Scott E. Miller

A Self-Sensing Piezolaminated Actuator Model for Shells Using a First Order Shear Deformation Theory

A composite piezolaminated shallow thin shell theory has been developed in which the individual laminae are capable of electromechanical transduction. Utilizing a first order shear deformation approximation and assuming that an electrical field may be applied only across the thickness of a given lamina, the resulting shell theory shows that piezolaminae are capable of exciting and sensing bending, torsion, inplane shearing, and inplane stretching. Piezolaminae are shown to be incapable of exciting and sensing transverse shear unless a three-dimensional electrical field is applied. Inplane shearing and torsion transduction only becomes possible when the dominant rolling axis of a given piezolamina is skewed such as not to coincide with a principal geometric axis. Constitutive relationships are derived which describe how each piezolamina may function simultaneously as both a sensor and an actuator. Two-dimensional piezoelectric field functions are introduced which describe how nonuniformly distributed electromechanical transduction will affect the nature of the applied excitation and acquired measurement. The equations of motion are also given for a shell in which transverse shear deformation is neglected according to Loves first approximation.

Modal control of piezolaminated anisotropic rectangular plates. I - Modal transducer theory

Selective modal transducers are developed for piezolaminated anisotropic plate systems that are capable of sensing and exciting any specified set of vibrational modes according to a specified set of modal participation factors. Transduction of selected modes is accomplished through combining the effect of three piezolaminate pairs whose piezoelectric fields are varied spatially. Each coupled pair contains a single layer located anywhere strictly above the reference plane, which is complemented by a second layer colocated below the reference plane. Piezoelectric constitutive properties associated with each layer in a given couple must be identical, whereas the constitutive properties of all three couples must be uniquely different. If all selective modal transducer layers are formed from the same stock material, the stock material must be piezoelectrically biaxial and the skew angles of all couples must be unique. Individual actuator inputs must be proportional to a common control function or, conversely, the sensed output must be a weighted sum of the measurements acquired by individual layers. An algorithm is presented that dictates how the piezoelectric field strength of each selective modal transducer layer must be varied spatially and is an explicit function of piezoelectric constants, mode shapes, and designer-chosen modal participation factors. Selective modal transducers for orthotropic systems are shown to require three piezolaminate layers rather than three coupled pairs.

Modal control of piezolaminated anisotropic rectangular plates - II Control theory

A general selective modal control design methodology is presented for piezolaminated anisotropic plate systems that utilizes selective modal transducers to realize any number of possible modal control strategies. A selective modal control design procedure is specified that defines a step-by-step framework through which the structural and control subdesign processes are effectively integrated. Several conditions that sufficiently ensure asymptotic stability are derived and then discussed in the context of deriving selective modal control methods that are stability robust to modeling and implementation errors Several selective modal control examples are then given in which selective modal transducers are designed and control laws chosen so as to allow for 1) the contributions of any given mode to the active energy extraction rate to be directly specified and 2) pole locations to be selectively and dynamically varied or 3) both pole locations and selective modal transducer design constants to be optimally determined. A numerical example is presented in which a stability-robust optimal selective modal control method is developed for a cantilevered anisotropic plate. Maintaining a linear feedback law, a single self-sensing selective modal transducer is employed whose design parameters were chosen to optimize the system response to a given initial excitation. Frequency and transient response analyses show a dramatic enhancement in system performance and accurately concur with theoretical predictions. The example serves both to illustrate the design process and to independently validate selective modal transducer and selective modal control theoretical results.

Selective Modal Transducers for Anisotropic Rectangular Plates: Experimental Validation

A general selective modal transducer (SMT) design methodology recently introduced by the authors for piezolaminated anisotropic plate systems is validated through an experimental test on a cantilevered orthotropic composite piezolaminated plate. Fundamental aspects of the SMT theory are reviewed. The SMT theory is extended to provide the means to predict the modal character of multilayered piezolaminated transducers embedded in an anisotropic plate in which the active subelements are both bidirectional and spatially varying. An experimental procedure is described involving a 10-layered orthotropic plate constructed from four graphite-epoxy layers sand(

Selective Modal Control Theory for Piezolaminated Anisotropic Shells

A general selective modal control design methodology is presented for piezolaminated anisotropic shell systems, which uses selective modal transducers recently developed by the authors for piezo-shells in order to realize any number of possible modal control strategies. A selective modal control design procedure, which dee nes a step-bystep framework through which structural and control subdesign processes are effectively integrated, is specie ed. Several conditions that sufe ciently ensure asymptotic stability are derived and then discussed in the context of deriving selective modal control methods, which are stability-robust to modeling and implementation errors. Several design examples are given. A numerical example is then presented in which a stability-robust optimal selective modal control design is developed for a cantilevered anisotropic cylindrical shell panel. Maintaining a linear feedback law, a selective modal transducer is employed, whose design parameters were chosen so as to optimize the system response to a given initial excitation. Frequency and transient response analyses demonstrate a dramatic enhancement in system performance and are shown to accurately concur with theoretical predictions.

