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This article establishes a nonlinear flutter system for a long-span suspension bridge, aiming to analyze its supercritical flutter response under the influence of nonlinear aerodynamic self-excited force. By fitting the experimental discrete values of flutter derivatives using the least squares method, a polynomial function of flutter derivatives with respect to reduced wind speed is obtained. Flutter critical value is determined by the linear matrix eigenvalues of a state-space equation. The occurrence of a supercritical Hopf bifurcation in the nonlinear system is determined by the Jacobian matrix eigenvalues of the state-space equation and the system's vibrational response at the critical state. The vibrational response of the supercritical state is obtained through Runge–Kutta integration, revealing the presence of stable limit cycle oscillation (LCO) and unstable limit cycle oscillation in the system, and through analyzing the relationship between the LCO amplitude and wind speed. Considering cubic nonlinear damping and stiffness, the effects of different factors on the nonlinear flutter system are analyzed. [ABSTRACT FROM AUTHOR]

This paper presents the problem of nonlinear aero-thermo-elastic response of cracked plate. Bending equations of two-dimensional simply supported cracked plate subjected to supersonic flow and thermal effect is derived based on classical plate theory (CPT) and Von Kármán nonlinear relations. Linear piston theory is utilized to evaluate the aerodynamic pressure with uniform temperature variations. By applying Galerkin's method and Runge-Kutta scheme, the equations are solved. The effects of parameters such as flow condition, crack dimension, temperature changes, plate aspect ratio, mass ratio, static pressure on the plate stability, flutter point and limit cycle oscillation (LCO) of the plate are examined. [ABSTRACT FROM AUTHOR]

This article establishes a nonlinear flutter system for a long-span suspension bridge, aiming to analyze its supercritical flutter response under the influence of nonlinear aerodynamic self-excited force. By fitting the experimental discrete values of flutter derivatives using the least squares method, a polynomial function of flutter derivatives with respect to reduced wind speed is obtained. Flutter critical value is determined by the linear matrix eigenvalues of a state-space equation. The occurrence of a supercritical Hopf bifurcation in the nonlinear system is determined by the Jacobian matrix eigenvalues of the state-space equation and the system’s vibrational response at the critical state. The vibrational response of the supercritical state is obtained through Runge–Kutta integration, revealing the presence of stable limit cycle oscillation (LCO) and unstable limit cycle oscillation in the system, and through analyzing the relationship between the LCO amplitude and wind speed. Considering cubic nonlinear damping and stiffness, the effects of different factors on the nonlinear flutter system are analyzed.

A digital low-dropout (DLDO) regulator is described which is controlled by voltage-controlled oscillator (VCO) based feedback loop. There are two VCOs in the control loop whose frequencies are controlled by the output voltage and reference level, respectively. By comparing the phase between the output clocks of the two VCOs and modulating the number of enabled power transistors and their on-times, the output voltage is regulated. The proposed VCO-based control is a hybrid of digital and analog control schemes because the number of enabled power transistors is controlled in discrete step while the on-time is modulated continuously. In order to improve the transient speed, transient detector is employed in the DLDO regulator. The DLDO regulator with the proposed VCO-based control has been implemented in a 65-nm CMOS process. The DLDO regulator can provide the output from 0.5 to 1.1 V from the input ranging from 0.9 to 1.2 V. The load transient time is smaller than 90 ns for both step-up and step-down changes of load current. The peak current efficiency is 99.3%. [ABSTRACT FROM AUTHOR]

An aerodynamic describing function (ADF)-based model for simulating the nonlinear self-excited forces on bridge decks is developed, where the ADFs can be conveniently identified using the experimentally or numerically obtained free or forced vibration data. An efficient calculation procedure based on the ADFs is accordingly established to predict the nonlinear flutter state and/or postflutter limit cycle oscillations (LCOs). Two numerical examples are utilized to demonstrate the simulation accuracy and efficiency of nonlinear bridge flutter with the proposed ADF-based model. The capabilities of the ADF-based model in capturing typical features of nonlinear postflutter vibration such as LCO and a hysteresis phenomenon are demonstrated. A nondimensional postflutter index is designed to quantitatively assess the postflutter performance of bridge decks. Finally, the effects of structural dynamics and aerodynamic properties (e.g., structural damping ratios, natural frequencies, and aerodynamic derivatives) on the postflutter behavior of a bridge deck are examined in terms of the wind speed extension after the critical state with acceptable postcritical vibrations and the proposed postflutter index. [ABSTRACT FROM AUTHOR]

