scholarly journals Thermally induced vibration suppression in a thermoelastic beam structure

2021 ◽  
pp. 82-82
Author(s):  
Kenan Yildirim
Keyword(s):  
Vibration Suppression ◽  
Initial Boundary ◽  
Control Force ◽  
Beam Structure ◽  
Thermally Induced ◽  
Distributed Parameters ◽  
Thermoelastic Beam ◽  
Thermally Induced Vibrations ◽  
Control Forces ◽  
Objective Functional

In this paper, the problem of thermally induced vibration suppression in a thermoelastic beam is studied. Physical equivalent of the present problem is that a thermoelastic beam is suddenly entering into daylight zone and vibrations are induced due to heating on the upper surface of the beam or thermoelastic beam in a spacecraft enters to intensive sunlight area just after leaving a shadow of a planet. Thermally induced vibrations are suppressed by means of minimum using of control forces to be applied to dynamic space actuators. Objective functional of the problem is chosen as a modified quadratical functional of the kinetic energy of the thermoelastic beam. Necessary optimality condition to be satisfied by an optimal control force is derived in the form of maximum principle, which converts the optimal vibration suppression problem to solving a system of distributed parameters system linked by initial-boundary-terminal conditions. Solution of the system is achieved via MATLAB? and simulated results reveal that thermally induced vibration suppression by means of dynamic space actuators are very effective and robust.

scholarly journals Vibration control of a linear flexible beam structure excited by multiple harmonics

2021 ◽  
Vol 9 (4B) ◽  
Author(s):  
Bassam A. Albassam ◽  
Keyword(s):  
Equations Of Motion ◽  
Superposition Principle ◽  
Nodal Point ◽  
Excitation Frequency ◽  
Stationary Points ◽  
Flexible Beam ◽  
Control Force ◽  
Algebraic Equations ◽  
Beam Structure ◽  
Control Forces

This paper deals with designing a control force to create nodal point(s) having zero displacement and/or zero slope at selected locations in a vibrating beam structure excited by multiple harmonic forces. It is shown that the steady state vibrations at desired points can be eliminated using applied control forces. The control forces design method is implemented using dynamic Green’s functions that transform the equations of motion from differential to algebraic equations, in which the resulting solution is analytic and exact. The control problem is greatly simplified by utilizing the superposition principle that leads to calculating the control forces to create node(s) for each excitation frequency independently. The calculated control forces can be realized using passive elements such as masses and springs connected to the beam having reaction forces equal to the calculated control forces. The effectiveness of the proposed method is demonstrated on various cases using numerical examples. Through examples, it was shown that creating node(s) with zero deflection, as well as zero slope, not only results in isolated stationary points, but also suppresses the vibrations along a wide region of the beam.

Thermally induced vibrations of a self-shadowed split-blanket solar array

1995 ◽  
Vol 32 (2) ◽  
pp. 302-311 ◽  
Author(s):  
Earl A. Thornton ◽  
Gregory P. Chini ◽  
David W. Gulik
Keyword(s):  
Solar Array ◽  
Thermally Induced ◽  
Thermally Induced Vibrations

Stability of a weak solution for a hyperbolic system with distributed parameters on a graph

2021 ◽  
pp. 55-67
Author(s):  
Vyacheslav V. Provotorov ◽  
Alexei P. Zhabko
Keyword(s):  
Weak Solution ◽  
Hyperbolic System ◽  
A Priori Estimates ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Summable Function ◽  
Weak Formulation ◽  
Weakly Compact ◽  
Generalized Fourier Series ◽  
Distributed Parameters

In the work, the stability conditions for a solution of an evolutionary hyperbolic system with distributed parameters on a graph describing the oscillating process of continuous medium in a spatial network are indicated. The hyperbolic system is considered in the weak formulation: a weak solution of the system is a summable function that satisfies the integral identity which determines the variational formulation for the initial-boundary value problem. The basic idea, that has determined the content of this work, is to present a weak solution in the form of a generalized Fourier series and continue with an analysis of the convergence of this series and the series obtained by its single termwise differentiation. The used approach is based on a priori estimates of a weak solution and the construction (by the Fayedo–Galerkin method with a special basis, the system of eigenfunctions of the elliptic operator of a hyperbolic equation) of a weakly compact family of approximate solutions in the selected state space. The obtained results underlie the analysis of optimal control problems of oscillations of netset-like industrial constructions which have interesting analogies with multi-phase problems of multidimensional hydrodynamics.

