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 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.

Nonlinear Marine Structures With Random Excitation

1988 ◽  
Vol 110 (3) ◽  
pp. 246-253 ◽  
Author(s):  
E. R. Jefferys
Keyword(s):  
Narrow Band ◽  
Equations Of Motion ◽  
Random Excitation ◽  
Wave Excitation ◽  
Offshore Structure ◽  
Chaotic Motions ◽  
Varying Coefficients ◽  
Excitation Time ◽  
Vessel Response ◽  
Time Varying Coefficients

Various important types of offshore structure contain significant nonlinearities or time-varying coefficients in their equations of motion. Well-known examples include tension leg platforms, free-hanging risers, single-buoy moorings, ships moored against fenders and vessels constrained by stiffening moorings. When subject to sinusoidal wave excitation, time domain mathematical models of these structures can display large subharmonic or chaotic motions. This paper shows that such behavior is often an artifact of the regularity of the excitation and is usually unlikely to present a significant problem in a random sea. Narrow-band vessel response can, however, generate near-harmonic motions to create conditions in which these instabilities may become important.

A Smooth Multimode Waveform Command Shaping Considering the Effect of Hoisting

2016 ◽  
Author(s):  
Khaled A. Alhazza
Keyword(s):  
Equations Of Motion ◽  
Optimization Technique ◽  
Large Body ◽  
Single Mode ◽  
Input Shaping ◽  
Double Pendulum ◽  
Scaled Model ◽  
Command Shaping ◽  
Varying Coefficients ◽  
Time Varying Coefficients

Input shaping and command shaping control techniques are the subject of large body of research in the past several decades. Most of the research is dedicated to time invariant single-mode systems. For a double pendulum hoisting system, hoisting results in a complex system of equations of motion. For rest-to-rest maneuvers, it is a common practice in research to split maneuvers into three consecutive independent stages; hoisting up the payload from an initial position, moving it horizontally, and finally lowering it to a final location. Input shaping is used is the horizontal travel motion stage to eliminate inertia excited vibrations. Although, this approach is effective, significant time penalties are involved due to the split motion approach. Further, traditional input shaping techniques involve significant jerks in the motion commands. To overcome these drawbacks, a new smooth waveform command shaping technique is proposed to enable concurrent hoisting and travel actions. The equations of motion including time varying coefficients are derived and used to determine the coefficients of an optimum waveform shaped command profile. Genetic algorithm optimization technique is used to find the optimal values of the command parameters. The initial values of these parameters are determined assuming a constant cable length. The effectiveness of the shaped command is demonstrated through numerical simulations and experiments on a scaled model of double pendulum using different maneuvers involving simultaneous travel and linear hoisting.

Approximate Response of Beam-Type Resonant Biosensors

2018 ◽  
Author(s):  
Pezhman A. Hassanpour
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Exponential Function ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Impact Force ◽  
Equations Of Motion ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
The Impact

In this paper, the effect of absorption of antigens to the functionalized surface of a biosensor is modeled using a single degree-of-freedom mass-spring-damper system. The change in the mass of the system due to absorption is modeled with an exponential function. The governing equations of motion is derived considering the change in the mass of the system as well as the impact force due to absorption. It has been demonstrated that this equation is a linear second-order ordinary differential equation with time-varying coefficients. The solution of this differential equation is approximated by expanding the exponential function with a Taylor series and applying the method of multiple scales. The advantage of using the method of multiple scales to derive an approximate solution is in the insight it provides on the effect of each parameter on the response of the system. The free vibration response of the biosensor is derived using the approximate solution under different conditions, namely, with and without viscous damping, with and without considering the impact force, and for different binding rates.

