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The article examines bifurcation and continuation in linear flutter equations. Topics covered include an example showing the possibility of bifurcation in linear frequency-domain flutter analyses, detection of bifurcations and branching from bifurcations and the conditions necessary for a simple bifurcation including the change in the orientation of the curve and one rank deficiency in the Jacobian positive discriminant.

The article presents a study of the adjoint sensitivity of unsteady low-speed flows using an efficient time-spectral harmonic balance approach. The study used a finite-difference approach to assess the accuracy of the adjoint senstivities. It suggests that the cost can be up to 3-5 times the cost of a single computational fluid dynamics (CFD) run when the number of design variables is in hundreds.

Motivated by a benchmark NASA experiment in 1992, the spatiotemporal, nonlinear, acoustic fluid-structure interaction of a two-dimensional panel in an inviscid compressible fluid is numerically investigated. The numerical coupling between the quadratic Euler fluid field and the acoustically excited viscoelastic panel with a cubic nonlinearity is obtained via a loose-coupling approach with grid adaption. Simulations reveal an intricate bifurcation structure near the fifth-mode panel resonance that includes coexisting symmetric and asymmetric periodic solutions. Furthermore, the emergence of a nonstationary, chaoticlike, spatiotemporal solution is established as an outcome of orbital stability loss of an m]n = 3/2 ultrasubharmonic response. It is also noted that the biharmonic acoustic input of the Maestrello experiment reveals distinct sum and difference frequency combination resonances that yield spatially stationary periodic and quasi-periodic panel dynamics. The former incorporates a combined interplay of third- and sixth-mode spatial responses, whereas the latter exhibits a significant widebanded spectral content at half of the fundamental exciting frequency corresponding to a combination resonance between the fifth-mode subharmonic and a superharmonic of the seventh mode. The scattered pressure field reveals a complex wave pattern in the acoustic near field, which becomes less significant with increasing distance from the panel. [ABSTRACT FROM AUTHOR]

Piezoelectric-based resonance frequency detuning can alleviate unwanted vibration of turbomachinery blades, thus reducing the dangers of high-cycle fatigue while also decreasing the blade weight. This semiactive approach applies to structures that are subjected to frequency-sweep excitation and involves altering the structural stiffness (here, by switching the piezoelectric electrical boundary conditions) to avoid a resonant condition, thus limiting the blade response. Detuning requires two switches per resonance/excitation frequency crossing, including a switch back to the original the original state, many fewer than other semiactive approaches that require four switches per cycle of vibration. Resonance frequency detuning applies to any mode of vibration with a positive electromechanical coupling coefficient, and it provides the greatest normalized vibration reduction for slow sweeps, low damping, and high coupling coefficient. Yet even for a moderate sweep rate α = 10-4 and modal damping ζ = 0.1%, optimally detuning a structure with an electromechanical coupling coefficient k² = 10% provides the same vibration reduction as increasing either the sweep rate or modal damping by an order of magnitude. With a lower sweep rate α = 10-5 and modal damping ζ = 0.01%, detuning with a coupling coefficient of only k² = 3% provides equivalent vibration reduction as an order of magnitude increase in sweep rate or modal damping. [ABSTRACT FROM AUTHOR]

The article describes an aerodynamic formulation for estimating the aerodynamic loads on a blade in a cascade of cambered airfoils which is based on D. S. Whitehead's aerodynamic theory for cascade of flat plates. Topics covered include the dependence of aerodynamic clamping on the tip clearance gap, determination of blade stability and the overlapping of flutter velocities in the bending mode and torsional mode at frequency ratios near unity.

