Number Of Nonclassical Effects Research Articles

Reduced order nonlinear aeroelasticity of swept composite wings using compressible indicial unsteady aerodynamics

Nonlinear dynamic aeroelasticity of composite wings in compressible flows is investigated. To provide a reasonable model for the problem, the composite wing is modeled as a thin walled beam (TWB) with circumferentially asymmetric stiffness layup configuration. The structural model considers nonlinear strain displacement relations and a number of non-classical effects, such as transverse shear and warping inhibition. Geometrically nonlinear terms of up to third order are retained in the formulation. Unsteady aerodynamic loads are calculated according to a compressible model, described by indicial function approximations in the time domain. The aeroelastic system of equations is augmented by the differential equations governing the aerodynamics lag states to derive the final explicit form of the coupled fluid-structure equations of motion. The final nonlinear governing aeroelastic system of equations is solved using the eigenvectors of the linear structural equations of motion to approximate the spatial variation of the corresponding degrees of freedom in the Ritz solution method. Direct time integrations of the nonlinear equations of motion representing the full aeroelastic system are conducted using the well-known Runge–Kutta method. A comprehensive insight is provided over the effect of parameters such as the lamination fiber angle and the sweep angle on the stability margins and the limit cycle oscillation behavior of the system. Integration of the interpolation method employed for the evaluation of compressible indicial functions at any Mach number in the subsonic compressible range to the derivation process of the third order nonlinear aeroelastic system of equations based on TWB theory is done for the first time. Results show that flutter speeds obtained by the incompressible unsteady aerodynamics are not conservative and as the backward sweep angle of the wing is increased, post-flutter aeroelastic response of the wing becomes more well-behaved.

Calculation of flutter and dynamic behavior of advanced composite swept wings with tapered cross section in unsteady incompressible flow

ABSTRACTIn this study, the aeroelastic stability and response of a swept composite wing in subsonic incompressible flow are investigated. The wing is modeled as an anisotropic tapered thin-walled beam with the circumferentially asymmetric stiffness structural configuration to establish proper coupling between bending and torsion. The structural model considers a number of nonclassical effects, such as transverse shear, material anisotropy, warping inhibition, nonuniform torsion, rotary inertia and three-dimensional strain effects. The aerodynamic strip method based on two-dimensional Wagner function in unsteady incompressible flow is used. Following the analysis, the mass, stiffness and the damping matrices of the nonconservative aeroelastic system are formed such that the extended Galerkin method and the separation of variables method can be employed. As a result, the coupled and linear governing system of dynamic equations is obtained. Then, by transforming matrices into the state-space and state-vector forms, the problem under study is finally converted into an eigenvalue problem. The flutter and the divergence speeds for various layer configurations with different geometric and material properties and fiber orientations are obtained. By solving the aforementioned equations of motion in the time domain, the aeroelastic responses of the tapered swept composite wing are computed. The obtained results are compared with the available literature.

Aeroelastic Stability and Response of Composite Swept Wings in Subsonic Flow Using Indicial Aerodynamics

In this study, the aeroelastic stability and response of an aircraft swept composite wing in subsonic compressible flow are investigated. The composite wing was modeled as an anisotropic thin-walled composite beam with the circumferentially asymmetric stiffness structural configuration to establish proper coupling between bending and torsion. Also, the structural model consists of a number of nonclassical effects, such as transverse shear, material anisotropy, warping inhibition, nonuniform torsional model, and rotary inertia. The finite state form of the unsteady aerodynamic loads have been modeled based on the indicial aerodynamic theory and strip theory in the subsonic compressible flow. Novel Mach dependent exponential approximations of the indicial aerodynamic functions have been developed. The extended Galerkin’s method was used to construct the mass, stiffness, and damping matrices of the nonconservative aeroelastic system. Eigen analysis of the system was performed to obtain the aeroelastic instability (divergence and flutter) boundaries. Also, solving the equations of motion in the time domain leads to the aeroelastic response of wing in different flight speeds. The obtained results are compared with the available results in the literature, which reveals an excellent agreement. The numerical results obtained in this article seek to clarify the effects of geometrical and material couplings and flight Mach number on the aeroelastic instability and response of composite wings in subsonic compressible flow.

Aeroelasticity of Composite Aerovehicle Wings in Supersonic Flows

A comprehensive aeroelastic model developed toward investigating the static divergence, e utter, and dynamic aeroelastic response of composite aerovehicle wings to sharp-edged gust and blast loads in supersonic e owe eld is presented. The aerovehicle wings are modeled as an anisotropic composite thin-walled beam structure featuring circumferentially asymmetric stiffness lay up that generates preferred elastic couplings. A number of nonclassical effects, such as transverse shear, warping restraint, and three-dimensional strain effects, are incorporated in the structural model. Based on the concept of two-dimensional indicial functions considered in conjunction with the aerodynamicstriptheoryextendedtothree-dimensionalwingmodel,theunsteadyaerodynamicloadsinsupersonic e ows are derived. The effect of elastic tailoring and the implications of transverse shear, warping restraint on divergence and dynamic response of selected wing cone gurations are investigated, and pertinent conclusions are outlined. Nomenclature AR = wing aspect ratio, L=b a.s/ = geometric quantity; see Eq. (2) and Fig. 3 aij = one-dimensional global stiffness coefe cients a1 = undisturbed speed of sound b;d = semichord and semidepth of the beam normal cross section, respectively bi = inertia coefe cient Eij = Young’ s modulus of orthotropic materials in the material coordinate system h.s/ = wall thickness as the function of the midline

On a shear-deformable theory of anisotropic thin-walled beams: further contribution and validations

Within the framework of an existing anisotropic thin-walled beam model, a number of non-classical effects are further incorporated and the model thereby developed is validated. Three types of lay-ups, namely, the cross-ply, circumferentially uniform stiffness, and circumferentially asymmetric stiffness are investigated. The solution methodology is based on the Extended Galerkin's Method and the non-classical effects on the static responses and natural frequencies are investigated. Comparisons of the predictions by the present model with experimental data and other analytical as well as numerical results are conducted and pertinent conclusions are drawn. This work is the first attempt to validate a class of refined thin-walled beam model that has been extensively used towards the study, among others, of dynamic response, static aeroelasticity and structural/aeroelastic feedback control.