Plate In Subsonic Flow Research Articles

A Novel Aerodynamic Force and Flutter of the High-Aspect-Ratio Cantilever Plate in Subsonic Flow

This paper focuses on the derivation of the aerodynamic force for the cantilever plate in subsonic flow. For the first time, a new analytical expression of the quasi-steady aerodynamic force related to the velocity and the deformation for the high-aspect-ratio cantilever plate in subsonic flow is derived by utilizing the subsonic thin airfoil theory and Kutta-Joukowski theory. Results show that aerodynamic force distribution obtained theoretically is consistent with that calculated by ANSYS FLUENT. Based on the first-order shear deformation and von Karman nonlinear geometric relationship, nonlinear partial differential dynamical equations of the high-aspect-ratio plate subjected to the aerodynamic force are established by using Hamilton’s principle. Galerkin approach is applied to discretize the governing equations to ordinary differential equations. Numerical simulation is utilized to investigate the relation between the critical flutter velocity and some parameters of the system. Results show that when the inflow velocity reaches the critical value, limit cycle oscillation occurs. The aspect ratio, the thickness, and the air damping have significant impact on the critical flutter velocity of the thin plate.

On the non-linear dynamics of a forced plate with boundary conditions correction in subsonic flow

• A complete modeling of a periodically driven plate with boundary conditions correction in subsonic ow is developed. • A transformation upon the Legendre polynomials is applied for converting the boundary conditions with correction. • The systems with or without correction show the similar global bifurcation structure and scaling property. • The correction can cause reversals which increase the diversity and complexity of the local bifurcation structure. When a plate is subjected to long-term vibration the original boundary conditions are no longer ideal and necessary correction should be considered during its dynamical modeling. This paper aims at the modeling of the boundary conditions correction and its influence on the nonlinear dynamics of a harmonic excited plate in subsonic flow . The plate boundary conditions with correction are non-autonomous and converted into autonomous by using a coordinate transformation upon the orthogonal Legendre polynomials. The fluid force is separated into the reactive and resistive parts. The reactive fluid force, due to plate motion, is derived from the bound and wake vorticity in Glauert’s expansion; the resistive force , which is independent on plate motion, is evaluated in drag coefficient . The governing nonlinear partial differential equation is discretized in space and time domains by using the Galerkin method. Results show that the present fluid model is in good agreement with other theories archived and is reliable. The unforced system loses its stability by divergence following a pitchfork-like bifurcation featured by the appearance of new bifurcated stable equilibrium points due to nonlinearity after instability. The boundary conditions correction can stabilize the system and does not change the bifurcation structure and scaling property. The symmetry-breaking/restoring bifurcations play an important role in the change of different period-1 motions, and the nature of such bifurcations is associated with the collision or division of attractors . Subharmonic motions and chaos appear alternatively, and the transition between chaos and periodic motions is generally in accompany with period-doubling bifurcations, explosion and condensation of attractors.

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

We have carried out a numerical study of the influence of the upstream Mach number on the flutter of a two-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 with a novel frequency-domain, finite differences 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 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. To the best of our knowledge, the analysis performed here is the first self-consistent, parametric study of the influence of the compressibility on the flutter point of a two-dimensional cantilevered plate in subsonic flow.

Stability analysis and active control of a nonlinear composite laminated plate with piezoelectric material in subsonic airflow

The stability analysis and active control of a nonlinear composite laminated plate in subsonic airflow are studied. The equation of motion of a plate with a piezoelectric patch in subsonic air flow is established by using the Hamilton’s principle with the assumed mode method. The perturbation aerodynamic pressure is derived from linear potential flow theory. For the linear system, the eigenfrequencies of the system are calculated for different flow velocities, and the critical instability flow velocity and the flutter flow velocity are obtained. For the nonlinear system, the bifurcation of the transverse displacement with respect to the flow velocity is analyzed by solving the equations of equilibrium of the nonlinear dynamic system. The effects of the ply angles on the critical instability flow velocities of the plate are analyzed. According to the mechanism for the instability of the plate in subsonic flow, the displacement feedback control strategy is adopted to stabilize the system. The influences of the control gain on the critical instability velocity of the plate are analyzed. From the analysis and numerical simulations, it can be concluded that with the ply angle increasing from \(0^{\circ }\) to \(90^{\circ }\), the critical instability flow velocity of the plate has a maximum at a finite critical angle. When the flow velocity exceeds the critical instability flow velocity, the stable point of the nonlinear system deviates from the zero point of the system. It also can be concluded that the displacement feedback control can effectively improve the aerodynamic properties of the plate by providing the active stiffness for the unstable system. With displacement feedback control gain increasing, the critical instability flow velocity increases.

