Chuh Mei

Suppression of Thermal Postbuckling and Nonlinear Panel Flutter Motions Using Piezoelectric Actuators

Active output feedback control of large amplitude nonlinear panel flutter at supersonic speeds with and without temperature effect is presented. A coupled structural-electrical modal formulation using finite elements is applied. Suppression of three types of panel response is studied: limit cycle oscillations, static thermal postbuckling, and chaotic motion. The controller, composed of a linear quadratic regulator and an extended Kalman filter, is developed and investigated. The extended Kalman filter considers the nonlinear state-space matrix and has a gain sequence evaluated online. The norms of the feedback control gain are employed for the optimal placement of piezoelectric actuators, and the norms of the Kalman filter estimation gain are used to validate the best locations for the sensors. A symmetric laminated composite plate at supersonic speeds with or without the influence of elevated temperatures is investigated. Two types of piezoelectric materials, PZT5A and macrofiber composite actuators, embedded in the composite panel are considered to suppress the nonlinear panel flutter. Simulation results show that the linear quadratic regulator/Kalman filter controller can suppress all three types of panel response with or without thermal effects.

Active Control of Nonlinear Panel Flutter Using Aeroelastic Modes and Piezoelectric Actuators

Suppression of nonlinear panel flutter at supersonic speeds has been investigated traditionally with system equations of motion in terms of in vacuo modal coordinates. For isotropic and symmetrically laminated orthotropic composite plates, the limit-cycle oscillations converged with six in vacuo natural modes at a zero yaw angle. However, as laminated composite plates undergo the effect of an arbitrary yawed flow angle, complicated characteristics emerge by increasing the required in vacuo natural modes for an analysis of limit-cycle oscillations. To design an effective controller, the large number of modes should be reduced. As a result, the small number of modes produces a capability to alleviate the costly computational effort in designing controllers for the suppression of nonlinear panel flutter. In the present study, aeroelastic modes that provide the reduced order basis are used for panel limit-cycle motion. Two or six to seven aeroelastic modes are implemented for developing an active controller of panel flutter with isotropic and anisotropic laminated composite plates at a zero or nonzero yaw angle. Along with the aeroelastic modal equations of lesser number, a linear quadratic regulator, which is one of the output feedback controllers, is constructed to suppress nonlinear panel flutter. An added extended Kalman filter compensates for the nonlinearity of structural motion resulting from updating the system information online. The norms of feedback control gain and the norms of Kalman filter estimation gain are employed for the optimal placement of PZT5A or macro-fiber composite piezoelectric actuators and sensors. Numerical results show that the designed controller based on aeroelastic modal coordinates can suppress the large-amplitude panel nonlinear flutter response. The maximum flutter-free dynamic pressure for isotropic and composite plates is evaluated to measure how much the performance is improved.

Discussion of finite element formulations of nonlinear beam vibrations

Abstract The Lagrange-type, Galerkin, and Ritz-type finite element formulations for large amplitude vibrations of immovably supported slender beams are reexamined. Inconsistency in the definition of frequency or criterion of defining nonlinearity is discussed, and validity of the frequency solution is examined. Improved finite element results by including both longitudinal displacement and inertia in the formulation are presented and compared with available Rayleigh-Ritz continuum solutions.

Nonlinear Random Response of Panels in an Elevated Thermal-Acoustic Environment

Sonic fatigue is generally considered as being one of the major design areas for the newest generation of high-speed flight vehicles. Efficient analysis methods for predicting nonlinear random response and fatigue life are urgently needed. This paper presents a finite element formulation for the prediction of nonlinear random response of thin isotropic/composite panels subjected simultaneously to high acoustic loads and elevated temperatures. Laminated plate theory and von Karman large displacement relations are used to derive the nonlinear equations of motion for an arbitrarily laminated composite panel subjected to combined acoustic and thermal loads. The nonlinear equations of motion in physical degrees of freedom are transformed to a set of coupled nonlinear equations in truncated modal coordinates, retaining fewer degrees of freedom. Numerical integration is employed to obtain the panel response to simulated Gaussian band-limited white noise. To validate the formulation, results are compared with existing linear and nonlinear solutions to assess the accuracy of nonlinear modal stiffness matrices and simulated random loads. Examples are given for an isotropic panel at various combinations of sound pressure levels and temperatures. Numerical results include rms values of maximum deflection and strain, time histories of deflection and strain response, probability distribution functions, power spectrum densities, and higher statistical moments. Numerical results predicted all three types of panel motions for a thermal buckled simply supported isotropic plate: linear random vibration about one of the buckled equilibrium position, snap-through motions between the two buckled positions, and nonlinear random response over both buckled positions.

Adaptive Control of Nonlinear Free Vibrations of Composite Plates Using Piezoelectric Actuators

A coupled structural-electrical finite element modal formulation is employed for the control of nonlinear free vibrations of beams and composite plates. Multiple modes of the nonlinear free vibration are considered in closed-loop simulations. Two different controllers are designed and investigated for the suppression of nonlinear free vibrations. The first is the position output feedback controller comprising a linear quadratic regulator (LQR) and an extended Kalman filter (EKF). The EKF is used to consider the nonlinear state-space matrix and has a gain sequence evaluated online. The second controller is the output feedback adaptive LQR/EKF controller. This adaptive controller includes an adaptive modal frequency identification and state estimation algorithm. Numerical simulations show that the adaptive LQR/EKF controller with system identification is effective in suppressing nonlinear free vibrations of a beam and a composite plate with unpredictable sudden frequency changes. The placement of piezoelectric self-sensing actuators is based on three approaches: one is the norm of optimal feedback control gain matrix method, the second is the H 2 norm, and the last one is the norm of Kalman filter estimation gain method.

