An open-loop control scheme for minimization of residual vibrations of a flexible robot

The aim of this study is to develop a practical control scheme, called the three-step input method, whereby a flexible robot arm is moved from one position to another with a minimum of residual vibration when the arm reaches its defined endpoint. This work is concerned with defining a simple practical method to utilize step inputs to achieve optimum response. The optimum response is achieved by using a self-adjusting input command function that is obtained during real-time processing. The practicality of this control scheme is demonstrated by using an analog computer to simulate a simple flexible robot and conventional servo controller. The experiments focus on point-to-point movement. Also, this method required little computational effort through the intelligent use of conventional servo control technology and the robot's vibration characteristics.     

Interaction between torsional and lateral vibrations in flexible rotor systems with discontinuous friction

In this paper, we analyze the interaction between friction-induced vibrations and self-sustained lateral vibrations caused by a mass-unbalance in an experimental rotor dynamic setup. This study is performed on the level of both numerical and experimental bifurcation analyses. Numerical analyses show that two types of torsional vibrations can appear: friction-induced torsional vibrations and torsional vibrations due to the coupling between torsional and lateral dynamics in the system. Moreover, both the numerical and experimental results show that a higher level of mass-unbalance, which generally increases the lateral vibrations, can have a stabilizing effect on the torsional dynamics, i.e. friction-induced limit cycling can disappear. Both types of analysis provide insight in the fundamental mechanisms causing self-sustained oscillations in rotor systems with flexibility, mass-unbalance and discontinuous friction which support the design of such flexible rotor systems.     

Wave-based control of non-linear flexible mechanical systems

The need to achieve rapid and accurate position control of a system end-point by an actuator working through a flexible system arises frequently, in cases from space structures to disk drive heads, from medical mechanisms to long-arm manipulators, from cranes to special robots. The system’s actuator must then attempt to reconcile two, potentially conflicting, demands: position control and active vibration damping. Somehow each must be achieved while respecting the other’s requirements. Wave-based control is a powerful solution with many advantages over previous techniques. The central idea is to consider the actuator motion as launching mechanical waves into the flexible system while simultaneously absorbing returning waves. This simple, intuitive idea leads to robust, generic, highly efficient, adaptable controllers, allowing rapid and almost vibrationless re-positioning of the remote load (tip mass). This gives a generic, high-performance solution to this important problem that does not depend on an accurate system model or near-ideal actuator behaviour. At first sight wave-based control assumes superposition and therefore linearity. This paper shows that wave-based control is also robust (or can easily be made robust) to non-linear behaviour associated with non-linear elasticity and with large-deflection effects.     

Three-dimensional vibrations of a flexible rod

Institute of Mechanical Engineering of the Soviet Academy of Sciences, Nizhne-Novogorod Branch. Translated from Prikladnaya Mekhanika, Vol. 27, No. 9, pp. 100–106, September, 1991.     

Stabilization of systems with distributed and lumped parameters

Kamsk Polytechnic Institute, Naberezhnye Chelny. Translated from Prikladnaya Mekhanika, Vol. 27, No. 3, pp. 102–208, March, 1991.     

Sensitivity analysis of closed-loop control systems on flexible structures

Local-velocity feedback (LVF) and linear-quadratic Gaussain (LQG) control schemes are implemented on passively tuned reaction mass actuators to control the vibrations of a flexible structure. The structure is lightly damped and possesses closely coupled low-frequency resonant modes. Both LVF and LQG controllers successfully eliminate the structure's vibrations. However, if the passive tuning parameters of the actuators are slightly mistuned, implementing LVF control actually results in an unstable system. On the other hand, LQG control proves to be insensitive to large changes in the passive tuning parameters of the actuators. In fact, the system with LQG control is never unstable, no matter what the actuator's passive tuning parameters are.     

Advances in stability,bifurcations and nonlinear vibrations in mechanical systems

Nonlinear Dynamics -     

Computation of wind-induced vibrations of flexible shells and membranous structures

A partitioned coupling approach for time-dependent fluid–structure interactions is applied to thin shells and membranous structures with large displacements. The frame algorithm connects a three-dimensional, finite volume-based multi-block flow solver for incompressible fluids with a finite element code for geometrically nonlinear structural problems using a commercial coupling interface. Thus a high modularity is achieved and the whole range of opportunities with these two powerful codes — each of them highly adapted to its specific field of application — can be used also for coupled simulations.Two completely different configurations were investigated. First, the coupling algorithm was applied to an academic test configuration consisting of one, two, and three flexible L-shaped plates being loaded by a steady far-field flow. Various investigations were carried out at different Reynolds numbers (Re=50,200, and 500) in order to study phenomena such as vortex shedding, resonance, influence of the interaction between several flexible plates, whereas the second and third plates were placed in the wake of the first.The second part of the paper shows that in principle the coupling procedure can also deal with real-life structures as they occur in civil engineering. A membranous roof of glass-fiber synthetics with a complex shape was exposed to a time-dependent wind gust from diagonally above which was superimposed on a constant basic wind flow parallel to the ground. The structural model contains the pre-stressed textile roof including the taut cables at its circumference which are fastened at the pylons. As a structural response, the wind gust led to a displacement of the textile roof which disappeared again when the gust subsided. With the coupled algorithm proposed in the paper it is possible to study dynamic interactions for engineering applications.     

