Flutter Characteristics Of Panels Research Articles

Effects of Mass Attachments on Flutter Characteristics of Thin-Walled Panels

Mass attachments may exist in the design and use of an aircraft panel, such as sensor layout, internal wiring, surface icing, etc. These mass attachments can change the flutter characteristics of the panel in supersonic flight and have important impacts on structural safety. In order to investigate the flutter characteristics of the panel with mass attachments, an assumed mode method is proposed to deal with the changes in the modal properties of the panel structure. Combined with the first order piston theory and p-k method, the flutter velocities and flutter frequencies of the panel under different cases can be obtained in the frequency domain. Firstly, based on the large displacement with a small strain assumption proposed by von Kármán and the proposed assumed mode method, the structural dynamic model of a simply supported panel with mass attachments and artificial dampers is constructed. Then, modal aerodynamic forces of the simply supported panel can be obtained based on first-order piston theory. Finally, flutter equations are transformed into the frequency domain and solved by the p-k method. The results showed that the existence of mass attachments can significantly change the flutter velocities and flutter frequencies of the panel. However, the flutter characteristics of the panel can be enhanced or recovered through some appropriate damper configuration schemes. Calculating the flutter characteristics of thin-walled panels with mass attachments can more accurately simulate real situations during flight, and one can obtain a safer design scheme of thin-walled panels.

Effects of Elastically Supported Boundaries on Flutter Characteristics of Thin-Walled Panels

In order to investigate flutter characteristics of thin-walled panels with elastically supported boundaries, a method for dealing with the stiffness matrix constraint relationship is developed based on penalty functions. Combined with the first-order piston theory, flutter velocities and frequencies of thin-walled panels with the different cases of elastically supported boundaries are calculated. Firstly, a thin-walled panel is discretized by the finite element method, and springs with real stiffness coefficients are introduced to simulate elastically supported boundaries. Then, the pressure difference between the outer and inner surfaces of the panel and modal aerodynamic expressions are obtained by introducing the first-order piston theory. Finally, flutter equations are obtained in the time domain by combining the structural dynamic equations with the modal aerodynamic forces. Subsequently, they are transformed to the frequency domain at the flutter state. Then, flutter characteristics of the panel are obtained using the U−g method. The results show that the existence of elastically supported boundaries may reduce the flutter velocity and flutter frequency of the panel but can be enhanced and recovered through some appropriate damping configuration schemes. Calculating the flutter characteristics of thin-walled panels under elastically supported boundaries can more accurately simulate real supported situations and result in a safer design scheme for thin-walled panel structures.

Nonlinear flutter of 2D variable stiffness curvilinear fibers composite laminates by a higher-order shear flexible beam theory with Poisson’s effect

In this work, the nonlinear supersonic panel flutter characteristics of two-dimensional variable stiffness curvilinear fibres based laminated composite panels are studied using a higher-order shear flexible theory represented by sine function coupled with first-order approximation leading to quasi-aerodynamic theory. The structural formation takes care of geometric nonlinearity with von Karman’s assumptions. The beam constitutive equation is modified for the laminated beam with general lay-up by accounting for Poisson’s effect. The nonlinear dynamic equilibrium equations developed by Lagrangian equations of motion are solved using finite element approach in conjunction with the direct iterative solution procedure. For limit cycle oscillation, critical dynamic pressure is predicted iteratively through eigenvalue analysis, thereby identifying the first coalescence of vibrational modes. Also, the flutter behavior of two-dimensional panel under static differential pressure is investigated considering nonlinear static equilibrium position of panel obtained by Newton-Raphson’s iterative approach and then followed by modes coalescence approach. These solution procedures are tested against the results in literature. A thorough numerical investigation is done to show the effect of the curvilinear fiber path orientation, limited cycle amplitude, static differential pressure, panel thickness, panel end condition flexibilities and thermal environment on the nonlinear supersonic panel flutter of two-dimensional variable stiffness laminated panels.

A Review Paper on Comparison of Numerical Techniques for Finding Approximate Solutions to Boundary Value Problems on Post-Buckling in Functionally Graded Materials

The use of finite element models as research tools in biomechanics and orthopedics grew exponentially over the last two decades. However, the attention to mesh quality, model validation and appropriate energy balance methods and the reporting of these metrics has not kept pace with the general use of finite element modeling. Therefore, the purpose of this review was to develop the nonlinear filter and thermal buckling of an FGM panel under the combined effect of elevated temperature conditions and aerodynamic loading is investigated using a finite element model based on the thin plate theory and von Karman strain-displacement relations to account for moderately large deflection. It is found that the temperature increase has an adverse effect on the FGM panel flutter characteristics through decreasing the critical dynamic pressure. Decreasing the volume fraction enhances flutter characteristics, but this is limited by the structural integrity aspect. Structural finite element analysis has been employed to determine the FGM panel's adaptive response while under the influence of a uniaxial compressive load in excess of its critical buckling value. By increasing the applications of using composite materials inside aviation stages, it is visualized that the versatile FGM plate setup will broaden the operational execution over traditional materials and structures, especially when the structure is presented to a raised temperature. The vicinity of air motion facilitating stream brings about delaying the locking temperature and in stifling under loads, while the temperature build gives route for higher thermal-cycle abundance.

