Doublet-point Method Research Articles

Numerical investigation of the effects of compressibility on the flutter of a three-dimensional, cantilevered plate in an inviscid, subsonic, open flow

In this work we carry out a numerical study of the influence of the upstream Mach number on the flutter of a three-dimensional, cantilevered, flexible plate subject to a subsonic, inviscid, open flow. We have assumed a linear elastic model for the plate and that the fluid flow is governed by the linearized potential theory. The fluid equations are solved by means of a doublet point method to obtain the generalized aerodynamic forces as a function of the plate displacements. Then, these generalized forces are coupled to the equation of motion of the plate, which is discretized with a spectral Galerkin method, and an eigenvalue analysis is performed to find the flutter point. The obtained results are in good agreement with those of related theoretical and experimental studies found in the literature.

Applicability of a Bending Element with Four Nodes on Flutter Analysis of Wings Utilizing the Doublet-point Method and Finite Element Method

Applicability of a Bending Element with Four Nodes on Flutter Analysis of Wings Utilizing the Doublet-point Method and Finite Element Method

ワイヤで懸垂された平板のフラッタ実験と解析

This paper deals with the flutter experiments and analysis of a flat plate suspended by wires. In the flutter analysis, Doublet-point method based on unsteady lifting surface theory is used to calculate the unsteady fluid force acting on the plate surface. Moreover, flutter velocity and frequency are examined through the root locus of the flutter determinant of the system with changing flow velocity. These results compared with experimental results. The influence of the suspension angle on the flutter velocity, frequency, and mode are clarified.

非定常揚力面理論に基づく有限幅矩形シートの三次元フラッタ解析と風洞実験

This paper presents a three-dimensional flutter analysis of a rectangular sheet in an axial fluid flow. The unsteady fluid force acting on the sheet surface is calculated using Doublet-point method based on the unsteady lifting surface theory. The equation of motion of the sheet coupled with the fluid flow is derived employing the finite element method. The characteristic roots are obtained from the flutter determinant, and the stability of the system is examined with changing flow velocity. The flutter characteristics are clarified comparing the analytical results with wind-tunnel experiments. Lastly, the local work done by the unsteady fluid force on the sheet surface is shown, and the flutter mechanism is discussed.

ワイヤで支持された矩形シートの三次元フラッタ解析と風洞実験（偏心のフラッタ特性および発生条件への影響）

This paper deals with the flutter analysis of a rectangular sheet supported by a wire in axial flow. In the flutter analysis, Doublet-Point Method based on unsteady lifting surface theory is used to calculate the unsteady fluid force acting on the sheet surface. The equation of motion of the sheet supported by a wire with tension is derived by using the finite element method. Flutter velocity and mode are examined through the root locus of the flutter determinant of the system with changing flow velocity. In this study, experiments are conducted and compared with the analytical results. The flutter velocity, flutter mode and the local work done by the fluid force acting on the sheet surface are determined. Moreover, the influence of eccentricity on the flutter velocity is clarified.

J1050505 斜め方向から局所流を受けるウェブのフラッタ解析と実験

This paper deals with a flutter analysis and experimental study of a inclined web received local cross-flow. The unsteady fluid force acting on the web surface is calculated by using Doublet-point method, which is based on the unsteady lifting surface theory. The equation of motion of the sheet coupled with the fluid flow is derived by employing the finite element method. The stability of the system is examined by the characteristic roots obtained from the flutter determinant. The effects of inclination angle, non-dimensional tension, aspect ratio, cross-flow distance on the flutter velocity and mode are clarified. Moreover, the local work by the fluid force on the sheet surface, and instability mechanism are clarified.

S1650102 非定常揚力面理論に基づく矩形シートのフラッタ解析と風洞実験 : アスペクト比の影響([S165]柔軟媒体ハンドリング技術とプリンティング技術)

This paper deals with a flutter analysis of a rectangular flexible sheet subjected to axial fluid flow. The unsteady fluid force acting on the sheet surface is calculated by using Doublet-point method, which is based on the unsteady lifting surface theory. The equation of motion of the sheet coupled with the fluid flow is derived by employing the finite element method. The unsteady fluid force acting on the sheet surface is calculated by using Doublet-point method, which is based on the unsteady lifting surface theory. Moreover, flutter velocity and flutter frequency are measured in the experiment. The effects of the aspect ratio, mass ratio and direction of gravity on the flutter velocity and mode are clarified.

