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 (SMT's) 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 SMT's 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 aero-Gaussian curvature.