Panels In Supersonic Airflow Research Articles

Nonlinear dynamic analysis and vibration suppression on the composite laminated plates with general boundary conditions in supersonic airflow

This paper performs the nonlinear dynamic analysis and vibration reduction of the panel structures subjected to supersonic airflow. The negative capacitance piezoelectric shunt damping circuit (PSDC) which contains bonded piezoelectric element and external negative capacitance is adopted. Based on the modified Ritz approach and energy approach, the formulations of the nonlinear panel structure with attached piezoelectric element are derived. A unified mathematical model for the nonlinear dynamic analysis of composite panels subjected to general edge boundaries in supersonic airflow is formulated. Furthermore, the Newmark approach and Newton iteration approach are utilized to calculate time domain responses of panel structures under aerodynamic pressure. Several numerical cases are further performed to verify the present formulations. Finally, impacts of several factors on the flutter characteristics of panel structures are investigated and the comparisons concerning the vibration responses of panels having and without PSDC are performed to verify vibration reduction properties of the present method. The numerical results show that the vibration and flutter of panels in supersonic airflow can be sufficiently suppressed by the present simple vibration reduction strategy.

Vibration and aeroelastic stability analysis of hexagonal honeycomb core sandwich panels in supersonic airflow

This work investigates the vibration and aeroelastic stability behavior of honeycomb core sandwich panels with four-side simply supported boundaries in supersonic airflow. The sandwich panel includes a hexagonal honeycomb core layer with equal wall thickness, and upper and lower isotropic face sheets. The quasi-steady first order piston theory is used to model the aerodynamic pressure, and aeroelastic equations are established using Hamilton’s principle and a finite element approach. The effects of honeycomb core parameters on vibration and critical dynamic pressures of the honeycomb core panel are analyzed in two cases: Case 1, the dimensions of the simply supported hexagonal honeycomb sandwich panel is the same as the basic isotropic model; Case 2, the masses of the honeycomb sandwich panels are n(0<n≤1) times of the basic isotropic panel. The results show that the hexagonal honeycomb core can improve the natural frequencies of the panel. The honeycomb core thickness has a major influence on the critical dynamic pressure of the honeycomb sandwich panel, and the cell thickness, the cell angle and internal aspect ratio have no significant effect on the critical dynamic pressure. Compared with the basic isotropic panel, the mass can be reduced by nearly 70% using the honeycomb panel in the condition of the same critical dynamic pressure, which is of great significance to reduce the weight of the aircraft panel.

Nonlinear thermal flutter analysis of variable angle tow composite curved panels in supersonic airflow

The advanced Automated Fibre Placement (AFP) technologies make the synthesis of Variable Angle Tow (VAT) composites possible, which provides an extended space for the design of lightweight structures. At the same time, the variable stiffness feature inherent in tow-steered composite panels also poses a huge challenge to solve the mechanical problems including the panel flutter problem. In this article, the nonlinear thermal flutter characteristics of an infinitely long VAT composite curved panel in supersonic airflow is investigated for the first time. The proposed panel model is based on the Donnell’s shallow shell theory and accounts for the von Kármán’s geometrical nonlinearity. The aerodynamic load induced by the supersonic airflow passing over the panel surface is constructed from the first-order piston theory, whilst the thermal load imposed on the curved panel follows the quasi-steady thermal stress theory. The aerothermoelastic equations of motion that govern the nonlinear thermal flutter problem are determined via Hamilton’s variational principle. The Galerkin’s method is applied to convert the partial differential governing equation with variable coefficients into a set of ordinary differential equations, and the resulting nonlinear equations dependent upon time are solved through the fourth order Runge–Kutta method. Several qualitative tools, including the time history, phase portrait, Poincaré map and bifurcation diagram, are employed to study the dynamic behaviours, and a variety of attractors, both regular and chaotic, are observed. The accuracy and effectiveness of the proposed Galerkin procedure are validated by comparing with those available in literature. Effects of height-rise parameter, temperature parameter and fibre orientation angle on the nonlinear flutter responses of VAT composite curved panels in thermal environments are discussed in details.

