Circumferentially Asymmetric Stiffness Research Articles

Influence of flexural-torsional couplings and rotational effects on vibration behaviour of tapered thin-walled anisotropic biconvex beam

Accurate modelling and prediction of dynamic characteristics for rotating thin-walled blades have drawn attention as it is an essential part of structural health monitoring for various engineering and civil applications such as wind turbine, helicopter and aeroplane blades. With the advent of structural tailoring techniques, various non-classical effects and couplings implicitly affecting the behaviour of such structures are yet not fully explored. In this regard, the present work proposes a numerical model for finding the free vibration characteristics of anisotropic tapered biconvex closed cross-section beam under rotating conditions. The model is derived based on energy method following the Ritz approximation. Circumferentially asymmetric stiffness (CAS) ply configuration is considered in order to study the impact of flexural torsional coupling on the vibration characteristics. Transverse shear effects, primary and secondary warping were also included in the current model. Mode switching phenomenon is dissected elaborately for the first few frequencies under rotating and nonrotating conditions. The impact of rotational effects like centrifugal acceleration, centrifugal warping, inertial warping on the first few frequencies is also demonstrated. An iterative technique is adapted to solve the equations having these rotational effects. Modal Assurance Criterion (MAC) is done in order to judge the consistency of the modes at different rotating speeds.

Improvement of structural characteristics of composite thin-walled beams using variable stiffness concept via curvilinear fiber placement

This study presents the use of variable stiffness concept via curvilinear fiber placement to achieve improved structural characteristics in composite thin-walled beams (TWBs). The TWB used in the study is constructed in circumferentially asymmetric stiffness (CAS) configuration. The variation of fiber angles along the span and the width of the TWB is included by defining two fiber path functions. A parametric study is performed to investigate the effects of different fiber paths on the structural performance metrics including frequency spacing, unit twist, and critical buckling load. For this purpose, a semi-analytical solution method is developed to conduct free vibration, deformation, and buckling analyses of the TWB with curvilinear fibers. The semi-analytical method is validated with several finite element (FE) analyses performed using ABAQUS. Elastic stress analyses of TWBs with selected fiber paths subjected to simplified distributed loading are also conducted using the FE method, and a ply failure criterion is applied to evaluate the strength of these TWBs. Overall results show that curvilinear fiber placement varied along the span leads to greater structural performance for a composite TWB than the straight fiber configuration.

Vibration control of cantilever blade based on trailing-edge flap by restricted control input

Vibration and control of cantilever blade with bending-twist coupling (BTC) based on trailing-edge flap (TEF) by restricted control input are investigated. The blade is a thin-walled structure using circumferentially asymmetric stiffness (CAS) configuration, with TEF embedded and hinged into the host composite structure along the entire blade span. The TEF structure is driven by quasi-steady aerodynamic forces. Vibration control is investigated based on linear matrix inequation (LMI) algorithm using restricted control input (LMI/RCI). Flutter suppression of BTC displacements and the angle of TEF (i.e. the practical control input) are illustrated, with apparently controlled effects demonstrated. The restricted control input signals are used to driven the TEF to explore the scope of the feasibility of the practical TEF angle, which is displayed by a virtual simulation platform. The platform verifies the feasibility of the hardware implementation for the control algorithms.

Flutter analysis of a sandwich composite beam using an analytical method

In this paper, the aeroelastic behavior of a composite wing is investigated in the compressible flow using the analytical method. The composite wing is simulated as a thin-walled single-cell closed cross-section beam with circumferentially asymmetric stiffness (CAS) configuration. The best layup configuration for the maximum flutter speed is determined by analyzing four layups configuration where the fiber orientation angle varies within the range of 0–90 degrees. Moreover, an included foam layer between composite layers resulted in higher bending stiffness and improved stability characteristics of the wing. It was shown that there is a significant improvement in the flutter speed for [Formula: see text] layup. Numerical results demonstrate the advantages of foam filled model over the model without foam in terms of the flutter speed to the weight ratio.

Sliding Mode Control of Active Trailing-Edge Flap Based on Adaptive Reaching Law and Minimum Parameter Learning of Neural Networks

Theoretical modeling and the sliding mode control (SMC) of an active trailing-edge flap of a wind turbine blade based on the adaptive reaching law are investigated. The blade is a single-celled thin-walled composite structure using circumferentially asymmetric stiffness (CAS) design, exhibiting displacements of flap-wise/twist coupling. A reduced structural model originated from the variation method is used to model the structure of the blade, the structural damping of which is computed. The trailing-edge flap is a rigid structure that is embedded in and hinged to the blade host structure, and it is driven by two pairs of pneumatic cylinders moving in reverse. Flutter suppression for the large-amplitude vibration of the blade tip is investigated based on an active trailing-edge flap structure and SMC algorithm using the adaptive reaching law. The controlled responses of flap-wise/twist displacements and control inputs (the angles of the trailing-edge flap) are illustrated, with obvious simulation effects demonstrated. An experimental platform for driving the pneumatic cylinders verifies the effectiveness of the control algorithm using the adaptive reaching law and the effectiveness of the selected pneumatic transmission scheme controlled by another adaptive SMC based on the minimum parameter learning of neural networks.