J0910201 非平面非定常揚力面理論に基づく長方形シェルのフラッタ解析と実験([J091-02]流体関連の騒音と振動(2))

This paper deals with flutter analysis of a rectangular shell based on the non-planar unsteady lifting surface theory. In this study, experiments are conducted with a cantilevered rectangular shell subjected to inner fluid flow, and vibration characteristic are examined. The unsteady fluid force acting on the shell surface is calculated by using Doublet-point method. The equation of motion of the shell coupled with the fluid flow is derived by employing the finite element method. The stability of the system is examined by using the root locus based on the complex eigenvalue obtained from the flutter determinant. The effects of the aspect ratio on the flutter velocity, frequency and mode are clarified.

Flutter and Divergence Characteristics of Composite Plate Wing

In the present work, an analytical investigation is introduced to determine the aeroelastic behavior of unswept, rectangular wings simulated by cantilevered composite plates using energy formulation and incompressible aerodynamic theory. Modified higher order shear deformation theory is used in the structural formulation. Doublet point method is used to solve the subsonic unsteady flow over the proposed rectangular wing. The flutter and divergence velocities are obtained using U-g method, which are validated by the analytical, finite element, wind tunnel test results available in the literature. The effect of composite fiber orientation on natural frequency, flutter and divergence speeds is discussed.

Effects of multiple structural nonlinearities on limit cycle oscillation of missile control fin

Aeroelastic analyses are performed for a 2-D typical section model with multiple nonlinearities. The differences between a system with multiple nonlinearities in its pitch and plunge spring and a system with a single nonlinearity in its pitch are thoroughly investigated. The unsteady supersonic aerodynamic forces are calculated by the doublet point method (DPM). The iterative V-g method is used for a multiple-nonlinear aeroelastic analysis in the frequency domain and the freeplay nonlinearity is linearized using a describing function method. In the time domain, the DPM unsteady aerodynamic forces, which are based on a function of the reduced frequency, are approximated by the minimum state approximation method. Consequently, multiple structural nonlinearities in the 2-D typical wing section model are influenced by the pitch to plunge frequency ratio. This result is important in that it demonstrates that the flutter speed is closely connected with the frequency ratio, considering that both pitch and plunge nonlinearities result in a higher flutter speed boundary than a conventional aeroelastic system with only one pitch nonlinearity. Furthermore, the gap size of the freeplay affects the amplitude of the limit cycle oscillation (LCO) to gap size ratio.

구조 비선형을 고려한 이차원 단면 날개 모델의 이중 제한 주기 운동

이선형 플런지 스프링을 가지는 2차원 단면 익형 모델에 대하여 초음속 비선형 공탄성 해석을 수행하였다. 초음속 비정상 공기력 계산을 위해 DPM을 사용하였고 최소상태접근법을 사용하여 근사하였다. 비선형 플러터 해석을 위해 구조 비선형성을 비대칭 이선형 스프링으로 모델링하고 기술 함수 법을 사용하여 선형화하였다. 선형 및 비선형 플러터 해석 결과들은 공력탄성학적 특성들이 주파수 비에 중요한 영향을 받는다는 것을 보여준다. 비선형 플러터 해석으로부터 다양한 제한 주기 운동이 선형플러터 속도 이하 또는 이상에서 관측되었다. 또한 플러터 특성과 응답을 시간영역에서도 조사하였다. Nonlinear aeroelastic characteristics of a two dimensional typical section model with bilinear plunge spring are investigated. Doublet-point method(DPM) is used for the calculation of supersonic unsteady aerodynamic forces which are approximated by using the minimum-state approximation. For nonlinear flutter analysis structural nonlinearity is represented by an asymmetric bilinear spring and is linearized by using the describing function method. The linear and nonlinear flutter analyses indicate that the flutter characteristics are significantly dependent on the frequency ratio. From the nonlinear flutter analysis, various types of limit cycle oscillations are observed in a wide range of air speeds below or above the linear flutter boundary. The nonlinear flutter characteristics and the nonlinear aeroelastic responses are investigated.