Computing Simulation of Post-buckling in Functionally Graded Materials - A Review

A review on the recent development in the non-linear flutter and thermal buckling of an FGM panel under the combined effect of elevated temperature conditions and aerodynamic loading is investigated using a finite element model based on the thin plate theory and von Karman strain-displacement relations to account for moderately large deflection. The governing non-linear equations are obtained using the principal of virtual work adopting an approach based on the thermal strain being a cumulative physical quantity to account for temperature dependent material properties. This system of non-linear equations is solved by Newton–Raphson numerical technique. It is found that the temperature increase has an adverse effect on the FGM panel flutter characteristics through decreasing the critical dynamic pressure. Decreasing the volume fraction enhances flutter characteristics but this is limited by structural integrity aspect. Structural finite element analysis has been employed to determine the FGM panel's adaptive response while under the influence of a uniaxial compressive load in excess of its critical buckling value. It is shown that, utilising the considerable control authority generated, even for a small actuator volume fraction, the out-of-plane displacement of the post-buckled FGM panel's can be significantly reduced. http://dx.doi.org/10.11591/telkomnika.v12i12.6672

Panel flutter characteristics of sandwich plates with CNT reinforced facesheets using an accurate higher-order theory

In this paper, the flutter characteristics of sandwich panels with carbon nanotube (CNT) reinforced face sheets are investigated using QUAD-8 shear flexible element developed based on higher-order structural theory. The formulation accounts for the realistic variation of the displacements through the thickness, the possible discontinuity in the slope at the interface, and the thickness stretch affecting the transverse deflection. The in-plane and rotary inertia terms are also included in the formulation. The first-order high Mach number approximation to linear potential flow theory is employed for evaluating the aerodynamic pressure. The solutions of the complex eigenvalue problem, developed based on Lagrange׳s equation of motion are obtained using the standard method for finding the eigenvalues. The accuracy of the present formulation is demonstrated considering the problems for which solutions are available. A detailed numerical study is carried out to bring out the efficacy of the higher-order model over the first-order theory and also to examine the influence of the volume fraction of the CNT, core-to-face sheet thickness, the plate thickness and the aspect ratio, damping and the temperature on the flutter boundaries and the associated vibration modes.

Static and dynamic instability characteristics of curved laminates with internal damage subjected to follower loading

This article deals with the study of vibration, buckling, and dynamic instability characteristics in damaged cross-ply and angle-ply curved laminates under uniform, uniaxial follower loading, using finite element approach. First-order shear deformation theory is used to model the doubly curved panels and is formulated according to Sandars' first approximation. Damage is modelled using an anisotropic damage formulation. Analysis is carried out on plate and three types of curved panels to obtain vibration, buckling, and dynamic instability (flutter) behaviour. The effect of damage on natural frequency, critical buckling load, flutter load, and flutter frequency is studied. The results show that the introduction of damage influences the flutter characteristics of panels more profoundly than the free-vibration or buckling characteristics. The results also indicate that, compared to undamaged panels, heavily damaged panels show steeper deviations in stability characteristics than mildly damaged ones.

Nonlinear thermal flutter of functionally graded panels under a supersonic flow

Abstract Thermal flutter characteristics of functionally graded (FG) ceramic/metal panels under the thermal and aerodynamic loads are investigated. The volume fractions of the constitutive materials are determined by a simple power-law distribution, and material properties are assumed to be a linear rule of mixture. The panels are considered as rectangular plates based on the first-order shear deformation theory, and the von Karman strain–displacement relations are used to account for the geometric nonlinearity. The first-order piston theory is adopted to represent aerodynamic pressures induced by supersonic airflows. The principle of virtual work is applied to derive equations of motion, and a finite element method is used to obtain numerical solutions. The Newton–Raphson method is adopted to obtain approximate solutions of the nonlinear governing equations. Flutter boundaries are defined by eigenvalue analysis, and the Guyan reduction is used to reduce degree of freedom. Flutter motions of FG panels are investigated using the Newmark method. The effects of volume fraction distributions, boundary conditions, temperature changes and aerodynamic pressures on panel flutter characteristics are analyzed in detail.

