The results of a combined analytical and experimental investigation of the unbalance vibrations of a rotor are presented. The analysis applies to a general rotor-bearing system in which the dynamic bearing forces are ...
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The results of a combined analytical and experimental investigation of the unbalance vibrations of a rotor are presented. The analysis applies to a general rotor-bearing system in which the dynamic bearing forces are represented by four spring coefficients and four damping coefficients. The rotor can be represented as either a lumped or a distributedparameter system, and gyroscopic moments are included. In general, the unbalance whirl motion of the rotor will be elliptical. The analysis has been programmed for a digital computer to obtain results for comparison with the experimental data. The test rotor is a uniform, flexible shaft with heavy wheels mounted at the ends and in the middle. The rotor is supported in two silicone fluid-lubricated, tilting-pad bearings. The rotor amplitude caused by an induced unbalance has been measured over a speed range of 3000 to 24,000 rpm for three different rotor configurations, obtained by removing one or both end wheels. This speed range extends to or through the third critical speed for each of the rotor configurations. The results are compared with the theoretical values and, in general, the agreement is found to be good.
In this paper, the problem of stability in distributed parameter systems with feedback controls is formulated directly in the framework of partial differential equations without resorting to further approximations. Su...
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In this paper, the problem of stability in distributed parameter systems with feedback controls is formulated directly in the framework of partial differential equations without resorting to further approximations. Sufficient conditions for Lyapunov asymptotic stability are derived for particular classes of systems with distributed, mixed distributed, and boundary control laws, and also for systems with time delay. The applications of the main results are illustrated by examples.
This paper provides guidelines for the discretizing of the space variables in continuous systems governed by the second-order partial differential diffusion equation. Such lumping is necessary in all digital and many ...
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This paper provides guidelines for the discretizing of the space variables in continuous systems governed by the second-order partial differential diffusion equation. Such lumping is necessary in all digital and many analog methods. To analyze the truncation error resulting from lumped analog or digital modelling, the authors demonstrate the applicability of an upper-bound criterion combining amplitude and phase errors in the frequency domain. Dimensionless variables are used to compare lumped networks corresponding to one-dimensional continuous systems. Computer results are presented which relate truncation error to frequency for lumped models containing one to ten sections.
Finite difference methods are used to implement the solution to optimal control of distributed parameter systems. The control is assumed to be intrinsic to the partial differential equation (PDE) as well as continuous...
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Finite difference methods are used to implement the solution to optimal control of distributed parameter systems. The control is assumed to be intrinsic to the partial differential equation (PDE) as well as continuous, such that the calculus of variations is used to obtain the control law. Several important principles are developed to formulate the difference approximations to the partial differential equations which describe the system and the control law. An iterative method of solution is employed on these two equations. The convergence of the iteration is assured by stability considerations of the finite difference expressions.
A method is proposed for identifying linear distributed parameter systems from measurements on the system and inputs. Based on characteristics, the method is direct and converges rapidly for the class of problems disc...
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A method is proposed for identifying linear distributed parameter systems from measurements on the system and inputs. Based on characteristics, the method is direct and converges rapidly for the class of problems discussed.
The optimal open loop control of systems described by a set of linear partial differential equations is investigated. The performance index is of quadratic type and the mean square error is considered as a special cas...
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The optimal open loop control of systems described by a set of linear partial differential equations is investigated. The performance index is of quadratic type and the mean square error is considered as a special case. Energy type inequality constraints are imposed on the control inputs. The problem is formulated as a minimization problem in Hilbert space. The necessary and sufficient conditions for a minimum are obtained and it is proved that these conditions yield the global minimum. It is shown how the solution to the constrained problem can be obtained from the solution of the unconstrained problem. The optimal control functions satisfy Fredholm integral equations with symmetric kernels. The paper presents an example where the solution is obtained by eigenfunction expansion.
The problem of optimum control of a distributedparameter system with boundary control is studied. The distributedparameter system considered is described by the N-dimensional wave equation. The error measure is quad...
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作者：
GARVEY, DCDSOUZA, AFD. C. Garvey
A. F. D’Souza Dept. of Mechanical and Aerospace Engineering Illinois Institute of Technology Chicago Ill.
The partial differential equations describing distributed parameter systems may often be reduced to transcendental transfer functions with the aid of appropriate boundary conditions. In the analysis and synthesis of c...
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The partial differential equations describing distributed parameter systems may often be reduced to transcendental transfer functions with the aid of appropriate boundary conditions. In the analysis and synthesis of closed loop systems, the transcendental transfer functions have to be approximated in a suitable manner. In this paper, discrete-time model of distributed parameter systems is obtained. The model employs a sample and hold circuit in the loop. The response of the model system is compared with the response obtained by approximating the transcendental transfer function by root factor and other approximations. The stability of linear and nonlinear systems with distributedparameters is investigated by employing the Mikhailov stability criterion.
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