Active Vibration Absorption Using Delayed Resonator With Relative Position Measurement

1995 ◽  
Author(s):  
Nejat Olgac ◽  
Martin Hosek
Keyword(s):  
Relative Position ◽  
Primary Structure ◽  
Vibration Suppression ◽  
Control Force ◽  
Range Analysis ◽  
Position Measurement ◽  
Harmonic Force ◽  
Stability Range ◽  
Vibration Absorption ◽  
Active Vibration

Abstract A novel active vibration absorption technique, the Delayed Resonator, has been introduced recently as a unique way of suppressing undesired oscillations. It suggests a control force on a mass-spring-damper absorber in the form of a proportional position feedback with a time delay. Its strengths consist of extremely simple implementation of the control algorithm, total vibration suppression of the primary structure against a harmonic force excitation and full effectiveness of the absorber in a semi-infinite range of disturbance frequency, achieved by real-time tuning. All this development work was done using the absolute displacements of the absorber in the feedback. These displacement measurements may be difficult to obtain and for some applications impossible. This paper deals with a substitute and easier measurement: the relative motion of the absorber with respect to the primary structure. Theoretical foundations for the Delayed Resonator (DR) are briefly recapitulated and its implementation on a single-degree-of-freedom primary structure disturbed by a harmonic force is introduced utilizing both absolute and relative position measurement of absorber mass. Methods for stability range analysis and transient behavior are presented. Properties acquired for the same system with these two different feedback are compared. Relative position measurement case is found to be more advantageous in most applications of the Delayed Resonator method.

Sensing and Control of Thermally Induced Vibrations of Stationary Blades Using Piezoelectric Materials

2017 ◽  
Vol 43 (3) ◽  
pp. 1301-1311 ◽  
Author(s):  
K. S. Al-Athel ◽  
H. M. Al-Qahtani ◽  
M. Sunar ◽  
L. Malgaca ◽  
A. Omar
Keyword(s):  
Piezoelectric Materials ◽  
Thermally Induced ◽  
Thermally Induced Vibrations ◽  
And Control

Spatial Actuation Effectiveness of Segmented Actuators on Parabolic Cylindrical Panels

2012 ◽  
Author(s):  
S. D. Hu ◽  
H. Li ◽  
H. S. Tzou
Keyword(s):  
Shape Control ◽  
Cylindrical Panel ◽  
Design Parameters ◽  
Modal Control ◽  
Control Force ◽  
Optimal Position ◽  
Meridional Direction ◽  
Cylindrical Panels ◽  
Active Vibration ◽  
Control Forces

With the distinct capability of line-focusing, open parabolic cylindrical panels are commonly used as key components of radar antennas, space reflectors, solar collectors, etc. These structures suffer unexpected vibrations from the fluctuation of base structure, non-uniform heating and air flow. The unwanted vibration will reduce the surface reflecting precision and even result in structure damages. To explore active vibration and shape control of parabolic cylindrical panels, this study focuses on actuation effectiveness induced by segmented piezoelectric patches laminated on a flexible parabolic cylindrical panel. The mathematical model of a parabolic cylindrical panel laminated with distributed actuators is formulated. The segmentation technique is developed and applied to parabolic cylindrical panels, and the piezoelectric layer is segmented uniformly in the meridional direction. The distributed actuator patches induced modal control forces are evaluated. As the area of actuator patch varies in the meridional direction, modal control force divided by actuator area, i.e., actuation effectiveness, is investigated. Spatial actuation effectiveness, including its membrane and bending components are evaluated with respect to design parameters: actuator size and position, shell curvature, shell thickness and vibration mode in case studies. The actuation component induced by the membrane force in the meridional direction mainly contributes to the total actuation effectiveness for lower modes. Average and cancellation effect of various actuator sizes and the optimal actuator position are also discussed. Results suggest that for odd vibration modes, the maximal actuation effectiveness locates at the ridge of the panel; while for even modes, the peak/valley closest to the ridge is the optimal position to obtain the maximal actuation effectiveness. A segmentation scheme of the meridian interval angle 0.0464rad for the investigated standard panel is a preferred tradeoff between the actuation effectiveness and practical feasibility. The modal actuation effectiveness increases with the shell curvature, whereas decreases when the shell thickens.

scholarly journals Control Force Recalculation for Balancing Problems

2019 ◽  
Vol 19 (05) ◽  
pp. 1941010
Author(s):  
Bálint Bodor ◽  
László Bencsik ◽  
Tamás Insperger
Keyword(s):  
Optimization Problem ◽  
Control Mechanism ◽  
Numerical Differentiation ◽  
Open Loop ◽  
Second Step ◽  
Control Force ◽  
New Approach ◽  
Numerical Errors ◽  
Linearized System ◽  
Control Forces

Understanding the mechanism of human balancing is a scientifically challenging task. In order to describe the nature of the underlying control mechanism, the control force has to be determined experimentally. A main feature of balancing tasks is that the open-loop system is unstable. Therefore, reconstruction of the trajectories using the measured control force is difficult, since measurement inaccuracies, noise and numerical errors increase exponentially with time. In order to overcome this problem, a new approach is proposed in this paper. In the presented technique, first the solution of the linearized system is used. As a second step, an optimization problem is solved which is based on a variational principle. A main advantage of the method is that there is no need for the numerical differentiation of the measured data for the calculation of the control forces, which is the main source of the numerical errors. The method is demonstrated in case of a human stick balancing.

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