Nonlinear Aeroelastic Analysis of a Deployable Missile Control Fin

The nonlinear aeroelastic characteristics of a deployable missile control fin have been investigated. Modes from free vibration analysis and a doublet-point method are used for the computation of supersonic unsteady aerodynamic forces. The minimum-state approximation is used to approximate the aerodynamic forces. The fictitious mass modal approach is applied to reduce the problem size and the computation time in the linear and nonlinear flutter analyses. For the nonlinear flutter analysis, the deployable hinge is represented by an asymmetric bilinear spring and is linearized using the dual-input describing function method. From the nonlinear flutter analysis, three different types of limit-cycle oscillations are observed in the wide range of airspeed over the linear flutter boundary. The aeroelastic characteristics of the missile control fin can become more stable due to the existence of the deployable hinge nonlinearity.

Convergence of the Subsonic Doublet Point Method

2Han, J.-H., Tani, J., and Lee, I., “Flutter Suppression of a Lifting Surface Using Piezoelectric Actuation,” Proceedings of the Second AsianAustralasian Conference on Composite Materials, The Korean Society for Composite Materials, Daejeon, Korea, 2000, pp. 843–848. 3Heeg, J., “Analytical and Experimental Investigation of Flutter Suppression by Piezoelectric Actuation,” NASA TP-3241, Feb. 1993. 4Kersey, A. D., Davis, M. A., Patrick, H. J., LeBlanc, M., Koo, K. P., Askins, C. G., Putnam, M. A., and Friebele, E. J., “Fiber Grating Sensors,” Journal of Lightwave Technology, Vol. 15, No. 8, 1997, pp. 1442–1463. 5Kim, C. G., Kim, D. H., and Hong, C. S., “Development of FBG Sensor System for Measuring the High Frequency Vibration of Structures and the Natural Frequency of Composites,” US–Korea Joint Workshop on Smart Infra-Structural Systems, Smart Infra-Structure Technology Center, Daejeon, Korea, 2002, pp. 3–9. 6Lo, Y.-L., “In-Fiber Grating Sensors Using Interferometric Interrogating for Passive Quadrature Signal Processing,” IEEE Photonics Technology Letters, Vol. 10, No. 7, 1998, pp. 1003–1005. 7Youn, S.-H., Han, J.-H., and Lee, I., “Neuro-Adaptive Vibration Control of Composite Beams Subject to Sudden Delamination,” Journal of Sound and Vibration, Vol. 238, No. 2, 2000, pp. 215–231. 8Torri, H., and Matsuzaki, Y., “Flutter Margin Evaluation for DiscreteTime Systems,” Journal of Aircraft, Vol. 38, No. 1, 2001, pp. 42–47.

Flutter of Winged Reentry Space Vehicles Affected by an Elastic Attachment in Launching Configuration

This paper reports the flutter investigation of a winged reentry space vehicle having rotational modes in dynamic deflection due to an elastic attachment between a vehicle and a booster rocket. The elastic rotational mode is taken into consideration as an elastic rolling mode or an elastic yawing mode. Flutter experiments have been conducted in a transonic wind tunnel. The doublet-point method (DPM) is used to calculate flutter boundaries for this model. It is shown that an elastic rolling mode may lower the critical speed of anti-symmetric mode flutter because its existence alters the natural vibration mode of anti-symmetric bending which causes flutter. On the other hand, a coupling between an elastic yawing mode and an anti-symmetric bending one becomes critical in the different model.