The post-flutter limit cycle oscillation (LCO) of a two-degree-of-freedom bridge deck involving aerodynamic nonlinearities is studied using computational fluid dynamics (CFD) simulations. To investigate the aerodynamic mechanism for the post-flutter LCO, a comprehensive energy budget analysis is conducted based on the simulated responses, in which the energy input properties of the 1st-order and higher-order force components are considered separately. Results show that only the 1st-order force components contribute significantly in the energy input, while the contributions of the higher-order force components are insignificant. The sensitivities of aerodynamic derivatives to vibration amplitudes and phase difference between vibration modes are investigated using forced vibration CFD simulations. For the concerned bridge deck, some aerodynamic derivatives are highly sensitive to vibration amplitude, while the influences of modal coupling effects are insignificant. A simplified multi-input multi-output nonlinear self-excited force model with amplitude-dependent aerodynamic derivatives is developed according to the sensitivity analysis. An example of bridge post-flutter LCO with two degrees of freedom is utilized to demonstrate the accuracy of the amplitude-dependent aerodynamic derivative-based model. The model also applies to single-degree-of-freedom LCOs, e.g., galloping and vortex-induced vibration, and hence it may serve as a unified analysis framework for nonlinear bridge aeroelasticity. [ABSTRACT FROM AUTHOR]

This paper presents an analog-assisted (AA) output-capacitor-free digital low-dropout (D-LDO) regulator with tri-loop control. For responding to instant load transients, the proposed high-pass AA loop momentarily adjusts the unit current of the power switch array, and significantly reduces the voltage spikes. In the proposed D-LDO, the overall 512 output current steps are divided into three sub-sections controlled by coarse/fine loops with carry-in/out operations. Therefore, the required shift register (SR) length is reduced, and a 9-bit output current resolution is realized by using only 28-SR bits. Besides, the coarse-tuning loop helps to reduce the recovery time, while the fine-tuning loop improves the output accuracy. To eliminate the limit cycle oscillation and reduce the quiescent current, a freeze mode is added after the fine-tuning operation. To reduce the output glitches and the recovery time, a nonlinear coarse word control is designed for the carry-in/out operations. The D-LDO is fabricated in a 65-nm general purpose CMOS process. A maximum voltage undershoot/overshoot of 105 mV is measured with a 10-mA/1-ns load step and a total capacitor of only 100 pF. Thus, the resulting figure-of-merit is 0.23 ps. [ABSTRACT FROM AUTHOR]

The digital low dropout regulator (D-LDO) has drawn significant attention recently for its low-voltage operation and process-scalability. However, the D-LDO inherently suffers from limit cycle oscillation (LCO). To address this issue, the modes and amplitudes of LCO are calculated in this work and verified by SPICE simulation in a 65-nm CMOS process. An LCO reduction technique for the D-LDO is then proposed, by adding two unit power transistors in parallel with the main power MOS array as a feedforward path. This technique sets the LCO mode to 1 and effectively reduces the ripple amplitude for a wide (0.5–20 mA) load current range. When compared with the dead-zone scheme, this technique minimizes LCO with negligible circuit complexity and design difficulty. [ABSTRACT FROM AUTHOR]

This paper provides insights into the stability of flexible orthotropic rectangular plates in supersonic flow by revealing the amplitude-speed dependency behavior for such panels in precritical and postcritical flight conditions. Flutter and postflutter behaviors are discussed to highlight the important effect of the structural and aerodynamic nonlinearities inherently present for panels in high-speed flows. The influence of transversal shear on stability is also illustrated. Depending on the plate's geometrical parameters, soft- and hard-type flutter behaviors are possible, and a graphical interpretation is provided along with pertinent conclusions. [ABSTRACT FROM AUTHOR]