The phase-lag concept in the thermal behavior of lumped systems

The phase-lag concept in the wave theory of heat conduction is extended to describe the thermal behavior of lumped systems. It is assumed that a phase-lag exists between the convection heat flux from the lumped system and the temperature difference between the lumped system and its surroundings. It is found that the dimensionless delay time τ is an important parameter in specifying the qualitative behavior of the lumped system. The phase-lag concept has no significant effects on the thermal behavior of lumped systems having τ < 1/4. In this case, the classical theory without delay can give an accurate prediction for the system thermal behavior. On the other hand, the phase-lag concept changes the quantitative and qualitative behavior of systems having τ > 1/4 and these changes are enhanced as τ increases. However, it is shown that the thermal behavior of systems having τ > 1/4 violates the second law of thermodynamics. The physical reasoning for this violation is explained. Also, the phase-lag concept is extended to describe the thermal behavior of composite system which consists of two domains each is lumped at different temperature.     

Transversal vibrations of double-plate systems

This paper presents an analytical and numerical analysis of free and forced transversal vibrations of an elastically connected double-plate system. Analytical solutions of a system of coupled partial differential equations, which describe corresponding dynamical free and forced processes, are obtained using Bernoulli’s particular integral and Lagrange’s method of variation constants. It is shown that one-mode vibrations correspond to two-frequency regime for free vibrations induced by initial conditions and to three-frequency regime for forced vibrations induced by one-frequency external excitation and corresponding initial conditions. The analytical solutions show that the elastic connection between plates leads to the appearance of two-frequency regime of time function, which corresponds to one eigenamplitude function of one mode, and also that the time functions of different vibration modes are uncoupled, for each shape of vibrations. It has been proven that for both elastically connected plates, for every pair of m and n, two possibilities for appearance of the resonance dynamical states, as well as for appearance of the dynamical absorption, are present. Using the MathCad program, the corresponding visualizations of the characteristic forms of the plate middle surfaces through time are presented.The English text was polished by Keren Wang.     

Free vibrations of flexible shallow shells of complex shape

A method is proposed for studying the free vibrations of flexible shallow shells with a complex planform. The method is based on variational and R-function methods. The R-function method allows constructing a system of basis functions in an analytic form. This makes it possible to reduce the Donnell-Mushtari-Vlasov equations to Duffing equations. The amplitude-frequency characteristics of shallow shells with a complex planform are given for different curvatures and boundary conditions. The results obtained are compared with published results for simply supported square shells to demonstrate the reliability and efficiency of the method __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 99–109, April 2007.     

Hydrodynamics of a flexible cylinder under modulated vortex-induced vibrations

Both amplitude modulation and frequency modulation of Vortex-induced Vibration (VIV) are observed in a recent model test of a flexible cylinder under oscillatory flow, but its hydrodynamics has not yet been broached in detail. This paper employs the Forgetting Factor Least Squares (FF-LS) method for identification of time-varying hydrodynamics of a flexible cylinder under modulated VIV. The FF-LS method’s applicability to accurately identify time-varying hydrodynamic coefficients is demonstrated through an elastically mounted rigid cylinder under flow with a given modulated motion. Furthermore, we propose a framework to predict instantaneous amplitude (envelope) and frequency using time-varying hydrodynamic coefficients to establish their analytical relationship. This prediction method is further extended to a highly tensioned flexible cylinder through Fourier series expansion in the spatial domain. By performing the identification procedure for all sampled data of a flexible cylinder undergoing oscillatory flow, we obtain the corresponding time-varying hydrodynamics in the cross-flow direction considering the amplitude and frequency modulation. The results show that, under modulated VIV, hydrodynamic coefficients of the flexible cylinder also show time-varying characteristics. We further investigate differences between identified hydrodynamic coefficients and those obtained from the database of a cylinder with modulated motion under flow. Prediction results using these identified time-varying coefficients reveal that the time-varying excitation coefficients mainly influence the amplitude modulation, and the time-varying added-mass coefficients contain the major information of frequency modulation. These results further suggest including the temporal derivative of the instantaneous amplitude as one determining parameter in building databases to improve the prediction of modulated VIV.     

Nonlinear and dual-parameter chaotic vibrations of lumped parameter model in blisk under combined aerodynamic force and varying rotating speed

Nonlinear Dynamics - In this paper, the nonlinear and dual-parameter chaotic vibrations are investigated for the blisk structure with the lumped parameter model under combined the aerodynamic force...