Free Vibration of Composite Thin-Walled Beams with Chordwise Asymmetric Closed Cross-Sections

In this paper, some analytical results via extended Galerkin method on free vibration characteristics of an anisotropic composite beam, which is modeled as a nonuniform thin-walled structure with a chordwise asymmetric closed cross-section and corrected the warping functions, are newly presented. For this study, nonclassical parameters such as warping restraint, transverse shear flexibility, and structural couplings induced by two special configurations, such as circumferentially uniform stiffness (CUS) and circumferentially asymmetric stiffness (CAS), are incorporated. And also, design parameters of the beam associated with preset angles, pretwist angles, taper ratios, and section ratios are additionally investigated. The results of this study could play an important role in more efficient designs of composite thin-walled beams.

Geometrically nonlinear aeroelastic behavior of pretwisted composite wings modeled as thin walled beams

Geometrically nonlinear aeroelastic behavior of pretwisted composite high aspect ratio wings, structurally modeled as thin walled beams (TWB) is studied. The structural equations of motion are obtained for the circumferentially asymmetric stiffness (CAS) configuration TWB based on the kinematic relations governing the thin walled beams, including the nonlinear strain–displacement relations and utilizing the principles of analytical dynamics. Unsteady aerodynamic loads in the incompressible flow regime are expressed using Wagner’s function in time-domain. The aeroelastic system of equations is augmented by the differential equations governing the aerodynamics lag states to come up with the final coupled fluid–structure equations of motion. The governing equations of the aeroelastic system is solved, for the TWB with CAS composite layup, by means of a Ritz based solution methodology utilizing the mode shapes of the linear structural system to approximate the spatial variation of degrees of freedom in the thin walled beam. Time response of the nonlinear aeroelastic system is obtained via the Runge–Kutta direct integration algorithm. Effects of the fiber angle and pretwist angle of the CAS layup configuration on the nonlinear aeroelastic stability margins and limit cycle oscillation behavior are studied in depth.

Experimental and numerical studies of a cracked thin-walled box-beams

This paper discusses the problem of detection and location of cracks in a cantilever beam. To solve this problem, a damage index based on the modal displacement method is applied in both experimental and numerical studies. Thin-walled composite box-beams with rectangular cross-section are tested. Two types of beam configuration are examined: circumferentially asymmetric stiffness (CAS) and circumferentially uniform stiffness (CUS). The CAS configuration is characterized by the coupling between bending in a flexible direction and torsion, while the CUS configuration is characterized by coupled bending in two perpendicular directions (flexible and stiff). Numerical models of the tested beams are made by the finite element method. A series of simulations are performed for different damage locations and ply orientations. The Lanczos method is used to solve the eigenvalue problem. Natural frequencies and free vibration modes of the beams are determined. To validate the numerical models, a test stand is build. The test specimens are made of unidirectional carbon-epoxy prepreg by the autoclave technique. The damage of the reinforcement fibres is induced by making a crack in the beam using a circular saw. Selected numerical results are validated with two different experimental methods. First, the experimental test is conducted using a non-contact laser vibrometer provided with a scanning head and a data acquisition-visualization unit. Next, a modal analysis is performed by the contact method using the LMS analyzer with a modal hammer and an acceleration sensor. All numerical and experimental results of the beams with cracks are compared with the findings obtained for the specimens without any damage.

Aeroelastic instability of composite wings by the consideration of different structural constitutive assumptions

The aeroelastic instability of composite wings modeled as Circumferentially Asymmetric Stiffness (CAS) thin-walled composite beams with closed cross-section is carried out. The objective has been to investigate the effects of different assumptions of constitutive equations on the aeroelastic instability behavior. Non-classical effects such as restrained warping and transverse shear are included in the beam model. The unsteady incompressible airloads are presented using Wagner׳s function. A comparison of the results based on different constitutive equations for a number of configurations including three types of stacking sequence for a box cross-section and two types of stacking sequence for a biconvex cross-section, is performed. The effects of the values of twist as well as twist-bending stiffness coefficients have been studied carefully on the results. As an outcome of this investigation it is revealed that the different choices of structural constitutive equations which result in different values of stiffness quantities; namely, twist and twist-bending stiffness, significantly affect the predicted results. For example, a difference of up to 45% in the aeroelastic critical speed has been observed between different sets of constitutive equations in some cases.

