Fictitious Mass Method Research Articles

Three dimensional aeroelastic analyses considering free-play nonlinearity using computational fluid dynamics/computational structural dynamics coupling

Most of the previous studies on free-play aeroelasticity were based on the linear aerodynamic theory, which cannot consider the aerodynamic nonlinear effects. This paper proposes a framework of computational fluid dynamics/computational structural dynamics (CFD/CSD) coupling approach that can deal with the three dimensional aeroelastic problems with both the free-play nonlinearity and the aerodynamic nonlinearity. The fictitious mass method is used to construct the reduced structural equations of motion and the switching point is detected using the bisection method. The adaptive time step obtained by the bisection method is returned to the CFD solver so that both the structural and the fluid equations are integrated using the same time step. An all-movable wing with free-play at the root is considered for numerical studies. Results demonstrate the CFD/CSD coupling method can predict the stable limit cycle oscillation (LCO) effectively. The initial condition study shows that the LCO behavior is subcritical and the hysteresis response can be predicted in time domain effectively by the presented method. The viscous effect is shown to increase the LCO boundary and shift the LCO amplitude to a larger velocity in transonic regime. The LCO boundary is determined from subsonic to transonic Mach numbers. The transonic dip in LCO boundary is found by the CFD/CSD coupling method, but the equivalent linearization with doublet lattice method fails to predict this phenomenon. From the results of this study, the LCO boundary is shown to be 43.5% below the flutter boundary at most.

Obtaining Hartree–Fock and density functional theory doubly excited states with Car–Parrinello density matrix search

The calculation of doubly excited states is one of the major problems plaguing the modern day excited state workhorse methodology of linear response time dependent Hartree-Fock (TDHF) and density function theory (TDDFT). We have previously shown that the use of a resonantly tuned field within real-time TDHF and TDDFT is able to simultaneously excite both the alpha and beta electrons to achieve the two-electron excited states of minimal basis H(2) and HeH(+) [C. M. Isborn and X. Li, J. Chem. Phys. 129, 204107 (2008)]. We now extend this method to many electron systems with the use of our Car-Parrinello density matrix search (CP-DMS) with a first-principles fictitious mass method for wave function optimization [X. Li, C. L. Moss, W. Liang, and Y. Feng, J. Chem. Phys. 130, 234115 (2009)]. Real-time TDHF/TDDFT is used during the application of the laser field perturbation, driving the electron density toward the doubly excited state. The CP-DMS method then converges the density to the nearest stationary state. We present these stationary state doubly excited state energies and properties at the HF and DFT levels for H(2), HeH(+), lithium hydride, ethylene, and butadiene.

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The aeroelastic characteristics of a wing with control surface freeplay are investigated. The transonic small disturbance equation is used for unsteady aerodynamic forces in subsonic/transonic region. The fictitious mass method is introduced to apply a modal approach to nonlinear structural models. Nonlinear aeroelastic time responses are calculated by the coupled time integration method. Using these methods, an efficient aeroelastic analysis is achieved for aerodynamic and structural nonlinearities simultaneously. The effects of the aerodynamic nonlinearity, initial flap amplitude, and freeplay magnitude in aeroelastic characteristics are investigated in this study. 섂돀좽?⨀塨?⨀炏?⨀餂돐졠잖⨀䡙잖⨀颏?⨀뤁뎀／ࠀ?⨀礁덐态Ȁ顲ꂪᡳꂪĀā?뤀댐჏?⨀ޚ䜄僈?⨀䀠ゾ?⨀䂾?⨀Ă逐煥獣愠獵扨敡瀀ｿｿｿｿ壑?⨀壑?⨀ꤠ돀좽?⨀塨?⨀ࠏ?⨀脠돐ꡙ잖⨀ꡙ잖⨀』?⨀夠뎐／ࠀꡢ잖⨀愁덀态Ȁ�嚛研嚛Āā?