層間はく離を有する積層板の超音速パネルフラッタ解析

The present paper treats a supersonic panel flutter of simply-supported symmetrical laminates with a delamination. The panel flutter characteristics of composite laminates are obtained by a finite element method based on the Mindlin plate theory and a quasi-steady aerodynamics based on the linearized piston theory in this paper. The penalty function method is adopted to ensure the displacement continuity condition at the delamination front, and the linear spring model is also adopted to describe the effect between the delaminated surfaces. The panel flutter boundary is obtained by solving the eigenvalue equation as the flutter equation. The validity of the present method and the effects of the size and location of a delamination on the panel flutter characteristics of laminated plates are examined through the numerical results.

Thermal Buckling and Nonlinear Flutter Behavior of Functionally Graded Material Panels

The nonlinear flutter and thermal buckling of an functionally gradient material panel under the combined effect of elevated temperature conditions and aerodynamic loading is studied. A nonlinear finite element model based on the first-order shear deformable plate theory and von Karman strain-displacement relations is adopted. The governing nonlinear equations are obtained using the principal of virtual work, adopting an approach based on the thermal strain being a cumulative physical quantity to account for temperature-dependent material properties. The aerodynamic pressure is modeled using the quasi-steady first-order piston theory. This system of nonlinear equations is solved by the Newton-Raphson numerical technique. It is found that the temperature increase has an adverse effect on the functionally gradient material panel flutter characteristics through decreasing the critical dynamic pressure. Decreasing the volume fraction enhances flutter characteristics, but this is limited by structural integrity aspect. The presence of aerodynamic flow results in postponing the buckling temperature and in suppressing the postbuckling deflection, and the temperature increase gives way for higher limit-cycle amplitude.

Non-linear panel flutter for temperature-dependent functionally graded material panels

The non-linear flutter and thermal buckling of an FGM panel under the combined effect of elevated temperature conditions and aerodynamic loading is investigated using a finite element model based on the thin plate theory and von Karman strain-displacement relations to account for moderately large deflection. The aerodynamic pressure is modeled using the quasi-steady first order piston theory. The governing non-linear equations are obtained using the principal of virtual work adopting an approach based on the thermal strain being a cumulative physical quantity to account for temperature dependent material properties. This system of non-linear equations is solved by Newton–Raphson numerical technique. It is found that the temperature increase has an adverse effect on the FGM panel flutter characteristics through decreasing the critical dynamic pressure. Decreasing the volume fraction enhances flutter characteristics but this is limited by structural integrity aspect. The presence of aerodynamic flow results in postponing the buckling temperature and in suppressing the post buckling deflection while the temperature increase gives way for higher limit cycle amplitude.

直交異方性だ円板のたわみ，固有振動数および超音速パネル・フラッタ

A small-deflection theory is used in conjunction with a Galerkin technique to calculate the deflection under uniform pressure, first and second natural frequencies, and supersonic panel flutter characteristics of orthotropic elliptical plate with clamped-edge in the case where the direction of principal axis of orthotropy is arbitrary and direction of the supersonic flow is coincide with the axis of ellipse. The deflection is expressed in power series. A rigorous solution is obtained for deflection subjected to uniform pressure, and the form of rigorous solution is similar to that of the isotropic plate. The natural frequencies of elliptical plate are clarified. The critical value of supersonic panel flutter is obtained in six-modes approximation. Furthermore the simple formula of critical value is drived in two-modes approximation. The experimental results for deflections and natural frequencies are in fairly close agreement with theory.

First-Order Frequency Effects in Supersonic Panel Flutter of Finite Cylindrical Shells

An improved calculation of the supersonic panel flutter characteristics of a thin cylindrical shell of finite length is presented. The aerodynamic load is determined with account taken of first-order terms in vibration frequency, and when this is introduced into the elastic shell equation an integro differential equation results. An equivalent eigenvalue problem is set up by applying Galerkin’s method to this equation. The flutter boundary, for given Mach number and circumferential mode n, corresponds to the shell thickness ratio at which the real part of any one of the eigenvalues first becomes non-negative. It is found that the most severe flutter condition, for given Mach number, occurs for a circumferential mode n = 7. The present calculations exclude second-order frequency terms in the elastic part of the flutter equation, even though they may have a first-order effect. A subsequent calculation referred to here shows that these terms indeed have no significant influence on the first-order analysis.

Panel-Flutter Analysis of a Thermal Protection-Shield Concept for the Space Shuttle

Analysis of the panel flutter characteristics of a candidate thermal protection system (TPS) for the space shuttle, using piston theory aerodynamics and Lagrange equations. The results show the TPS candidate panel array to be deep in the 'no-flutter' region during launch and, therefore, safe from panel flutter.