Smart skin structures are analyzed for thermal stability behaviors and limit cycle oscillations in supersonic range of airflows. The skin is made up of multi-layered sandwich panel using carbon/epoxy, glass/epoxy, and dielectric polymer layers. And the model is based on the first-order shear deformation plate theory, and von Karman strain-displacement relationships are used to consider the moderate geometrical nonlinearity of the structure. In order to study the effects of the airflow, first-order piston theory is adopted to represent the pressures. Also, Newmark time integration method is applied to obtain the numerical results in this work. To check the validity of present outcomes, results are compared with previous data. Specifically, the stability boundaries are obtained for various ranges of temperatures and aerodynamic pressures. Then, the regions for buckling, post-buckling, dynamic instability, and limit cycle oscillation of the structures are clearly discussed. For more analysis, the smart skin is investigated for the different sizes and shapes of dielectric portion within enclosure layer in detail. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the nonlinear aeroelastic behavior of functionally graded plates is studied in supersonic flow. For this purpose, the von Karman strains and piston theory have been employed to model structural nonlinearity and quasi-steady aerodynamic panel loading, respectively. The material properties of the plate are assumed to be graded continuously in the direction of thickness. The variation of the properties follows a simple power-law distribution in terms of the volume fractions of constituents. The Hamilton’s principle is used to construct the coupled nonlinear partial differential equations of motion. The derived equations are transformed into a set of coupled ordinary differential equations using the Galerkin method and then solved by numerical time integration. It is found that the use of functionally graded materials greatly changes the flutter behavior of the plate especially in post-flutter region. [Copyright &y& Elsevier]

In this paper we present, the design and modeling of the novel nonlinear limiter control feedback control plant [Myneni et al., 1999; Corron et al., 2000; Corron & Pethel, 2002], applied for the first time here in an aeroelastic system, and actuated as a jet reaction torquer control of a wing with potentially chaotic dynamics. This study will provide a better understanding of the nonlinear dynamics of the open/closed-loop aeroelasticity of flexible wings with either steady or unsteady aerodynamic loads. The limiter control can be applied to either the plunging or pitching characteristic of the wing or to both of them. We show that the control can effectively suppress Limit Cycle Oscillations (LCO) and chaos well beyond the nominal flutter speed. This could lead to a practical implementation of the control mechanism on actual and future generation aircraft wings via implementation of a combination of propulsive/jet type forces, micro surface effectors and fluidic devices. Analysis of this control produced favorable results in the suppression of LCO amplitude and increased flutter boundaries for plunging and pitching motion. The limiting control has asymptotically zero power, and is simply implemented, making it a feasible solution to the problem of the chaotic dynamics of the oscillating airfoil. [ABSTRACT FROM AUTHOR]

Abstract: We show that a cascade of resonance captures constitutes the triggering mechanism of limit cycle oscillations (LCOs) due to aeroelastic instability of rigid wings in flow. We consider a two-degree-of-freedom (2-dof) wing model in subsonic flow with cubic nonlinear stiffnesses at the support. Under the assumption of quasi-steady aerodynamics, we apply a complexification/averaging technique to express the dynamics of fluid–structure interactions in terms of three fast-frequency components; these are the two linear natural frequencies corresponding to heave and pitch, and a super-harmonic at three times the pitch frequency. Bifurcation analysis of the resulting set of modulation equations governing the slow dynamics is carried out via the method of numerical continuation, and reveals the different types of steady state motions realized as parameters vary. It turns out that the LCO triggering mechanism consists of a combination of different dynamic phenomena, taking place at three main stages or regimes: attraction to transient resonance captures (TRCs), escapes from these captures and, finally, entrapments into permanent resonance captures (PRCs). We examine numerically and analytically the dynamics at each of these stages by means of wavelet transform analysis, study of the evolution of appropriately defined phase variables in projections of the phase space of the dynamics, and analysis of instantaneous energy exchanges between the various nonlinear modes involved. The general conclusion is that an initial excitation of the heave mode by the flow acts as the triggering mechanism for the excitation of the pitch mode through nonlinear interactions resulting from the resonance captures and escapes. The eventual excitation of the pitch mode signifies the appearance of an LCO of the in-flow wing. [Copyright &y& Elsevier]