Complex damping influences on the oscillatory/static instability characteristics of heated panels in supersonic airflow

The aim of this study is to investigate the complex damping influences on the oscillatory/static instability characteristics of heated panels in supersonic airflow. Firstly, by assuming a constant, uniform thermal loading and adopting the piston theory, the panel aeroelastic governing equation is obtained. After deriving the panel buckling and vibration modes, the reduced order model can be built and adopted to investigate the system primary instability in the modal coordinates. Then, introducing the modal damping coefficients ratio η>0, the critical parameters of the panel flutter oscillation are theoretically evaluated based on the non-conservative energy balance principle, thus the system instability characteristics can be investigated. The results show that the system oscillatory and static buckling instability characteristics are significantly regulated by the thermal loading and modal damping. For the oscillatory instability, there exists the damping paradox, which is associated with the system energy dissipation efficiency, and can be quantitatively evaluated by the ratio 2η/1+η. The system static buckling instability characteristics is also affected by the modal damping, and this damping destabilization is clarified based on Hamiltonian energy conservation law. The results agree well with that obtained by Routh-Hurwitz criteria, and lead an in-depth understanding of the complex role played by the damping within the non-conservative dissipative systems.

A Combined Energy Method for Flutter Instability Analysis of Weakly Damped Panels in Supersonic Airflow

A combined energy method is proposed to investigate the flutter instability characteristics of weakly damped panels in the supersonic airflow. Based on the small damping assumption, the motion governing partial differential equation (PDE) of the panel aeroelastic system, is built by adopting the first-order piston theory and von Karman large deflection plate theory. Then by applying the Galerkin procedure, the PDE is discretized into a set of coupled ordinary differential equations, and the system reduced order model (ROM) with two degrees of freedom is obtained. Considering that the panel aeroelastic system is non-conservative in the physical nature, and assuming that the panel exhibits a single period oscillation on the flutter occurrence, the non-conservative energy balance principle is applied to the linearized ROM within one single oscillation period. The obtained result shows that the ROM modal coordinate amplitudes ratio is regulated by the modal damping coefficients ratio, though each modal damping coefficient is small. Furthermore, as the total damping dissipation energy can be eliminated due to its smallness, the He’s energy balance method is applied to the undamped ROM, therefore the critical non-dimensional dynamic pressure on the flutter instability occurrence, and the oscillation circular frequency amplitude relationship (linear and nonlinear form) are derived. In addition, the damping destabilization paradoxical influence on the system flutter instability is investigated. The accuracy and efficiency of the proposed method are validated by comparing the results with that obtained by using Routh Hurwitz criteria.

Influence mechanism of lumped masses on the flutter behavior of structures

It is well known that lumped masses can change the frequency characteristics of the structural system, and aeroelastic flutter happens due to the coalescence of two modes. Therefore, it can be expected to improve the aeroelastic stability by the lumped mass. This paper studies the influence mechanism of the lumped mass on the aeroelastic behaviors of two-dimensional (2D) panels in supersonic airflow, and proposes an axially functionally graded design method using the lumped mass. In this investigation, the finite element method (FEM) is used to formulate the aeroelastic equation of motion for the panels with the lumped mass and spring constraint. For 2D panels with the lumped mass, the local mode coalescence is observed, and the influences of the weight and location of the lumped mass on the flutter stability and their mechanism are analyzed. The optimal ranges for the weight and location of the lumped mass are given out. For 2D panels with the spring constraint, the sudden decrease of the flutter bound due to the mode veering are analyzed, and an effective method to eliminate it by using the lumped mass is proposed. Finally, a structural optimization method based on the axially functionally graded design is proposed.

