Raymond Jacquot

Optimal dynamic vibration absorbers for general beam systems

A technique is developed to give the optimal dynamic vibration absorber parameters for the elimination of excessive vibration in sinusoidally forced Bernoulli-Euler beams. The result is presented in a general form so as to include all possible sets of ordinary boundary conditions and absorber attachment points. This is done by employing a single mode expansion for the beam in an assumed mode approach. The general equations developed are then applied to a point-forced cantilever beam with a viscously damped dynamic absorber attached at the beam midpoint. The optimal values developed for the single mode approximation are then evaluated with account taken of the first five beam modes where discrepancies are noted near the higher order beam resonances which are shifted somewhat due to the absorber.

The effects of discrete masses and elastic supports on continuous beam natural frequencies

Abstract Natural frequencies and modes are determined for beams having a continuous mass distribution as well as a finite number of concentrated masses with rotary inertia. The method also includes the effects of discrete elastic supports and torsional restraints. Solutions are obtained by expanding the time dependent deflection curve in terms of well known characteristic beam functions and then solving a set of linear equations for eigenfrequencies and modes. Solutions for a simple beam having a torsional end restraint and a cantilever beam with a concentrated end mass and stiffness are obtained in order to illustrate the method.

Optimal damper location for randomly forced cantilever beams

The work reported here considers the attachment of a viscous damper to a cantilever beam that is driven by temporally white noise with several different spatial distributions. The variables in the problem to be optimized are the location and the value of the damper. For each of the spatial distributions, there is a location and damper value that will minimize the mean square motion averaged over the beam length. These minima are shown to be not a strong function of the spatial distribution of the forcing function with the best location being at 70% of the length from the fixed end. The optimal value of the damper is shown to be 50 times the product of the beam mass and the first radian natural frequency for the beam.

The forced vibration of singly modified damped elastic surface systems

Abstract A technique is developed to predict the forced vibration of membranes, beams, plates or shells when they have attached to them at a single point a linear lumped parameter element or assembly of elements. The distributed parameter element is treated as viscously damped and the lumped parameter assembly may also contain viscous dampers. Solution is obtained in terms of generalized Fourier series in the unmodified eigenfunctions for the distributed portion of the system and the principle of superposition is used to handle the imposed forces and those generated at the attachment. The method is illustrated by investigating a uniformly forced simply supported rectangular plate with a lumped mass at its center and that of a point forced simple beam with a rigid pin support imposed at some arbitrary point.

The response of a system when modified by the attachment of an additional sub-system

Abstract A technique is developed by which the effect of the attachment of a sub-system on frequency domain and time domain responses may be evaluated. This involves working with driving point and transfer functions in the frequency domain. Transition to the time domain is accomplished by use of the Fast Fourier Transform algorithm. The technique developed is applied to find the optimal damping for a dynamic vibration absorber attached to the tip of a forced elastic cantilever beam.

A Microprocessor System for the Discrete-Time Control Laboratory

The topics studied in discrete-time signal processing and control are particularly abstract and some aid to learning these concepts is needed. One possible type of aid is discussed which employs state-of-the-art hardware to implement a programmable digital filter which may be useful in discussing sampling, digital filtering or may be inserted as a discrete-time compensator into a continuous-time control loop. The device employs modern microprocessor hardware including ROM, RAM, interval timer, digital-to-analog, and analog-to-digital converters. Digital filters up to fourth order may be programmed as may the sampling interval to be employed. Several applications to the control of a typical continuous-time plant are given.

Generalized gain plots for proportional digital control for second-order all-pole plants

The concept of gain plots provides a geometric connection between classical SISO control design tools. The work discussed is an attempt to generalize the gain plot concept to the digital control of two classes of second-order plants and to present the results in nondimensional form so they may be useful in a broad class of controller design problems. The proportional digital control of all second-order all-pole plants has been generalized in the form of dimensionless performance parameter curves. Here, the closed-loop performance is functionally dependent on the open-loop plant parameters, the sampling interval, and the controller gain. Plots are presented in dimensionless form so they are applicable to a wide range of second-order plants.

Teaching digital control and filtering using MATLAB and VisSim

The authors report the revision for a course entitled Discrete Data Systems which is a blend of classical and modem digital control, and digital filtering. This revision reflects computing resources now available and as a result no longer are low order system problems assigned. The authors have incorporated symbolic computing in several appropriate places where it can increase understanding and yield error-free algebraic manipulations. In most exercises, the computing is of the numerical type using algorithms developed in the course. Simulation employing a graphical-oriented simulation language lends reality as to how control laws and estimation algorithms are implemented in practice and lets students explore the effects of controller parameters and sampling interval on responses.

Dynamic dynamics: Projection software for engineering dynamics

In an attempt to close the gap between teaching and learning styles, the authors embarked on a project to develop in-class, MS-DOS computer enhancement material for lectures in engineering dynamics. The materials presented in this work provide the instructor with a means to improve the teaching environment by allowing visual demonstrations of the principles of dynamics that he or she is attempting to teach in any particular lecture. The authors present some specific information regarding the development of the animations, show the current list of animations that are available, and present one example in relative detail.<<ETX>>

The application of sinusoidally derived beam receptances to calculation of transient responses for damped composite systems

Abstract A method in which transcendental sinusoidal beam receptances are employed for calculation of transient responses of composite systems containing Bernoulli-Euler beams is given. In the actual response calculations the Gaver-Stehfest algorithm is employed for inverting the transcendental functions of the complex s variable. Several example applications are given.