Nonlinear analysis of dynamic instability of aircraft wing structure based on first order shear beam theory and differential quadratic solution method

In this paper, for the first time, a nonlinear analysis of the dynamic instability of a relatively thick curved structure equivalent to a composite wing layer is performed. For this purpose, the wing structure of the aircraft is considered as a relatively thick curved beam and modelling has been done using first-order shear theory. Van Carmen's large non-linear strain relationships have been used in strain components in a curved line environment. One of the most complex instability modes is axial excitation of the curved beam under a harmonic dynamic load despite a static constant value. These static loads (positive or negative) and dynamic harmonic load coefficient have a significant relationship with static buckling load. Considering the dynamic axial load, the dynamic equations governing the system and the equations of the boundary conditions are obtained using the Hamilton principle and the method of calculating the changes, and to solve them, the generalized numerical differential squaring method is used. Also in this paper, for the first time, by solving the final algebraic nonlinear equations, the stability region of a relatively thick curved beam is determined as changes in the excitation frequency in terms of dynamic load. To determine the effects of different parameters on natural frequencies, critical buckling load and beam stability range, different modes including different linear and nonlinear kinematic models, different values of static load, length to beam thickness ratio and radius of curvature along with beam types Flat and curved composite layers have been considered. As one of the most important results, the results show that considering different combinations of fibbers, the amount of curvature as well as the geometric nonlinearity of the material is important and will have a great impact on the predicted responses for the dynamic instability region.