Nonlinear Aeroelastic Analysis of Heated Curved Panels in Supersonic Air Flow

A nonlinear aeroelastic model for a two-dimensional heated curved panel in supersonic air flow is established by using Galerkin method. The von Karman large deflection theory and the third-order piston theory appended with the static aerodynamic loading are used in the governing equations. The static aero-thermal deflection of the curved panel is firstly obtained by using Newton iterative approach. Then the stability boundary under different temperature elevations is achieved by using Lyapunov’s indirect method. Lastly, the motion equations of a heated curved panel in supersonic air flow are solved by a fourth-order Runge–Kutta numerical scheme. Time history responses, phase plots, Poincare maps and bifurcation diagrams are used for better understanding of the pre/post-flutter responses of a curved panel by varying parameters, including curvatures, dynamic pressures and temperature elevations. The results demonstrate that the flutter boundary drops significantly with increasing temperature elevation for panels with small curvatures. However, the flutter boundary almost keeps the same for panels with large curvatures. The nonlinear flutter characteristics of the curved panel differs from those of flat panels significantly, the nonlinear flutter response of heated curved panels changes from static equilibrium point or LCO to chaos with the increase of temperature elevation or dynamic pressure and the static, LCO motions also exist in the chaotic area. For panels with large curvatures, the chaotic motions cannot occur, and the amplitude of LCO is limited in a certain range.

Axially functionally graded beams and panels in supersonic airflow and their excellent capability for passive flutter suppression

Mode localization in the airflow direction can be observed in aeroelastic structures. On the contrary, can the aeroelastic stability of the structure be enhanced if the geometric sizes and material properties vary along the airflow direction? The present study mainly solves this problem. The mode localization phenomenon in panel flutter in supersonic airflow is displayed. Three arbitrary thickness functions according to the flutter mode are taken into account. Their panel flutter behaviors show that although the consistency between the variation of thickness and flutter mode can increase the flutter bound slightly, the increments are limited. Consequently, a novel strategy for passive control of the panel flutter is proposed by the optimal axially functionally graded (AFG) design of the panel. By investigating the sensitivity of each element in the aerodynamic stiffness matrix to the aeroelastic stability of the structure, the optimal thickness and Young's modulus functions are given out. Simulation results show that the optimal AFG design in this study can suppress the flutter essentially. It can increase the flutter bound of the structure by changing the flutter modes rather than only makes a slight extension on the original basis. Moreover, the designed thickness and Young's modulus are reasonable and applicable.

An energy flow model for high-frequency vibration analysis of two-dimensional panels in supersonic airflow

Many energy flow models have been proposed for high-frequency forced vibration analysis of structures. In this paper, a novel energy flow model is developed to predict the high-frequency vibration response of panels in supersonic airflow and quantify the effects of supersonic airflow on high-frequency forced vibration characteristics. The additional damping due to supersonic airflow is derived from the motion equation of a two-dimensional panel. The relationship between the wavenumber and the group velocity is introduced to describe the energy transmission property considering the effects of supersonic airflow. Then the energy density governing equation (i.e. energy flow model) is established and solved by the energy flow analysis (EFA) and the energy finite element method (EFEM). Finally, comparing the vibration responses obtained by the present energy flow model with the corresponding exact analytical solutions, the developed energy flow model is verified to be effective for high-frequency vibration analysis of panels in supersonic airflow. Furthermore, the numerical simulations indicate that supersonic airflow can affect the equivalent damping of the propagating elastic waves, and thus change the energy density distribution of the panel.

