Spatially Convolving Wave Propagation Sensors for Structural Control-Part I: Analytical Development for One-Dimensional Structures

A novel method for sensing actual disturbance information which can propagate along one-dimensional structural waveguides is developed. The motivation for this work arises from the inability to realize most active wave control designs using output information from physical measurements such as deflection, slope, curvature and internal shear force. Often the use of actual physical measurements leads to instability and suboptimal performance of certain active wave control loops. Thus, there is a desire to develop wave-propagation filters which can extract magnitude and direction of structural disturbances along dispersive and non-dispersive members. In this work a distributed wave sensing scheme is reported which exploits the characterization of 1-dimensional structural motion in terms of traveling waves. This form of the solution is then combined with distributed sensors to convolve future and past measurements into a single temporal signal to overcome the problem of causality and spatial aliasing inherent in discrete sensor approaches. Thus, by imposing specific shapes to spatially convolving sensors, it is possible to combine the output of these sensors with point measurements to observe directional propagating wave components. Because this method requires some approximation of the spatial domain, there will be errors due to spatial discretization and truncation. This work addresses these issues and presents analytical results for one-dimensional structural elements.

[1]  M. A. Swinbanks.  The active control of sound propagation in long ducts , 1973 .

[2]  H. G. Leventhall,et al.  An experimental study of swinbanks' method of active attenuation of sound in ducts , 1976 .

[3]  M. Bérengier,et al.  Broad-band active sound absorption in a duct carrying uniformly flowing fluid , 1980 .

[4]  J. E. Naugle,et al.  Just over the horizon in space , 1980 .

[5]  C. F. Ross.  An adaptive digital filter for broadband active sound control , 1982 .

[6]  Von Flotow.  A travelling wave approach to the dynamic analysis of large space structures , 1983 .

[7]  A. H. von Flotow,et al.  Disturbance propagation in structural networks , 1984 .

[8]  T. Bailey,et al.  Distributed Piezoelectric-Polymer Active Vibration Control of a Cantilever Beam , 1985 .

[9]  J. S. Mixson,et al.  Review of research on structureborne noise , 1985 .

[10]  Earl H. Dowell,et al.  Asymptotic Modal Analysis and Statistical Energy Analysis of Dynamical Systems , 1985 .

[11]  A. V. Flotow,et al.  Experimental comparison of wave-absorbing and modal-based low-authority controllers for a flexible beam , 1985 .

[12]  J. E. Ffowcs Williams,et al.  Anti-phase noise reduction , 1985 .

[13]  A. V. Flotow,et al.  Wave absorbing. controllers for a flexible beam , 1986 .

[14]  A. H. Von Flotow,et al.  Traveling wave control for large spacecraft structures , 1986 .

[15]  William Redman-White,et al.  Experiments on the active control of flexural wave power flow , 1987 .

[16]  S. E. Burke,et al.  Active vibration control of a simply supported beam using a spatially distributed actuator , 1987, IEEE Control Systems Magazine.

[17]  On the Active Vibration Control of Distributed Parameter Systems , 1987 .

[18]  David W. Miller,et al.  Active Modification of Wave Reflection and Transmission in Flexible Structures , 1987, 1987 American Control Conference.

[19]  T. W. Parks,et al.  Digital Filter Design , 1987 .

[20]  Brian R. Mace,et al.  Active control of flexural vibrations , 1987 .

[21]  T. Bailey,et al.  Nonlinear Control of a Distributed System: Simulation and Experimental Results , 1987 .

[22]  H. Tzou,et al.  Active vibration isolation by polymeric piezoelectret with variable feedback gains , 1988 .

[23]  B. Fornberg.  Generation of finite difference formulas on arbitrarily spaced grids , 1988 .

[24]  Satya N. Atluri,et al.  Large Space Structures: Dynamics and Control , 1988 .

[25]  James E. Hubbard,et al.  Low Authority Control of a Composite Cantilever Beam in Two Dimensions , 1988, 1988 American Control Conference.

[26]  Leonard Meirovitch,et al.  Active suppression of traveling waves in structures , 1989 .

[27]  W.-W. Chiang,et al.  Piezoelectric modal sensors and actuators achieving critical active damping on a cantilever plate , 1989 .

[28]  H. S. Tzou,et al.  Integrated distributed sensing and active vibration suppression of flexible manipulators using distributed piezoelectrics , 1989, J. Field Robotics.

[29]  Horn-Sen Tzou,et al.  Theoretical analysis of a multi-layered thin shell coupled with piezoelectric shell actuators for distributed vibration controls , 1989 .

[30]  Javier de Luis.  Design and implementation of optimal controllers for intelligent structures using infinite order structural models , 1989 .

[31]  Alan V. Oppenheim,et al.  Discrete-Time Signal Pro-cessing , 1989 .

[32]  David W. Miller,et al.  Optimal Control of Power Flow at Structural Junctions , 1989, 1989 American Control Conference.

[33]  Andress U. Kuehnie.  Control of Longitudinal Waves in a Rod with Voigt Damping , 1989, 1989 American Control Conference.

[34]  J. Wallaschek,et al.  Active Vibration Damping in Beams , 1989, 1989 American Control Conference.

[35]  R. J. Mckinnell.  Active vibration isolation by cancelling bending waves , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[36]  Darryll J. Pines,et al.  Active control of bending wave propagation at acoustic frequencies , 1990 .

[37]  David W. Miller,et al.  Development of spatially convolving sensors for structural control applications , 1990 .

[38]  Raymond J. Nagem,et al.  Control of a One-Dimensional Distributed Structure Based on Wave Propagation Analysis∗ , 1990 .

[39]  C. I. Tseng,et al.  Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems: A piezoelectric finite element approach , 1990 .

[40]  Robert L. Clark,et al.  Optimal placement of piezoelectric actuators and polyvinylidene fluoride error sensors in active structural acoustic control approaches , 1991 .

[41]  Steven R. Hall,et al.  Control of uncertain structures using an H(infinity) power flow approach , 1991 .

[42]  Clemans A. Powell.  Second International Congress on Recent Developments in Air‐ and Structure‐borne Sound and Vibration , 1992 .

[43]  Asymptotic modal analysis and statistical energy analysis , 1992 .

[44]  Robert L. Clark,et al.  Experiments on Active Control of Plate Vibration Using Piezoelectric Actuators and Polyvinylidene Fluoride (PVDF) Modal Sensors , 1994 .

[45]  Shawn E. Burke,et al.  Distributed transducer design for plates: spatial shape and shading as design parameters , 1994, Smart Structures.

[46]  Michael J. Brennan,et al.  Strategies for the active control of flexural vibration on a beam , 1995 .

[47]  Experimental demonstration of active broadband vibration suppression of a rectangular plate using gain-weighted, shaped distributed transducers , 1995 .

[48]  Robert L. Clark,et al.  OPTIMAL TRANSDUCER PLACEMENT FOR OUTPUT FEEDBACK CONTROL OF BROADBAND STRUCTURAL ACOUSTIC RADIATION , 1997 .