Separated-Form Equations of Motion of Controlled Flexible Multibody Systems

1994 ◽  
Vol 116 (4) ◽  
pp. 702-712 ◽  
Author(s):  
Junghsen Lieh
Keyword(s):  
Multibody Systems ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Second Order ◽  
Active Suspensions ◽  
Physical Term ◽  
Moving Base ◽  
Matrix Expansion ◽  
Generalized Force ◽  
Coordinate Partitioning

This paper introduces a method leading to separated-form formulation of dynamic equations of multibody systems subject to control. The algorithm is derived from the virtual work principle and includes the moving base effects. The elastic members are treated as Euler-Bernoulli beams. Equations of motion are expanded using generalized coordinate partitioning and a Jacobian matrix expansion. The formulation of each physical term is separated, i.e., the inertia matrix, nonlinear coupling vector, generalized force vector and base motion-induced terms are established individually. The formulation is implemented on a workstation using MAPLE. Nonlinear and linearized equations with control are generated in FORTRAN format. The control design adopts second-order models directly. Several examples including a spin-up cantilever beam, an elastic vehicle with active suspensions and an elastic slider-crank mechanism are given. Numerical results for nonlinear and linear spin-up beam models are provided. Simulation for the active vehicle model using second-order control theory is presented.

The Specification of Unknown Force within Dynamic Analysis of Slider Crank Mechanism by Three Various Access

2014 ◽  
Vol 1016 ◽  
pp. 239-243 ◽  
Author(s):  
Katarina Monkova ◽  
Andrea Cizikova ◽  
Peter Monka
Keyword(s):  
Analytical Solution ◽  
Dynamic Analysis ◽  
Virtual Work ◽  
Final Decision ◽  
Graphical Solution ◽  
Principle Of Superposition ◽  
Basic Principles ◽  
Computer Aid ◽  
Advantages And Disadvantages ◽  
Crank Mechanism

The article deals with the specification of unknown force within dynamic analysis of slider crank mechanism by three various access. The method of virtual work was used at the analytical solution; the principle of superposition was used at the graphical solution and the software PTC Creo was used at the solution with computer aid. All three types of the solution have their self-advantages and disadvantages. The final decision, which of methods should be selected for the solution, depends on required result precision and on the abilities of investigator. In all cases, however, it is necessary to know the basic principles of mechanics.

scholarly journals The VIT Transform Approach to Discrete-Time Signals and Linear Time-Varying Systems

Eng ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 99-125
Author(s):  
Edward W. Kamen
Keyword(s):  
Discrete Time ◽  
Initial Conditions ◽  
Linear Time ◽  
Order Term ◽  
Initial Time ◽  
Time Varying ◽  
Varying Coefficients ◽  
Time Signals ◽  
Time Varying Systems ◽  
Time Varying Coefficients

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z−1, which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z−i by time functions, which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of zi at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

scholarly journals Estimating latent group structure in time-varying coefficient panel data models

2019 ◽  
Author(s):  
Jia Chen
Keyword(s):  
Panel Data ◽  
Data Models ◽  
Panel Data Models ◽  
Time Varying ◽  
Clustering Method ◽  
Varying Coefficient ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
Latent Group ◽  
Group Structures

Summary This paper studies the estimation of latent group structures in heterogeneous time-varying coefficient panel data models. While allowing the coefficient functions to vary over cross-sections provides a good way to model cross-sectional heterogeneity, it reduces the degree of freedom and leads to poor estimation accuracy when the time-series length is short. On the other hand, in a lot of empirical studies, it is not uncommon to find that heterogeneous coefficients exhibit group structures where coefficients belonging to the same group are similar or identical. This paper aims to provide an easy and straightforward approach for estimating the underlying latent groups. This approach is based on the hierarchical agglomerative clustering (HAC) of kernel estimates of the heterogeneous time-varying coefficients when the number of groups is known. We establish the consistency of this clustering method and also propose a generalised information criterion for estimating the number of groups when it is unknown. Simulation studies are carried out to examine the finite-sample properties of the proposed clustering method as well as the post-clustering estimation of the group-specific time-varying coefficients. The simulation results show that our methods give comparable performance to the penalised-sieve-estimation-based classifier-LASSO approach by Su et al. (2018), but are computationally easier. An application to a panel study of economic growth is also provided.

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