Component Mode Synthesis of a Vehicle System Model Using the Fictitious Mass Method

Abstract A new procedure for dynamic analysis of complex structures, based on the fictitious-mass component mode synthesis method, is presented. Normal modes of separate components are calculated by finite-element analysis with the interface coordinates loaded with fictitious masses that generate local boundary deformations in the low-frequency modes. The original fictitious-mass method is extended to include three types of component interconnections: displacement constraints, connection elements, and structural links. The connection elements allow the introduction of springs and dampers between the interface points without adding structural degrees of freedom. The structural links facilitate the inclusion the discrete finite-element representation of typically small components in the coupling equations. This allows a convenient treatment of loose elements and the introduction of nonlinear effects and parametric studies in subsequent analyses. The new procedure is demonstrated with the structural model of a typical vehicle with four major substructures and a relatively large number of interface coordinates. High accuracy is obtained in calculating the natural frequencies and modes of the assembled structure and the separate components with the fictitious masses removed. Dynamic response analysis of the vehicle travelling over a rough road, performed by modal coupling, is in excellent agreement with that performed for the full model.

Aeroelastic Analysis of a Wing with Freeplay in the Subsonic/Transonic Regions

An efficient aeroelastic analysis where both aerodynamic and structural nonlinearities are considered is performed. The analysis is based on the computational fluid dynamics (CFD) and computational structural dynamics (CSD) techniques in the time domain. Moving shock wave on the lifting surface, which is the aerodynamic nonlinearity in this study, is taken into account using the transonic small disturbance (TSD) equation. Freeplay, which is the local structural nonlinearity, is considered in the modal coordinate using fictitious mass method. The aeroelastic response results of a wing with freeplay are presented in the subsonic and transonic regions. Also, the effects of an airfoil thickness on the aeroelastic responses are investigated.

Nonlinear Aeroelastic Instability of a Supersonic Missile Wing. with Pitch Axis Freeplay

In this study, nonlinear aeroelastic characteristics of an supersonic missile wing with strong shock interferences are investigated. The missile wing model has a freeplay structural nonlinearity at its pitch axis. To practically consider the effects of freeplay structural nonlinearity, the fictitious mass method is applied to structural vibration analysis based on finite element method. Nonlinear aerodynamic flows with unsteady shock waves are also considered in supersonic flow regions. To solve the nonlinear aeroelastic governing equations including the freeplay effect, a modal-based coupled time-marching technique based on the fictitious mass method is used in the time-domain. Various aeroelastic computations have been performed for the nonlinear wing structure model. Linear and nonlinear aeroelastic analyses have been conducted and compared with each other in supersonic flow regions. Typical nonlinear limit cycle oscillations and phase plots are presented to show the complex vibration phenomena with simultaneous fluid-structure nonlinearities.

Reduced-Order Design-Oriented Stress Analysis Using Combined Direct and Adjoint Solutions

A new method for extracting accurate stress information from reduced-order structural and aeroelastic models is presented. The method has second-order accuracy when approximate reduced-order direct and adjoint solutions (based on different reduced-order bases) are used simultaneously to obtain approximate stresses. The method is applicable to both static and dynamic linear analysis. A review of four common methods for structural model order reduction [two variants of the mode displacement method (standard mode displacement and the fictitious mass method), the mode acceleration method, and the Ritz vector method] identifies sources of difficulty and causes of errors in stress behavior sensitivity calculations. Considerations used for selection of the reduced-order direct and adjoint bases are discussed. A series of static and dynamic test cases is used to assess accuracy of the new method in an analysis mode. Accuracy studies of sensitivity calculations follow. We hope to contribute to the field of design-oriented structural dynamics in terms of both insight and practice.

Flutter analysis for control surface of launch vehicle with dynamic stiffness

The root locus and iterative V- g method have been applied to analyze the flutter for a control surface of a launch vehicle with control actuators. The actuator is considered as a spring with dynamic stiffness. The fictitious mass method is adopted for an efficient modal flutter analysis. The methods are applied to the flutter analysis of a control wing with a pneumatic actuator at a rotating axis in the supersonic region. The effect of the sweep angle on the flutter characteristics of the wing with dynamic stiffness is investigated and is compared with that of the wings with several values of static stiffness.