Aerothermoelastic analysis of composite laminated trapezoidal panels in supersonic airflow

The aerothermoelastic properties of composite laminated trapezoidal panels considering the compressibility of supersonic airflow and shock wave are studied. Due to the irregular configuration of composite laminated trapezoidal panel and complex thermal fluid–structure interaction, it is impossible to solve this problem by analytical methods. An effective finite element method (FEM) is developed to establish temperature equation and aerothermoelastic equation of motion of the complex trapezoidal panel. The first order piston theory is employed to evaluate the aerodynamic pressure. Based on the developed FEM, the thermal diffusion equation and the Galerkin’s method are applied to establish the temperature equation of the panel, and the complex temperature distribution of the panel is obtained. Combining the thermal and aeroelastic models, the aerothermoelastic equation of motion of the composite trapezoidal panel is established using Hamilton’s principle. Through the numerical analyses, some useful and significant results are obtained, and the advantages and disadvantages of various parameters of the panels are summarized. Because of the aerodynamic heating under the supersonic airflow, the buckling of the panel caused by thermal effect and the flutter caused by supersonic airflow are discussed considering the influences of various parameters. The interaction of the thermal and aerodynamic forces is also analyzed.

Dynamic responses of aerothermoelastic functionally graded CNT reinforced composite panels in supersonic airflow subjected to low-velocity impact

Abstract The low-velocity impact behaviors of aeroelastic functionally graded CNT (carbon nanotube) reinforced composite panels in supersonic airflow are investigated. Thermal effects are taken into account. Reddy's higher-order shear deformation theory is applied in the structural modeling. The effective material properties of the functionally graded CNT reinforced composite panel are calculated by the rule of mixture. The aerodynamic pressure is evaluated by the first-order piston theory. The contact force between the panel and the impactor is simulated by the Hertz law. Hamilton's principle and the assumed modes method are used to formulate the equation of motion which is then solved by the numerical method because of the high nonlinearity. A simplified mass-damping-spring model is also introduced to solve the problem. Influences of the aerodynamic pressure, CNTs distribution and volume fraction and thermal effects on the impact responses of the functionally graded CNT reinforced composite panels are investigated. The simulating results using the numerical model and the mass-damping-spring model are compared. The affect factor considering the inertial effect of the panel in the low-velocity impact for the CNT reinforced composite panel is given out.

A new method of smart and optimal flutter control for composite laminated panels in supersonic airflow under thermal effects

In most of the active flutter controls, the feedback control gains are selected arbitrarily or by trial and error. These methods are inaccurate and time-consuming. In the present study, a smart and optimal method is proposed to investigate the thermal flutter control of composite laminated panels in supersonic airflow based on a genetic algorithm (GA), in which the feedback control gains of all the piezoelectric actuators are represented by the chromosomes and the fitness is set to be the difference between the present flutter bound and the expected one. Then, according to the GA process, a set of optimal feedback control gains can be obtained, and the flutter bounds of the structural system can be suppressed to any expected values by means of the optimal control gains. Furthermore, the maximum flutter bound of the panel and the corresponding feedback control gains can also be obtained. In the investigations, the aerodynamic pressure is evaluated by the supersonic piston theory and the controller is designed by the displacement feedback method. The influences of the placements of piezoelectric patches on the active flutter control effects are analyzed. Some interesting phenomena are obtained and discussed.

Investigations on the influences of elastic foundations on the aerothermoelastic flutter and thermal buckling properties of lattice sandwich panels in supersonic airflow

The lattice sandwich panels supported on elastic mediums are often applied in the construction of aerospace structures because of the low specific weight, excellent bending rigidity and outstanding vibration properties. This elastic medium can be any spring materials including damping tapes or heat shields which are attached to one side of the sandwich panel. Therefore, in this paper, aerothermoelastic flutter and thermal buckling characteristics of sandwich panels with the pyramidal lattice core resting on elastic foundations in supersonic airflow are studied. The influences of geometrical parameters and elastic foundation on the panel flutter and thermal buckling of the structures are analyzed in detail. In the structural modeling, the first-order shear deformation theory is applied, and the effective material properties of the lattice core are used. The aerodynamic pressure is evaluated by the supersonic piston theory. Hamilton's principle and the assumed modes method are applied to formulate the equation of motion. The highlight point of this investigation is that an effective thermal buckling suppression method utilizing the elastic foundation is proposed, based on which the thermal buckling of the structure can be completely eliminated with the natural frequencies remaining unchanged when the shearing layer parameter is equal to the thermal load. Through the numerical results, the influences of the elastic foundation, aspect ratio, core-to-facesheet thickness ratio, and inclination angle of the core truss on the aerothermoelastic behaviors of the lattice sandwich panel are analyzed, and the thermal buckling elimination effects are also examined.