Robust Aeroelastic Control of a Thin-Walled Wing Structure with Model Uncertainty

AbstractThe robust vibration control and dynamic response analysis of an advanced aircraft wing structure are addressed in this paper. The wing structure is modeled as a thin-walled beam with fiber-reinforced composite materials featuring a circumferentially asymmetric stiffness (CAS) configuration that completely splits into two coupled groups of motion. The time-dependent external loads are considered with unsteady aerodynamics in an incompressible flow field. To demonstrate the robust characteristics of the sliding mode methods, both the conventional linear quadratic Gaussian (LQG) regulator and the proposed method are compared with respect to model uncertainty and external excitation. The numerical results demonstrate that the sliding mode control (SMC) on the basis of the sliding mode observer (SMO) is an efficient way to control the unstable dynamic response subjected to various external loads associated with model uncertainty.

Robust aeroelastic instability suppression of an advanced wing with model uncertainty in subsonic compressible flow field

This paper addresses the robust aeroelastic instability suppression of an advanced aircraft wing modeled as a thin-walled beam structure with fiber-reinforced composite material featuring a circumferentially asymmetric stiffness (CAS) configuration. The unsteady aerodynamic loads in subsonic compressible flow are derived through the indicial function approach. Aeroelastic instability suppression is achieved via sliding mode control (SMC) based on sliding mode observer (SMO). To demonstrate the robustness of the SMC based on SMO, linear quadratic Gaussian (LQG) methodology is compared with respect to the model uncertainty. To this end, the obtained numerical simulation results emphasize the efficiency of the sliding mode control based on sliding mode observer to control the unstable aeroelastic phenomenon in conjunction with the model uncertainty.

Dynamic responses of composite H-beams with different elastic couplings

Governing equations are derived via Hamilton’s principle for composite thin-walled H-type open cross-section beams that show a number of non-classical effects such as transverse shear, primary and secondary warping, and anisotropy of constituent materials. The vibration characteristics of composite thin-walled beams with different elastic couplings, such as circumferentially asymmetric stiffness (CAS) and circumferentially uniform stiffness (CUS) configurations are investigated with respect to the bending-transverse shear coupling and the bending-twist coupling resulting from the directional properties of fiber reinforced composite materials. The dynamic responses of anisotropic thin-walled beams to harmonic and exponentially time-dependent loads are also investigated. It was revealed that transverse shear, elastic couplings, and warping effects greatly influence the free vibration and dynamic response characteristics of composite H-type open cross-section beams.

Vibration and flutter of wind turbine blade modeled as anisotropic thin-walled closed-section beam

Based on a variational asymptotic analytical model, vibration and aeroelastic stability of rotor blades modeled as anisotropic thin-walled closed-section beams are systematically addressed. The analysis is applied to a laminated composite construction of the circumferentially asymmetric stiffness (CAS) that produces bending-twist coupling. The vibration characteristics of composite beam are determined by the Extended Galerkin Method. The unsteady aerodynamic loads and centrifugal force are integrated with the classical aerodynamic model to deal with aeroelastic stability analysis. The influence of some related factors, ply angle, rotating velocity, and wind speed, is investigated. The paper gives methods of eigenvalue analysis and aeroelastic response, and gives the approaches to restrain classical flutter.

Aeroelastic Stability Analysis of Composite Wind Turbine Blade Dynamic Stall

A nonlinear aeroelastic analysis model of the composite wind turbine blade is presented.The composite structural model is an anisotropic thin-walled closed-section beam with bending-twist coupling produced by a special ply-angle configuration,referred to as circumferentially asymmetric stiffness(CAS).The aerodynamic model used in the present paper is the differential dynamic stall model developed at ONERA.By means of Galerkin's method,the nonlinear aeroelastic equations are reduced to ordinary equations.The general aerodynamic forces are obtained from strip theory.The resulting equations are then linearized for small perturbation about the equilibrium point and the stability characteristics are investigated through eigenvalue analysis and time domain integration.

Vibration of Wind Turbine Blade Modeled as Composite Thin-Walled Closed-Section Structure

Based on a laminated composite structure, vibration and nonlinear stall aeroelastic stability of rotor blades modeled as anisotropic thin-walled closed-section beams are systematically addressed. The analysis is applied to a laminated construction of the circumferentially asymmetric stiffness (CAS) that produces bending-bending-twist coupling. The vibration characteristics of composite beam are determined by the Galerkin Method. The unsteady aerodynamic loads and centrifugal force are integrated with the nolinear aerodynamic model to deal with aeroelastic stability analysis. The influence of some related factors, pretwisted angle, ply-angle rotational speed, and wind speed, is investigated. The paper gives methods of eigenvalue analysis and aeroelastic response, which can determine the stability of the blade forced by the nolinear aerodynamics.