Modal transducers for piezolaminated anisotropic zero-Gaussian curvature shell systems

Selective Modal Transducers (SMTs) are developed for piezolaminated anisotropic zero-Gaussian curvature shell systems which are capable of sensing and exciting any specified set of vibrational modes according to a specified set of modal participation factors. Transduction of selected modes is accomplished through combining the effect of three piezolaminate pairs whose piezoelectric fields are varied spatially. Each coupled pair contains a single layer located anywhere strictly above the reference plane which is complemented by a second layer colocated below the reference plane. Piezoelectric constitutive properties associated with each layer in a given couple must be identical, while the constitutive properties of all three couples must be uniquely different. If all SMTs are formed from the same stock material, the stock material must be piezoelectrically biaxial and the skew angles of all couples must be unique. Individual actuator inputs must be proportional to a common control function, or conversely the sensed output must be a weighted sum of the measurements acquired by individual layers. An algorithm is presented which dictates how the piezoelectric field strength of each SMT layer must be varied spatially, and is an explicit function of piezoelectric constants, modeshapes, and designer-chosen modal participation factors. A numerical example is given which both illustrates and validates the SMT design concept.

EXPERIMENTAL VALIDATION OF A MODAL TRANSDUCER FOR AN ORTHOTROPIC RECTANGULAR PLATE

A general Selective Modal Transducer (SMT) design methodology previously derived by the authors for piezolaminated anisotropic plate systems is validated through experimental test on a cantilevered orthotropic composite piezolaminated plate. Fundamental aspects of the SMT theory are first reviewed. The SMT theory is then extended to provide the means to predict the modal character of multilayered piezolaminated transducers embedded in an anisotropic plate in which the active subelements are both bi-directional and spatially varying. An experimental procedure is described involving a ten-layered orthotropic plate constructed from four graphite-epoxy layers sandwiched between six piezoelectrically active PVDF sublaminae. Three PVDF sublaminae stacked on one face are combined electrically to provide a single sensed measurement, while the three remaining PVDF sublaminae stacked on the opposing face are combined to provide single channel actuation. Lead compensation is employed to provide active control. Open and closed loop frequency and transient response data are then analyzed in order to determine both the natural frequencies and damping coefficients of the first four vibrational modes. Significant active vibration attenuation is observed. A numerical simulation directly based on an SMT-derived transducer model is developed, and simulation results are then compared to the actual system behavior. The theoretically based numerical results are seen to closely resemble the measured response to within an expected range of accuracy, thus validating the transducer theoretical model predicted by the SMT theory.

Selective modal control of composite piezolaminated anisotropic shells

A general Selective Modal Control (SMC) design methodology is presented for piezolaminated anisotropic shell systems which utilizes Selective Modal Transducers (SMTs) recently developed by the authors for piezo-shells in order to realize any number of possible modal control strategies. An SMC design procedure is specified which defines a step-by- step framework through which structural and control sub- design processes are effectively integrated. Several conditions which sufficiently ensure asymptotic stability are derived and then discussed in the context of deriving SMC methods which are stability robust to modeling and implementation errors. Several SMC examples are then given in which SMTs are designed and control laws chosen so as to allow for (1) the contributions of any given mode to the active energy extraction rate to be directly specified, (2) pole locations to be selectively and dynamically varied, or else (3) both pole locations and SMT design constants to be optimally determined. A numerical example is presented in which a stability-robust optimal SMC method is developed for a cantilevered anisotropic cylindrical shell panel. Maintaining a linear feedback law, a single self-sensing SMT is employed whose design parameters were chosen so as to optimize the system response to a given initial excitation. Frequency and transient response analyses show a dramatic enhancement in system performance and accurately concur with theoretical predictions. The example serves both to illustrate the design process and to independently validate SMT and SMC theoretical results as applied to shell systems characterized by zero-Gaussian curvatures.