• A unified model for geometrically nonlinear aeroelasticity of plates is presented. • Supersonic flow is captured by using the first order piston theory. • Bifurcation plots for aeroelastic VSCL plates are given for the first time. • Effects of fiber path, taper ratio and skew angle are studied. [Display omitted] Aeroelastic stability of tapered/skew variable stiffness composite cantilevered plates are considered in the current study at flutter and post-flutter regions. The variable stiffness behavior is obtained by altering the fiber angles continuously according to a selected curvilinear fiber path function in the composite laminates. Flutter speed, limit cycle oscillations (LCOs), and bifurcation diagrams of tapered/skewed plates are obtained at two different fiber path functions. Nonlinear structural model is utilized based on the virtual work principle. Fully nonlinear Green's kinematic strain relations are used to account for the geometric nonlinearities and the first order shear deformation theory (FSDT) is employed to generalize the formulation for the case of moderately thick plates including transverse shear effects. One prominent target of the present study is to determine how the variable stiffness parameters affect the nonlinear behavior. Consequently, one may find the best fiber path with improved flutter and post-flutter characteristics for tapered/skew plates in supersonic flow. First order linear piston theory is used to model the aerodynamic loading. In order to get a reliable solution, the Generalized Differential Quadrature (GDQ) method is employed. Moreover, time integration of the equations of motion is carried out using the Newmark's average acceleration technique. It will be shown that taperness/skewness as well as variable stiffness lamination parameters have significant effects on the aeroelastic stability margins. In addition, the post-critical behavior is found to be periodic or quasi-periodic at all the presented simulations with no specific route to chaos. [ABSTRACT FROM AUTHOR]

In the present study, nonlinear panel flutter and bifurcation behavior of functionally graded ceramic/metal wing-like tapered and skewed plates are investigated. Porosities are distributed over the cross-section of the functionally graded structure. The flutter speed, limit cycle oscillations, and bifurcation diagrams of the functionally graded plate with two types of geometrical non-uniformities being skewness and taperness are explored. Nonlinear structural model is utilized based on the virtual work principle by including the von-Karman nonlinear kinematic strain assumption. The first order shear deformation theory is employed to consider the transverse shear effect in the structural model. First-order linear piston theory is used to model the aerodynamic loading while the generalized differential quadrature method is employed to solve the governing equations of motion. Time integration of the final ordinary equations of motion is carried out using the Newmark average acceleration method. Different volume fractions are investigated to enhance the flutter instability margins and post-flutter behavior of functionally graded plates. Results demonstrate that the volume fraction and porosity coefficients have significant effects on dynamic behavior and limit cycle oscillation amplitudes. • Results demonstrate that the volume fraction and porosity coefficient have significant effects on the dynamic behavior and LCOs of the FG plates. • LCO characteristics of FG ceramic/metal and porous plates in supersonic flow are determined by bifurcation diagrams. Three volume fraction exponents of FG plate along with two types of porosity distributions are studied to investigate the subcritical and supercritical behaviors for the FG cantilevered plates. • This is the first bifurcation analysis of functionally graded wing-like plates with complex geometries, skewback angles, taper ratio in conjunction with two porosity distributions. It is the first time that the effect of porosity is investigated on the post flutter behavior of the FG plates using bifurcation diagrams. All previous studies of FG porous plates are focused on the linear aeroelastic analysis. [ABSTRACT FROM AUTHOR]

A quantitative analysis of the wind-induced post-critical performance of bridge decks is presented in order to highlight the underlying wind-resistant capacity after the critical wind speeds. Two simple indices, i.e., the wind speed extension (after the critical state) with acceptable post-critical vibrations and the relative post-critical capacity (i.e., the ratio between the aforementioned wind speed extension and the critical speed value), are utilized to quantify the post-critical performance of bridge decks. A short review on available limit states of vibration in literatures and design codes is presented in order to define a suitable threshold for acceptable post-critical vibrations. The post-critical performances of three typical cross-sections are quantitatively analyzed with the proposed indices, in which the limit states of vibration are reasonable defined considering either structural normal operation or structural safety. The effects of various mechanical and aerodynamic properties (e.g., mechanical damping ratio, natural frequency, initial angle of attack, and aerodynamic derivatives) on the post-critical behaviors of the selected cross-sections are highlighted. The quantitative analysis of the post-critical performance in the present work may deepen the understanding of the wind-resistant performance of bridges and potentially serve as a building block for a more economic wind-resistant design framework for future long-span bridges. • Limit states of vibration for bridge decks are briefly reviewed to define a suitable threshold for post-critical vibration. • Two simple indices are introduced to quantify post-critical performance of bridge decks. • Effects of various mechanical and aerodynamic properties on post-critical performances of three cross-sections are analyze. • The indices potentially serve as criteria in a more economic wind-resistant design framework for future long-span bridges. [ABSTRACT FROM AUTHOR]