This paper presents a vibration control strategy based on the passive piezoelectric shunt damping technique for mistuned bladed disks. Resonant shunted piezoelectrics are attached onto the disk surface between adjacent blades to dissipate the mechanical energy. This strategy is of engineering interest because piezoelectric transducers are placed outside of the main stream in turbomachinery. This idea is developed based on a lumped-parameter bladed disk model. Both piezoelectric shunt damping and piezoelectric mistuning are introduced to minimize the blade mistuning effect. First, a tuning design is carried out to damp a specified mode for the tuned bladed disk. When blade mistuning is taken into account, a further vibration reduction is achieved by introducing an optimal piezoelectric mistuning pattern obtained by a genetic algorithm. In reality, the blade mistuning pattern is not constant in the long run. Because of various complexities, a perturbation of the blade mistuning pattern might result. In benefitting from the manageability and controllability of piezoelectric shunt circuits, an adaptive control strategy is developed to adjust the "optimal" piezoelectric mistuning pattern according to the perturbation. Numerical simulation reveals that good performance is achieved in terms of reducing the vibration of slowly time-variant, mistuned bladed disks. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to analyze and discuss the performance and stability of a tailless micro aerial vehicle with flexible articulated wings. The dihedral angles can be varied symmetrically on both wings to control the aircraft peed independently of the angle of attack and flight-path angle, while an asymmetric dihedral setting can be used to control yaw in the absence of a vertical tail. A nonlinear aeroelastic model is derived, and it is used to study the steady- state performance and flight stability of the micro aerial vehicle. The concept of the effective dihedral is introduced, which allows for a unified treatment of rigid and flexible wing aircraft. It also identifies the amount of elasticity that is necessary to obtain tangible performance benefits over a rigid wing. The feasibility of using axial tension to stiffen the wing is discussed, and, at least in the context of a linear model, it is shown that adding axial tension is effective but undesirable. The turning performance of an micro aerial vehicle with flexible wings is compared to an otherwise identical micro aerial vehicle with rigid wings. The wing dihedral alone can be varied asymmetrically to perform rapid turns and regulate sideslip. The maximum attainable turn rate for a given elevator setting, however, does not increase unless antisymmetric wing twisting is employed. [ABSTRACT FROM AUTHOR]

A reduced order model (ROM) of linearized compressible fluid flow coupled with a von Kármán plate is developed. Separate ROMs for both the fluid and structure are derived and are coupled through a solid wall boundary condition at the interface boundary. The structural ROM is formulated using the method of quadratic components, which postulates that the full kinematics of the plate can be represented using linear and quadratic terms. The fluid ROM is constructed via a proper orthogonal decomposition method. Both ROMs are further reduced via a Galerkin discretization, and the coupled system is implicitly integrated in time. The coupled model is subsequently compared with previously validated models that used either a linearized plate model with the linearized compressible fluid model or a quasi-static fluid model with the von Kármán plate model. The comparisons are conducted in high-Mach-number regimes where the comparison is admissible, and excellent agreement is found. Analysis of the resulting limit cycles shows two sets of discontinuities in the limit cycle amplitudes. These discontinuities have two salient features: a snap through phenomenon in phase space is observed in the higher modes, and the coalescing of several of the lower modes is observed below the critical dynamic pressures followed by a sudden separation above the critical dynamic pressures. [ABSTRACT FROM AUTHOR]

Nonlinearities can be present in an aeroelastic system because of some aerodynamic factors that occur in transonic flight regimes or at a large angle of attack. The sources are shock wave motions and separated flows. Complex aeroelastic problems due to the aerodynamic nonlinearity can be studied using high-fidelity computational fluid dynamics (CFD) codes. However, the computational cost may be very high. Hence, this kind of problem is conveniently solved using the reduced-order model (ROM) for unsteady aerodynamic analysis. Many studies have been done using reduced-order modeling for aeroelastic analysis. However, most of the reduced-order aerodynamic models are dynamic linear models and have loads proportional to the structural motions. In the current paper, a nonlinear unsteady reduced-order aerodynamic model is constructed using the radial basis function neural network model. This kind of ROM is used to analyze the limit cycle oscillation (LCO) for two linear structural models with large shock motions in transonic flow. Unlike the input signals in the traditional design method, the signals of the self-excited vibration of the aeroelastic system are designed as the input signals in the current paper. Coupling the structural equations of motion and nonlinear aerodynamic ROM, the system responses are determined by time marching the governing equations using a hybrid linear multistep algorithm. Then, the LCO change with velocities (dynamic pressure) was analyzed. The two transonic aeroelastic examples show that both the structural responses and the LCO characteristics simulated using the nonlinear ROM agree well with those obtained using the direct CFD method. Moreover, the computational efficiency of the nonlinear ROM-based method is improved by one to two orders of magnitude compared with that of the direct CFD method. [ABSTRACT FROM AUTHOR]