Stability of Rectangular Plates in Subsonic Flow with Various Boundary Conditions

The aeroelastic stability of rectangular plates in subsonic flow is well documented in literature. For example, the stability of a cantilever plate with a clamped edge parallel to the flow is well understood due to the similarity of this system to an aircraft wing. However, an ongoing push for lighter aerospace structures and novel designs requires advancing the understanding of the aeroelastic stability of plates with nonconventional boundary condition combinations. This paper summarizes the aeroelastic theory and experimental results on the flutter and/or divergence mechanisms of a rectangular plate with different sets of structural boundary conditions. The theory combines a linear plate structural model with a three-dimensional vortex lattice aerodynamic mode to create a high-fidelity frequency domain aeroelastic model. The paper also discusses the development of a modular experimental test bed to test the different boundary conditions. A pair of well-understood boundary condition configurations acts as validation points, and then results of additional configurations that have not been extensively explored are presented. The results of this paper can be used to support the design efforts of projects involving plates or plate membranes. In addition, the paper adds to the fundamental understanding of plate aeroelasticity and provides experimental data for comparison and future validation.

Chaotic motion of a composite laminated plate with geometric nonlinearity in subsonic flow

The bifurcation and chaotic motion of a two-dimensional (2D) composite laminated plate with geometric nonlinearity subjected to incompressible subsonic flow and transverse harmonic excitation is investigated. Based on von Karman's large deformation theory and incompressible subsonic aerodynamic model, the equation of motion of the composite laminated plate is established using the Hamilton's principle. The variable separation method is adopted to transform the equation of motion of the laminated plate into nonlinear ordinary differential equations (ODE). For the first-order expansion of the transverse displacement, the critical divergence velocity corresponding to the pitchfork bifurcation of the laminated plate is obtained by analyzing the stiffness term in the nonlinear ODE and the Melnikov's method is adopted to predict the chaotic motion of the plate after the bifurcation. The effects of the flow velocity and the amplitude and angular frequency of the external excitation on the chaotic motion of the plate are analyzed. Numerical simulations of the transverse displacement–time history, phase portrait, Poincaré map and bifurcation diagrams of the transverse displacement are used to verify the validity of the analytical results. For higher-order expansion of the transverse displacement, the critical divergence velocity is obtained by analyzing the stiffness matrix in the ODEs. The displacement–time histories and phase portraits of the transverse displacement obtained from higher-order expansions are compared with those obtained from the first-order expansion. The effects of the ply angles of the laminated plate on the critical divergence velocity are also discussed for both the first-order expansion and higher-order expansion of the transverse displacement. It can be seen from the results that the critical divergence velocity of the laminated plate decreases with the increasing ply angle. The parameters of the flow velocity and the amplitude and angular frequency of the external excitation for generating the chaotic motion of the plate obtained by the numerical simulations are within the range predicted by the Melnikov's method. Comparing with the results obtained by the higher-order expansions of the displacement, the first-order expansion can qualitatively reflect the dynamic characteristics of the composite laminated plate in subsonic flow.

The scattering of vorticity waves by an infinite cascade of flat plates in subsonic flow

The scattering of a harmonic vorticity wave by an infinite, two-dimensional cascade of thin blades in subsonic mean flow is studied analytically, as a model problem of relevance to the question of sound generation by modern aeroengines. The work aims to extend a previous study by Koch, who considers only the scattered radiation, by deriving expressions for the detailed unsteady lift distribution on the blades. In an earlier paper, the present author has calculated this lift distribution in the asymptotic limit of large reduced frequency, but here that analysis is generalised to the case of arbitrary reduced frequency. This is achieved by the solution of two scattering problems using the Wiener-Hopf technique, one in the leading-edge region of the cascade and one in the trailing-edge region, in terms of an infinite sequence of (unknown) duct-mode coefficients, and these unknowns are then determined by matching the two solutions together inside the cascade. Exact analytical expressions for the detailed lift distribution on each blade are given, which are in closed form apart from the need to invert a single matrix numerically.

Flutter analysis of cantilever composite plates in subsonic flow

The high-precision 18-degree-of-freedom triangular plate-bending finite element is used to study the effects of composite filament angle, orthotropic modulus ratio, sweep angle, and aspect ratio on the vibration and flutter/divergence characteristics of cantilever plates in subsonic flow. The element stiffness and mass matrices are generated according to the classical lamination theory. Unsteady airload acting on the plate is evaluated by the use of lifting surface theory, which is solved numerically by the doublet-lattice method. To facilitate flutter analysis, interpolation using a surface spline is employed to interconnect the structural nodal and aerodynamic control points. The flutter/divergence tradeoff of aeroelastic tailoring is found, in a more involved manner, for the present plate-like low-aspect-ratio wings as compared to that associated with the beam model first discovered by Weisshaar. Effective enhancement on flutter/divergence performance can be attained by varying the orthotropic modulus ratio while as appropriate fiber orientation is selected. Also, as discovered previously, the present numerical results confirm that the structural tailoring can provide a harmonious balance to the sweep angle effect upon the aeroelastic stability characteristics of a wing. From the numerical examinations performed, it is concluded that substantial improvement upon flutter/divergence characteristics can be achieved by using composite materials. Nevertheless, the benefit can be gained only through a thorough parametric investigation because the aeroelastic stabilities are also complicated by the directional stiffness of composites, in particular for the cases of low-aspect-ratio wings.