Optimum design of electrodynamic shaker’s support spring to improve low frequency performance

The purpose of the present study is to improve the conventional electrodynamic shaker’s performance at low frequency through the optimization of its support spring. It is acknowledged that to improve its low frequency performance, a shaker’s support spring has to be lightweight and simultaneously of high lateral but low axial rigidity. Meanwhile it should have few resonance points in the useable frequency range. But both experimental modal analysis (EMA) and finite element analysis (FEA) in this study indicated that of the support spring of conventional shaker presents undesirable humps in its frequency response (FR) in low frequency area. The first order resonance frequency of the shaker (whose value decides the minimum of the shaker’s useable frequency range) also turned out big. Hence a new support spring plate of laminated composite structure embedded with viscoelastic damping material is proposed in this study whose parameter values are further optimized. The optimization adopts damping thickness, angle and thickness of composite layer as the design variables. It targets at achieving minimum weight while satisfying the shaker’s first order elastic natural frequency and the plate’s intensity. The optimized support spring plate is then put to frequency response analyses. The findings indicate that it not only can suppress the humps in low frequency area, but also widens the shaker’s useable low frequency range. Meanwhile it reduces the shaker’s additional rigidity on the test object. Hence it can ensure the shaker’s performance at low frequency

Stability and local bifurcation analysis for a nonlinear coupled helicopter blade-absorber system via normal form method

Consider the effect of nonlinear spring and linear viscous damping in structure, the motion equations of a helicopter blade-absorber system has been established by Lagrange equation. Since the helicopter blade-absorber system exists motion coupling, the inertia and stiffness terms of equations are decoupled via equivalent principal coordinate transformation. The stability and local bifurcation behaviors of the principal coordinate equations are investigated with the aid of multiple scales method and normal form theory. Two kinds of critical points for the bifurcation response equations near the combination resonance are considered, which are characterized by a pair of purely imaginary eigenvalues and double zero eigenvalues. The Hopf bifurcation solution, bifurcation path, and transition curves of the model are investigated respectively. For each case, the numerical results obtained by Runge-Kutta method coincide with the analytical predictions. These results may provide some guidance for parameter design of helicopter blade-absorber system

Molecular Dynamics in a Grand Ensemble: Bergmann-Lebowitz model and Adaptive Resolution Simulation

This article deals with the molecular dynamics simulation of open systems that can exchange energy and matter with a reservoir; the physics of the reservoir and its interactions with the system are described by the model introduced by Bergmann and Lebowitz.Despite its conceptual appeal, the model did not gain popularity in the field of molecular simulation and, as a consequence, did not play a role in the development of open system molecular simulation techniques, even though it can provide the conceptual legitimation of simulation techniques that mimic open systems. We shall demonstrate that the model can serve as a tool to devise both numerical procedures and conceptual definitions of physical quantities that cannot be defined in a straightforward way by systems with a fixed number of molecules. In particular, we discuss the utility of the Bergmann-Lebowitz (BL) model for the calculation of equilibrium time correlation functions within the Grand Canonical Adaptive Resolution method (GC-AdResS) and report numerical results for the case of liquid water.Comment: 31 pages, 6 figure

Optimum design of new high strength electrodynamic shaker in broad work frequency range

The purpose of the present study is to improve the performance of conventional high strength electrodynamic shaker. With dual armature structure, the shaker can produce strong output force. But both experimental modal analyses and finite element analyses carried out in this study indicate the structure leads to undesirable hump in its work frequency range. Hence a new shaker with single-skeleton dual coils is proposed whose shape is further optimized. The optimization adopts auxiliary boundary shape method to simulate the skeleton boundary and targets at achieving minimum weight while satisfying the first order elastic natural frequency. Then the optimized shaker is put to frequency response analyses which indicate that while maintaining the high output force of conventional shaker, the new shaker eliminates steep hump in frequency response, expands work frequency range and reduces the influence of additional mass loading of the shaker on the test object. Hence it effectively solves the flaws of the conventional high strength electrodynamic shaker

Is there a third order phase transition for supercritical fluids?