The article explains the use of algebraic method to compute eigensolution derivatives for symmetric and asymmetric systems with nonviscous damping. It describes the eigensolution derivatives for self-adjoint and nonself-adjoint cases. The derivatives of eigenvalues and their associated eigenvectors in systems with nonviscous damping are described.

Qualitative changes can occur in the dynamics of nonlinear systems even for small parameter variations. Such changes are manifestations of bifurcation in dynamical systems. In the context of differential game theory, bifurcations offer insights into the underlying mechanisms driving strategic interactions and identify transitions between different types of behavior. Such critical transitions are tipping points that can dramatically change the outcomes of the game. This work explores the possibility of predicting such qualitative shifts, including supercritical Hopf bifurcations, before they occur using a data-driven forecasting technique. This concept is demonstrated for an attacker-defender game in a limited resource scenario and for an active cybersecurity defense game. The time histories of the system dynamics as it approaches a bifurcation allow one player to detect the existence of bifurcations. This capability provides that player insights into the dynamics of the game and potential defense mechanisms in resource-constrained scenarios., Competing Interests: Declarations. Competing interests: The authors declare no competing interests., (© 2024. The Author(s).)

Synaptic deficiencies are a known hallmark of neurodegenerative diseases, but the diagnosis of impaired synapses on the cellular level is not an easy task. Nonetheless, changes in the system-level dynamics of neuronal networks with damaged synapses can be detected using techniques that do not require high spatial resolution. This paper investigates how the structure/topology of neuronal networks influences their dynamics when they suffer from synaptic loss. We study different neuronal network structures/topologies by specifying their degree distributions. The modes of the degree distribution can be used to construct networks that consist of rich clubs and resemble small world networks, as well. We define two dynamical metrics to compare the activity of networks with different structures: persistent activity (namely, the self-sustained activity of the network upon removal of the initial stimulus) and quality of activity (namely, percentage of neurons that participate in the persistent activity of the network). Our results show that synaptic loss affects the persistent activity of networks with bimodal degree distributions less than it affects random networks. The robustness of neuronal networks enhances when the distance between the modes of the degree distribution increases, suggesting that the rich clubs of networks with distinct modes keep the whole network active. In addition, a tradeoff is observed between the quality of activity and the persistent activity. For a range of distributions, both of these dynamical metrics are considerably high for networks with bimodal degree distribution compared to random networks. We also propose three different scenarios of synaptic impairment, which may correspond to different pathological or biological conditions. Regardless of the network structure/topology, results demonstrate that synaptic loss has more severe effects on the activity of the network when impairments are correlated with the activity of the neurons.

The interaction between nonlinearity and seasonal forcing in childhood infectious diseases often leads to multiyear cycles with large amplitude. Regular biennial cycles in particular were observed in measles reports throughout the world. The objective of this paper is to understand the mechanism of such biennial cycles, especially the conditions under which the large amplitude biennial oscillation might appear. It is proposed that such biennial cycles are caused by parametric resonance, which might occur when varying the parameter at a frequency close to twice the natural frequency of the system. The analysis is carried out by solving an SIR model semi-analytically using method of multiple scales (MMS). This analysis shows how parametric resonance occurs due to the interaction between nonlinearity and periodic forcing. Using the MMS solution, the boundary between the resonance region and the non-resonance region in the parameter space is obtained. The effects of different parameters on the triggering of parametric resonance are studied, such as transmission rate, recovery rate, birth rate and amplitude of seasonality. The effects of stochasticity on the onset of parametric resonance are also studied., (Copyright © 2016 Elsevier Ltd. All rights reserved.)