Limit cycle oscillation of missile control fin with structural non-linearity

Non-linear aeroelastic characteristics of a deployable missile control fin with structural non-linearity are investigated. A deployable missile control fin is modelled as a two-dimensional typical section model. Doublet-point method is used for the calculation of supersonic unsteady aerodynamic forces, and aerodynamic forces are approximated by using the minimum-state approximation. For non-linear flutter analysis structural non-linearity is represented by an asymmetric bilinear spring and is linearized by using the describing function method. The linear and non-linear flutter analyses indicate that the flutter characteristics are significantly dependent on the frequency ratio. From the non-linear flutter analysis, various types of limit cycle oscillations are observed in a wide range of air speeds below or above the linear divergent flutter boundary. The non-linear flutter characteristics and the non-linear aeroelastic responses are investigated.

有翼宇宙往還機打ち上げ形態における結合部弾性モードが影響するフラッタ

This paper reports a flutter investigation of a re-entry space vehicle having an elastic rotational mode caused by its launching rocket. The elastic rotational mode is taken into consideration as an elastic roll mode or an elastic yaw mode. Flutter experiments were conducted in NAL Transonic Wind Tunnel. The DPM (Doublet-Point Method) is used to calculate flutter boundaries. It is shown that the elastic roll mode may lower critical flutter speed, because its existence alters the natural frequency of an anti-symmetric bending mode with which flutter occurs. A coupling between the elastic yaw mode and an anti-symmetric bending mode of a tip-fin wing is also shown to be critical.

이선형 비선형성을 포함하는 접는 미사일 조종날개의 공탄성 해석

Aeroelastic characteristics of a deployable missile control fin have been investigated. A deployable missile control fin is modeled by a 2-dimensional typical section. Supersonic Doublet-Point method is used for the computation of supersonic unsteady aerodynamic forces and Karpel`s Minimum-State approximation is used for the aerodynamic approximation. Root-locus method and time-integration method are used for the linear and nonlinear flutter analyses. For the nonlinear flutter analysis the deployable hinge is represented by a asymmetric bilinear spring and is linearized by using the describing function method. From the flutter analyses, the effects of nonlinear parameters on the aeroelastic characteristics are investigated.

Aeroelastic Characteristics of Double-Swept Isotropic and Composite Wings

A new planform of a wing having two sweep angles is proposed to enhance the aeroelastic stability with no loss of the aerodynamic benee ts of a swept-forward wing. Aeroelastic analysis is performed with the e nite element method to model wing structure and the doublet point method to predict aerodynamic loads. The sweep angle of the inboard wing is varied in this analysis, whereas the outboard wing is swept forward to a preselected amount. The results show that the aeroelastic stability can be drastically enhanced by adjusting the sweep angle of the inboard wing. The effect of the e ber orientation on the aeroelastic stability of the double-swept composite wing is studied, and the proper ply angle is identie ed to maximize critical speed.

有翼機の単独飛行／打ち上げ形態におけるフラッタ特性と風洞模型支持法の開発

A winged space reentry vehicle is under development in Japan. The vehicle will be launched atop of a rocket and fly back to the Earth. Flutter characteristics of this vehicle should be considered differently between launching and free-flight. Two kinds of supporting system were newly developed to put each configuration into practice for wind tunnel tests. They possess a function to control flutter during the tests. Flutter experiments were conducted by using these supporting systems in TWT. As the results, the anticipated flutter occurred under each configuration and the effectiveness of the supporting system has been demonstrated. Moreover, the flutter characteristics could be explained clearly by the numerical analyses with the non-planar DPM (Doublet-Point Method).

Continuity of Lifting Surface Theory in Subsonic and Supersonic Flow

The continuity of linear theory for lifting surfaces in subsonic and supersonic e ow is discussed. The unsteady pressure kernel functions of the singular integral equation are summarized for all Mach numbers in the Laplace transform domain. The sonic kernel in the steady e ow is obtained as a e nite limit from both the subsonic and supersonic sides when the Mach number tends to unity. Numerical examples are given using the doublet-point method with three different kernel functions, showing continuous results through the unit Mach number. The results also show how a rectangular wing with various Mach numbers approaches to the two-dimensional airfoil as the aspect ratio increases.