We prove that according to Molecular Dynamics (MD) simulations of liquid mixtures of Lennard-Jones (L-J) particles, there is no third order phase transition in the supercritical regime beyond Andrew's critical point. This result is in open contrast with recent theoretical studies and experiments which instead suggest not only its existence but also its universality regarding the chemical nature of the fluid. We argue that our results are solid enough to go beyond the limitations of MD and the generic character of L-J models, thus suggesting a rather smooth liquid-vapor thermodynamic behavior of fluids in supercritical regime.Comment: 13 pages, 6 figure

Effect of engine thrust on nonlinear flutter of wings

The propulsion of wing-mounted engine is a typical follower force and may cause significant influences upon wing flutter characteristics. An integrated flutter analysis method has been presented, within which the effects of engine thrusts and geometrical nonlinearities are both considered. Firstly the method has been applied to evaluate the effects of thrusts on the flutter boundary of a high-altitude, long-endurance aircraft wing. The numerical results have an excellent agreement with the published ones. Furthermore the finite element model of a wing carrying two engines has been established, and the influences of propulsion magnitude and position on wing flutter speed are mainly investigated. The results indicated that the effects of engine thrusts are indispensable for wing flutter analysis

Identification of second-order kernels in aerodynamics

Volterra series is one of the powerful system identification methods for representing the nonlinear dynamic system behavior. The methods of step response and impulse response are commonly applied to a discrete aerodynamic Computational Fluid Dynamic (CFD) to identify the first- and second-order Volterra kernels. A critical problem, however, is the difficulty of identifying the second-order Volterra kernels correctly in CFD-based method. In this paper the second-order Volterra kernel function is expanded in terms of Chebyshev functions to reduce the size of the problem and the accuracy of the identification is also improved based on a third-order reduced model of Volterra series

Model validation of aeroelastic system for robust flutter prediction

The problems of uncertainty modeling and model validation of aeroelastic system are investigated. The parametric uncertainty is considered to denote the uncertainties in structure, and both parametric form and unmodeled dynamics are used to represent the influences and mechanism of uncertainties in unsteady aerodynamic forces. The Linear Fractional Transformation representation of the uncertain aeroelastic system is established to perform model validation and robust flutter analysis. A testing method for the existence of a validating model set in frequency-domain is developed, then the model validating sets are parameterized and the problem of searching the uncertainty magnitudes can be formulated as an optimization process. The influence of exogenous disturbances and noise, which are inevitable in actual testing environment and commonly unknown but energy bounded is considered, and consequently the conservatism of the uncertainty bounds is reduced. At last, for the uncertain aeroelastic system with the obtained uncertainty magnitudes, the robust flutter analysis based on structured singular value theory is performed to predict the robust stability boundary. The comparison of the results associated with two different uncertainty descriptions and the influences of disturbance and noise are discussed. Two numerical examples are presented and the results of the simulation demonstrate the validity of the developed method

Identification of piecewise linear aeroelastic systems

The work presented in this paper is concerned with the identification of a piecewise linear aeroelastic system from input-output data. The main challenge with this problem is that the data are available only as a mixture of observations generated by a finite set of different interacting linear subsystems such that one does not know a prior which subsystem has generated which data, that is, the switching points of the freeplay nonlinearity. The linear part of the nonlinear aeroelastic system is represented by the orthonormal basis functions constructed by the physical poles of the linear part, and the nonlinear part is represented by a Hammerstein model. By a simple rearrangement of the data corresponding to the degree-of-freedom of freeplay and selecting a segment of the data, the identification of the physical poles could be reduced to a linear parametric problem. Afterwards, estimates of the unknown parameters of linear regression models are calculated by processing respective particles of input-output data. The iterative sequence of the switching points is constructed, and solved by a method synthesizing the non-iterative and iterative algorithms. Then the parameters of the linear and nonlinear parts of the nonlinear system including the switching points are successfully obtained. A two-dimensional airfoil with nonlinear structural freeplay in the pitch degree-of-freedom is presented to demonstrate the validity of the proposed identification algorithm

Stability and local bifurcation analysis for a nonlinear coupled helicopter blade-absorber system via normal form method

Consider the effect of nonlinear spring and linear viscous damping in structure, the motion equations of a helicopter blade-absorber system has been established by Lagrange equation. Since the helicopter blade-absorber system exists motion coupling, the inertia and stiffness terms of equations are decoupled via equivalent principal coordinate transformation. The stability and local bifurcation behaviors of the principal coordinate equations are investigated with the aid of multiple scales method and normal form theory. Two kinds of critical points for the bifurcation response equations near the combination resonance are considered, which are characterized by a pair of purely imaginary eigenvalues and double zero eigenvalues. The Hopf bifurcation solution, bifurcation path, and transition curves of the model are investigated respectively. For each case, the numerical results obtained by Runge-Kutta method coincide with the analytical predictions. These results may provide some guidance for parameter design of helicopter blade-absorber system