitution. For the convenience of the computation, the established dynamic equations containing convolution integration are changed into ordinary differential equations. By means of the Kineto-Elastodynamic theory, the system dynamic equation of elastic linkage mechanism is gained. In order to solve the high order differential equations, the state space method is employed. An example is given to show that the model proposed in this paper is more accurate and stable than the three parameters damping model.

Modeling and Dynamic Analysis of a Slider-Crank Mechanism With Flexible Coupler and Joint

1991 ◽  
Author(s):  
Junghsen Lieh ◽  
Imtiaz Haque
Keyword(s):  
Dynamic Analysis ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Joint Stiffness ◽  
Mechanism Model ◽  
Double Frequency ◽  
Varying Coefficients ◽  
Matrix Expansion ◽  
Time Varying Coefficients ◽  
Crank Mechanism

Abstract Modeling and dynamic analysis of a slider-crank mechanism with flexible joint and coupler is presented. The equations of motion of the mechanism model are formulated using a virtual work multibody formalism and cast in terms of a minimum set of generalized coordinates through a Jacobian matrix expansion. Numerical results show the influence of time-varying coefficients on the mechanism dynamic behavior due to a repeated task. The results illustrate that the joint motion and coupler deformation are highly coupled. The joint response is dominated by double frequency of input, however, the coupler deformation is influenced by the same frequency as that of excitation. Increase in joint stiffness tends to decrease the variations in coupler deformation.

Dynamic Characteristics Analysis for Seismic Vibrator

2014 ◽  
Vol 472 ◽  
pp. 48-55
Author(s):  
Li Qiang An ◽  
Fan Peng Kong ◽  
Yong Fang Wang
Keyword(s):  
Modal Analysis ◽  
Dynamic Characteristics ◽  
Data Transfer ◽  
Element Model ◽  
Dynamics Simulation ◽  
Characteristic Analysis ◽  
Characteristics Analysis ◽  
Stiffness And Damping ◽  
Multi Body ◽  
Seismic Vibrator

Seismic vibrator is one of the most widely used equipments in exploration field. In recent years, with the development of exploration field, as well as the growing needs of high quality seismic data, the seismic vibrator's tonnage has increased a lot, which makes the stress of the vehicle frame very complicated in working state. And some local structure of the vehicle frame often appears crack phenomenon in working state. Therefore, the dynamic characteristic analysis is essential to the Seismic vibrator. In this paper, the finite element model of vehicle frame is established by ANSYS software. Through the modal analysis, the natural frequencies are obtained, and each vibration modes are analyzed. On the basis of the modal analysis, the modal neutral file of the vehicle frame is established. Using the data transfer function between ANSYS and ADAMS, the rigid-flexible coupling multi-body model is built for the dynamics simulation of the seismic vibrator. In this model, the stiffness and damping of air springs, hydraulic oil and soil are simulated by the spring-damper in the ADAMS software. The dynamic characteristics of vehicle frame under excited forces with different amplitude are obtained and analyzed. The stresses for some of the hot spots of the vehicle frame are extracted, which can be used to analyze the dynamic failure of the vehicle frame.

scholarly journals Fractional Relaxation and Fractional Oscillation Models Involving Erdélyi-Kober Integrals

2015 ◽  
Vol 18 (5) ◽  
Author(s):  
Moreno Concezzi ◽  
Roberto Garra ◽  
Renato Spigler
Keyword(s):  
Differential Equations ◽  
Numerical Approach ◽  
Numerical Results ◽  
Cauchy Type ◽  
Time Varying ◽  
Varying Coefficients ◽  
Fractional Relaxation ◽  
Time Varying Coefficients ◽  
Damped Oscillator

AbstractWe consider fractional relaxation and fractional oscillation equations involving Erdélyi-Kober integrals. In terms of the Riemann-Liouville integrals, the equations we analyze can be understood as equations with time-varying coefficients. Replacing the Riemann-Liouville integrals with Erdélyi-Kober-type integrals in certain fractional oscillation models, we obtain some more general integro-differential equations. The corresponding Cauchy-type problems can be solved numerically, and, in some cases analytically, in terms of the Saigo-Kilbas Mittag-Leffler functions. The numerical results are obtained by a treatment similar to that developed by K. Diethelm and N.J. Ford to solve the Bagley-Torvik equation. Novel results about the numerical approach to the fractional damped oscillator equation with time-varying coefficients are also presented.

scholarly journals Stability with general decay rate of hybrid neutral stochastic pantograph differential equations driven by Lévy noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Tian Zhang ◽  
Chuanhou Gao
Keyword(s):  
Differential Equations ◽  
Decay Rate ◽  
Broad Class ◽  
General Decay ◽  
Polynomial Decay ◽  
Almost Sure Stability ◽  
General Decay Rate ◽  
Varying Coefficients ◽  
Highly Nonlinear ◽  
Time Varying Coefficients

<p style='text-indent:20px;'>This paper focuses on the <inline-formula><tex-math id="M2">\begin{document}$ p $\end{document}</tex-math></inline-formula>th moment and almost sure stability with general decay rate (including exponential decay, polynomial decay, and logarithmic decay) of highly nonlinear hybrid neutral stochastic pantograph differential equations driven by L<inline-formula><tex-math id="M3">\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula>vy noise (NSPDEs-LN). The crucial techniques used are the Lyapunov functions and the nonnegative semi-martingale convergence theorem. Simultaneously, the diffusion operators are permitted to be controlled by several additional functions with time-varying coefficients, which can be applied to a broad class of the non-autonomous hybrid NSPDEs-LN with highly nonlinear coefficients. Besides, <inline-formula><tex-math id="M4">\begin{document}$ H_\infty $\end{document}</tex-math></inline-formula> stability and the almost sure asymptotic stability are also concerned. Finally, two examples are offered to illustrate the validity of the obtained theory.</p>