Aerothermoelastic flutter analysis and active vibration suppression of nonlinear composite laminated panels with time-dependent boundary conditions in supersonic airflow

Aerothermoelastic flutter properties of nonlinear composite laminated panels in supersonic airflow are studied, and investigations on active flutter and aerothermal postbuckling suppression for the panels with time-dependent boundary conditions are also carried out using macro fiber composite actuator and sensor. The von Karman strain–displacement relation in conjunction with the supersonic piston theory is applied in structural modeling. Nonlinear dynamic equations of motion for the structural system are established using Hamilton’s principle and the assumed mode method. Frequency- and time-domain methods are used to investigate the aerothermoelastic characteristics and active flutter and aerothermal postbuckling suppression of the panels. Effects of aspect ratio and ply angle on the nonlinear aerothermoelastic behaviors are studied. The displacement feedback control is used to conduct the active flutter and postbuckling suppression. The nonlinear output controller consisting of a linear quadratic regulator and a nonlinear state estimator of extended Kalman filter is also used in designing the controller. Controlled vibration responses of the structural system under the two different controllers are compared. The results show that the developed linear quadratic regulator/extended Kalman filter controller is more effective than the displacement feedback control controller in flutter and postbuckling control of the panels with time-dependent boundary conditions in supersonic airflow.

Aeroelastic analysis of CNT reinforced functionally graded composite panels in supersonic airflow using a higher-order shear deformation theory

This paper presents an aeroelastic analysis of carbon nanotube (CNT) reinforced functionally graded composite panels in supersonic airflow using a higher-order shear deformation theory. There are four types of CNT distributions considered in this investigation. Since the panel studied here is relatively thick, Reddy’s third-order shear deformation theory is applied to evaluate the displacement fields of the panel. Applying Hamilton’s principle, the equation of motion of the structural system is formulated. The CNT reinforced functionally graded composite panels investigated in this study are simply-supported on two opposite edges and therefore, in order to solve the coupling set of differential equations of motion, the state-space Levy method is applied. Based on the Levy solution, the aeroelastic properties of the CNT reinforced composite panels are analyzed using the frequency-domain method. The effects of CNT distributions and boundary conditions on the aeroelastic stabilities of the CNT reinforced functionally graded panels are researched. Different types of aeroelastic instability under different boundary conditions are observed. Moreover, vacuo and fluttering mode shapes of the CNT reinforced functionally graded panels are presented.

Computation of aerothermoelastic properties and active flutter control of CNT reinforced functionally graded composite panels in supersonic airflow

This paper presents an aerothermoelastic analysis of carbon nanotube (CNT) reinforced functionally graded composite panels in supersonic airflow. Meanwhile, the active flutter control of CNT reinforced functionally graded composite panels is also carried out using the piezoelectric actuator and sensor. Reddy’s third-order shear deformation theory is applied in the structural modeling. The equation of motion of the structural system is formulated using Hamilton’s principle and the assumed mode method. The displacement feedback algorithm is used to design the controller. The frequency domain method is applied to investigate the aerothermoelastic properties and active flutter control effects of the panels. The influences of CNT distribution, aspect ratio and thickness-to-length ratio on the aerothermoelastic properties of the CNT reinforced functionally graded composite panels are analyzed. Active flutter control effects under different thicknesses of CNT reinforced functionally graded composite panels are investigated. The optimal area and position of piezoelectric patches are also obtained by the genetic algorithm.