복합재료 H-형 단면 보의 동적응답 해석

Equations of motion of thin-walled composite H-type cross-section beams exposed to concentrated harmonic and non-harmonic time-dependent external excitations, incorporating a number of nonclassical effects of transverse shear, primary and secondary warping, and anisotropy of constituent materials are derived. The forced vibration response characteristics of a composite H-type cross-section beam exhibiting the circumferentially asymmetric stiffness(CAS) configuration are exploited in connection with the structural bending-torsion coupling resulting from directional properties of fiber reinforced composite materials.

Exact solutions for coupled free vibrations of tapered shear-flexible thin-walled composite beams

In this paper, analytical solutions for the free vibration analysis of tapered thin-walled laminated-composite beams with both closed and open cross-sections are developed. The present study is based on a recently developed model that incorporates in a full form the shear flexibility. The model considers shear flexibility due to bending as well as warping related to non-uniform torsion. The theory is briefly reviewed with the aim to present the equilibrium equations, the related boundary conditions and the constitutive equations. The stacking sequences in the panels of the cross-sections are selected in order to behave according to certain elastic coupling features. Typical laminations for a box-beam such as circumferentially uniform stiffness (CUS) or circumferentially asymmetric stiffness (CAS) configurations are adopted. For open cross-sections, special laminations behaving elastically like the CAS and CUS configurations of closed sections are also taken into account. The exact values (i.e. with arbitrary precision) of frequencies are obtained by means of a generalized power series methodology. A recurrence scheme is introduced with the aim to simplify the algebraic manipulation by shrinking the number of unknown variables. A parametric analysis for different taper ratios, slenderness ratios and stacking sequences is performed. Numerical examples are also carried out focusing attention in the validation of the present theory with respect to 2D FEM computational approaches, as well as to serve as quality test and convergence test of former finite elements schemes.

BEHAVIORS OF CAS AND CUS THICK-WALLED CHANNEL COMPOSITE BEAMS

Recently the thick open section composite beams are extensively used to replace conventional metal load carrying members and stiffeners of structural elements. However, most of studies on the open section composite beams are confined to the thin composite beams. There are some works focused on the thick composite beams but they are limited only to closed section beams. Therefore, it is required to develop an appropriate model to analyze the thick open section composite beams. In this study, the cantilever beams of two specific lay-up configurations are considered which are the circumferentially asymmetric stiffness (CAS) and circumferentially uniform stiffness (CUS) beams. Under the vertical loading at the free end, loading induced deformations are obtained for the thick beams using the suggested model. The model includes coupled stiffness and secondary warping effects. The results are compared with those obtained using thin beam model to observe the thickness effects. Those results are also compared with the finite element analysis results for the verification of the suggested model. A good agreement is obtained between the results from the suggested model and those from finite element analysis.

Structural Modeling and Aeroelastic Analysis of High-Aspect-Ratio Composite Wings

A unified structural model for high-aspect-ratio composite wing with arbitrary cross-section is developed. Two types of lay-ups of the composite wing, namely, circumferentially uniform stiffness (CUS) configuration and circumferentially asymmetric stiffness (CAS) configuration, are investigated. The present structural modeling method is validated through ANSYS FEM software for the case of a composite box beam. Then, the case of a single-cell composite wing with NACA0012 airfoil shape is considered. To investigate the aeroelastic problem of high-aspect-ratio composite wings, the linear ONERA aerodynamic model is used to model the unsteady aerodynamic loads under the case of small angle of attack. Finally, flutter speeds of the high-aspect-ratio wing with various composite ply angles are determined by using U-g method.

EFFECT OF WASH-IN AND WASH-OUT ON THE FLUTTER CHARACTERISTICS OF COMPOSITE AIRCRAFT WINGS

In recent years composite materials are increasingly employed in a variety of aerospace applications because of its obvious merits. The present paper presents and discusses firstly the effect of the fibre orientations 0, bending-torsion material coupling, K on the eigenvalues and associated eigenvectors of a composite wing structure in a more realistic manner. The cantilevered composite wing structure is modeled in a way to simulate both Circumferentially Uniform Stiffness (CUS) and Circumferentially Asymmetric Stiffness (CAS) configurations. Secondly, the effect of wash-in and wash-out deformations on the flutter speed of both composite wing configurations. The wing models are generated using the finite element program FEMAP, v6 and analyzed using the standard FE software, MSC/NASTRAN, v70.5. Results from both model configurations are compared and discussed. It is shown that bending frequency is decreasing with increasing the fibre angle, where as the torsion frequency is a maximum at 0=±30° and ±45° for the CAS and CUS wing models respectively. It is found that bending-torsion coupling is more beneficial to the torsion frequency compared to the bending frequency. The positive coupling stiffness, which causes the wash-in behaviour, is found to increase the flutter speed of composite wings compared to the wash-out behaviour. Further more, coupling material stiffness is more beneficial to the flutter speed as in the case of CAS wing model compared to the CUS wing model.