Computing Numerical Solutions of Delayed Fractional Differential Equations With Time Varying Coefficients

2014 ◽  
Vol 10 (1) ◽  
Author(s):  
Venkatesh Suresh Deshmukh
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Metal Cutting ◽  
Numerical Solutions ◽  
Viscoelastic Damping ◽  
Time Varying ◽  
Varying Coefficients ◽  
Fractional Differential ◽  
Time Varying Coefficients ◽  
Cutting Processes

Fractional differential equations with time varying coefficients and delay are encountered in the analysis of models of metal cutting processes such as milling and drilling with viscoelastic damping elements. Viscoelastic damping is modeled as a fractional derivative. In the present paper, delayed fractional differential equations with bounded time varying coefficients in four different forms are analyzed using series solution and Chebyshev spectral collocation. A fractional differential equation with a known exact solution is then solved by the methodology presented in the paper. The agreement between the two is found to be excellent in terms of point-wise error in the trajectories. Solutions to the described fractional differential equations are computed next in state space and second order forms.

Solutions of Delayed Partial Differential Equations With Space-Time Varying Coefficients

2011 ◽  
Vol 7 (2) ◽  
Author(s):  
Venkatesh Deshmukh
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Initial Boundary ◽  
Time Varying ◽  
Initial Boundary Value Problems ◽  
Weakly Nonlinear ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
Initial Boundary Value

A constructive algorithm using Chebyshev spectral collocation is proposed for computing trustworthy approximate solutions of linear and weakly nonlinear delayed partial differential equations or initial boundary value problems, with continuous and bounded coefficients. The boundary conditions are assumed to be Dirichlet. The solution of linear problems is obtained at Chebyshev grid points in space and a given interval of time. The algorithm is then extended to systems with weak nonlinearities using perturbation series, which yields nonhomogeneous initial boundary value problems without delay. The proposed methodology is illustrated using examples of linear and weakly nonlinear heat and wave equations with bounded continuous space-time varying coefficients.

Dynamics of Nonautonomous Ordinary Differential Equations with Quasi-Periodic Coefficients

2017 ◽  
Vol 27 (06) ◽  
pp. 1750092 ◽  
Author(s):  
Xu Zhang
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Vector Fields ◽  
Nonlinear Term ◽  
Time Varying ◽  
Periodic Functions ◽  
Periodic Coefficients ◽  
Varying Coefficients ◽  
Nonautonomous Systems ◽  
Time Varying Coefficients

We investigate the dynamics of two types of nonautonomous ordinary differential equations with quasi-periodic time-varying coefficients and nonlinear terms. The vector fields for the nonautonomous systems are written as [Formula: see text], [Formula: see text], where [Formula: see text] is the spacial part and [Formula: see text] is the time-varying part, and [Formula: see text] and [Formula: see text] are real parameters. The first type has a polynomial as the nonlinear term, another type has a continuous periodic function as the nonlinear term. The polynomials and periodic functions have simple zeros. Several examples with numerical experiments are given. It is found by numerical calculation that there might exist only one attractor for the systems with polynomials as nonlinear terms and [Formula: see text], and there might exist infinitely many attractors for systems with periodic functions as nonlinear terms and [Formula: see text]. For [Formula: see text] sufficiently small, the parameter regions for [Formula: see text] are roughly divided into three parts: the spacial region ([Formula: see text]), the balance region ([Formula: see text]), and the time-varying region ([Formula: see text]); (i) for [Formula: see text], the orbits approach some planes depending on the zeros of the polynomials or the periodic functions; (ii) for [Formula: see text], there exist attractors with the number no less than the number of zeros of the polynomials or the periodic functions, implying the existence of infinitely many attractors for systems with periodic functions as nonlinear terms; (iii) for [Formula: see text], the orbits wind around some region depending on the choice of the initial position. The shape of the attractors might be strange or regular for different parameters, and we obtain the existence of ball-like (regular) attractors, two-wings (strange) attractors, and other attractors with different shapes. The Lyapunov exponents are negative. These results reveal an intrinsic relationship between the existence of attractors (or strange dynamics) and the parameters [Formula: see text] and [Formula: see text] for nonautonomous systems with quasi-periodic coefficients. These results will be very useful in the understanding of the dynamics of general nonautonomous systems, nonautonomous control theory and other related fields.

Linear Time-Varying Dynamic Systems Optimization via Higher-Order Method Using Shifted Chebyshev’s Polynomials

1999 ◽  
Vol 121 (2) ◽  
pp. 258-261 ◽  
Author(s):  
Xiaochun Xu ◽  
Sunil K. Agrawal
Keyword(s):  
Differential Equations ◽  
Dynamic Systems ◽  
Linear Time ◽  
Optimal Solution ◽  
Higher Order ◽  
Time Varying ◽  
Varying Coefficients ◽  
Higher Order Method ◽  
Time Varying Coefficients ◽  
Higher Order Differential Equations

For optimization of classes of linear time-varying dynamic systems with n states and m control inputs, a new higher-order procedure was presented by the authors that does not use Lagrange multipliers. In this new procedure, the optimal solution was shown to satisfy m 2p-order differential equations with time-varying coefficients. These differential equations were solved using weighted residual methods. Even though solution of the optimization problem using this procedure was demonstrated to be computation efficient, shifted Chebyshev’s polynomials are used in the paper to solve the higher-order differential equations. This further reduces the computations and makes this algorithm more appropriate for real-time implementation.

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