FLOW ANGLE, TEMPERATURE AND AERODYNAMIC DAMPING ON SUPERSONIC PANEL FLUTTER STABILITY BOUNDARY

The effects of flow yaw angle, temperature, and aerodynamic damping on supersonic flutter of plates are investigated. Quasisteady, first-order piston theory is employed for formulation of aerodynamic forces. The von Karman large-deflection plate theory is adapted for the aerothermal deflection. Two types of thermal effects are considered: 1) plate expansion by uniform temperature and 2) thermal moment induced by temperature gradient across the plate thickness. A finite element modal formulation and a two-step procedure are presented for the predictions of stability boundaries and nonlinear aerothermal deflection and shown to be efficient in solution. Results have shown that flow angle has lesser effect on stability boundaries as compared with temperature for isotropic square plates. However, both flow angle and temperature have a large influence on stability boundaries for rectangular isotropic and laminated composite plates. The presence of the ripple characteristics of stability boundaries for composite plates caused by the frequency coalescence of higher modes and the smaller effect of aerodynamic damping is investigated. The stabilization effects on panel motions induced by variations of flow angle, temperature, and aerodynamic damping are discussed.

Supersonic Nonlinear Panel Flutter Suppression Using Shape Memory Alloys

An efficient finite element procedure is developed to predict large-amplitude nonlinear flutter response of shape memory alloy hybrid composite plates at an arbitrary supersonic yawed angle and an elevated temperature. The temperature-dependent material properties of shape memory alloy and traditional composites, as well as the von Karman large deflections, are considered in the formulation. Finite element system equations of motion are transferred to aeroelastic modal coordinates to reduce the large number of structural-node degrees of freedom. Time-domain numerical integration is employed to analyze flutter behaviors of the shape memory alloy hybrid composite panel under thermal loads. The flutter stability regions under the combined aerodynamic and thermal loads are studied. All of the possible behaviors, including the two types of static behavior and four types of dynamic motion of flutter, can be predicted for shape memory alloy hybrid composite plates. The static behaviors are 1) flat and stable and 2) aerothermally buckled but dynamically stable. The four types of dynamic motion are nearly simple harmonic limit-cycle oscillation, periodic limit-cycle oscillation, quasi-periodic oscillation, and chaotic oscillation. The flutter response of shape memory alloy hybrid composite plates are compared with those of traditional composite plates without a shape memory alloy. Results show that the desired flat and stable region can be greatly enlarged by using a shape memory alloy.

Thermal Buckling Suppression of Supersonic Vehicle Surface Panels Using Shape Memory Alloy

An efficient finite element method for the prediction of critical temperature, postbuckling deflection, and vibration characteristics is presented for traditional composite plates embedded with prestrained shape memory alloy (SMA) wires. The temperature-dependent material properties of SMA and composites and the large deflections are considered in the formulation. An iterative eigensolution is presented to determine the critical temperature, the Newton-Raphson method is employed to obtain postbuckling large deflection, and the eigensolver is used to predict free vibration frequencies about the thermally buckled equilibrium positions. Results show that the critical buckling temperature can be raised high enough and that the postbuckling deflection can be completely suppressed for surface panels of supersonic vehicle applications by the proper selection of SMA volume fraction, prestrain, and alloy composition. Weight savings based on critical temperature in the use of SMA as compared with the traditional composite and titanium plates are demonstrated.

Nonlinear random response of internally hinged beams

Nonlinear responses of beams with an internal hinge under stationary, ergodic, Gaussian and zero mean uniform random pressure are studied. Two types of support condition: clamped-clamped and clamped-simply supported are considered. The equivalent linearization method is employed on the basis of finite element modal formulation to assess the influence of hinge location on root mean square (RMS) maximum deflection and RMS maximum micro-strain. The internal hinge is modeled with two transition elements that proved to be effective and convenient. Internal hinge location is optimized based upon lowest RMS maximum deflection and/or micro-strain. Numerical simulation results are obtained and compared with results from equivalent linearization to show the good agreement between the two methods.

Nonlinear Response and Fatigue Life of Isotropic Panels Subjected to Nonwhite Noise

In stochastic structural dynamics, the majority of the analyses have dealt with linear structures under stationary Gaussian and band-limited white-noise excitation. Recorded aircraft acoustic pressure fluctuations have shown 1) the high levels of acoustic excitation that can drive the surface panels to nonlinear large deflection response and 2) the nonwhite power spectral density characteristic that can affect panel response and fatigue life. This paper presents the nonlinear response and fatigue life estimation of isotropic panels subjected to nonwhite acoustic excitation. An efficient finite element time-domain modal formulation was employed to determine the panel response. The Palmgren-Miner cumulative damage theory in combination with the rainflow counting cycles method was used to estimate the panel fatigue life. To assess the effects of nonwhite power-spectral-density characteristics, an equivalent band-limited white-noise excitation, which has the same acoustic power within the bandwidth as the recorded data, was simulated. Nonlinear response and fatigue life to recorded and simulated data were determined for comparison. Results show that the actual flight data with nonwhite power spectral density can yield higher stress characteristics and shorter fatigue life than the corresponding equivalent white noise.