Dynamic response of thin-walled composite structures with application to aircraft wings
A general analytical method is developed to study first the buckling behaviour and then the dynamic characteristics of thin-walled composite structures with the presence of bending torsion coupling. The dynamic response theory incorporates the dynamic stiffness matrix approach and generalised coordinates using the normal mode method. Structural components considered are thin-walled laminated composite beams with carbon-fibre, glass-fibre or other reinforced plastic lay-ups. The examples of such beams and their applications include aircraft wings, hulls of ships, helicopter and wind turbine blades. All assumptions made in this work are based on elastic linear small deflection beam theory so that the overall response of the beam is represented by the superposition of all individual responses in each mode. Bending-torsion coupling effects arising from the anisotropic nature of fibrous composites, as well as due to non-coincident centroid and geometric shear centre of the beam crosssection, are the main contributory elements when developing the theory. The beam is subjected to time dependent forces and/or torques which can be either concentrated or distributed over its length. Both deterministic and random loads are considered. An important example of a deterministic load is one that varies harmonically in time. The Duhamel integral is employed to calculate the response to any arbitrary time dependent deterministic load. The random load is assumed to be Gaussian, having both stationary and ergodic properties. The evaluation of the response to the random load is carried out in the frequency domain by relating the Power Spectral Density (PSD) of the output to that of the input using the complex frequency response function. A number of PSD distributions are considered as random input in order to determine the PSD of the dynamic response. Atmospheric turbulence, which is considered to be one of the forms of random excitation, is modelled using the von Karman spectra for composite aircraft wings. In order to establish the methodology, bending-torsion coupled metallic beams are first ,investigated. The bending-torsion coupling in such beams occurs due to non-coincident centroid and geometric shear centre of the beam cross-section. The natural frequencies and mode shapes in undamped free vibration are obtained and the significance of generalised ,mass in each of the modes of vibration is evaluated. A normal mode method is then used to compute the frequency response function of the beam. The effects of shear deformation rotatory inertia and axial load on the frequencies, mode shapes and dynamic response characteristics are demonstrated. It was essential at an earlier stage of the investigation to validate the chosen composite beam modelling. Among all the different techniques used to determine the rigidities of a composite beam, the buckling load provides a reasonable estimate. The elastic critical buckling loads of thin-walled laminated composite columns for various end conditions are established theoretically using the exact stiffness method. The effect of shear deformation on the buckling characteristics of the column is demonstrated. Experiments are carried out to establish the elastic critical buckling load of metallic and laminated composite columns. Theoretical predictions of the buckling behaviour are corroborated by experimental results and other published results. The investigation is then focused on composite beams, but the response analysis of such beams is significantly more complicated than that of their metallic counterparts. This is mainly due to anisotropic characteristics of laminated fibrous composites. A detailed parametric study with the variation of significant composite parameters, such as ply angle, is undertaken and the importance of the results are highlighted. A suite of computer programs in FORTRAN is developed to predict the bucklingbehaviour, the free vibration and the responsec characteristics of thin-walled composite or metallic beams based on the theory proposed. Numerical results are presented, fully discussed and commented on.