Aerothermoelastic analysis of lattice sandwich composite panels in supersonic airflow

This paper is devoted to investigate the aerothermoelastic properties of the composite sandwich panels with two- and three-dimensional lattice cores in supersonic airflow. Both the top and bottom face sheets of the sandwich panels are composite laminated panels. The two- and three-dimensional lattice cores are composed of triangular grids and pyramidal trusses, respectively. The first-order shear deformation theory is used in the structural modeling. The equivalent thermal expansion coefficients of the triangular grid are obtained by the physical and geometric relations of the deformed core only under the temperature change. The equation of motion of the structural system is formulated using the Hamilton’s principle. The supersonic piston theory is used to evaluate the aerodynamic pressure. The aerothermoelastic properties of the lattice sandwich panels are analyzed by the frequency-domain method. The influences of parameters of the lattice core on the aeroelastic stability of the sandwich panel are investigated. The aerothermoelastic properties of the sandwich composite panels with two- and three-dimensional lattice cores are compared. Some useful results are obtained from the present study.

Active flutter and aerothermal postbuckling control for nonlinear composite laminated panels in supersonic airflow

In this article, active flutter and aerothermal postbuckling control of the nonlinear composite laminated panel with large deformation in supersonic airflow using the piezoelectric material are investigated. The distributed piezoelectric actuator and sensor pairs are bonded on the top and bottom surfaces of the laminated panel. The von Karman strain–displacement relation is used in the structural modeling. Unsteady aerodynamic pressure is evaluated by the supersonic piston theory. Hamilton’s principle and the assumed mode method are applied to formulate the equation of motion of the structural system. A discrete linear-quadratic-Gaussian controller is designed in this study to conduct the active flutter and postbuckling control. The proportional feedback control method is also applied in designing the controller. Time domain responses of the structural system are computed using the Runge–Kutta method. The control effects of the two control methods are compared. The influences of the placements of the piezoelectric actuator and sensor pairs on the control effects are also investigated. This study is helpful for the active aeroelastic design of the nonlinear structural system.

Vibration and aeroelastic properties of ordered and disordered two-span panels in supersonic airflow

Abstract In this paper, the analysis of vibration and aeroelastic properties of ordered and disordered two-span panels is carried out. The equation of motion of each sub-panel of the two spans is formulated using Hamilton׳s principle. Supersonic piston theory is applied to evaluate the unsteady aerodynamic pressure. The partial differential equation of motion of the two-span panel is solved, and the mode shapes of the panels with and without aerodynamic pressure are obtained. The free vibration behaviors of the two-span panel are analyzed. Time-domain responses of the panel are computed by the mode superposition method using the mode shapes obtained previously. It is noted from the free vibration analysis that the vibration localization will happen on the disordered two-span panel. Aeroelastic analyses of ordered and disordered two-span panels are also carried out through the frequency-domain method. Characteristics of the aeroelastic stability and fluttering mode of the disordered two-span panel are analyzed. Simulation results show that the disorder of the two-span panel will decrease the critical flutter aerodynamic pressure of the structural system. The influences of the disorder degree on the vibration localization and the flutter bound of the two-span panel are investigated. The present results are useful for the analysis and design of the multi-span structures.

Nonlinear Aeroelastic Panel Flutter Based on Proper Orthogonal Decomposition

It is commonly accepted that 36 in vacuo natural modes (NMS) are needed for converged, limit-cycle oscillations (LCOs) of isotropic or laminated anisotropic rectangular panels in supersonic air flow. It’s computationally costly for nonlinear aeroelastic panel response using such a large number of modes, and it also causes complexity and difficultly in designing controllers for panel flutter suppression. Based on Hamilton principle, the aeroelastic finite element motion equations of the 3-D panel are established by using the von Karman large deflection theory, first-order piston theory aerodynamics, the proper orthogonal decomposition (POD) method are adopted to construct a reduced order model of the panel, then the reduced panel flutter equations are solved in time domain using a numerical integration method. Comparing with the LCOs calculated by using 36NMS, the results obtained by using the reduced order model based on POD method (POD/ROM) show a good agreement.