Statics, dynamics, buckling and aeroelastic stability of planar cellular beams

This chapter examines cellular beams, made up of longitudinal and transverse fibers, equipped with flexural and shear stiffnesses. It presents continuous models for planar cellular structures are derived, namely: the shear beam and the Timoshenko beam. The chapter addresses several mechanical problems, statics, dynamics, buckling and aeroelasticity, in the linear, as well as in the nonlinear field. The elastic buckling of a planar cellular beam is studied. The shear beam model has been adopted in the literature, to study complex nonlinear dynamical problems. The chapter addresses the static problem for a grid beam, with regular mesh, for which the elastic constants are identified, under different hypotheses concerning the stiffness of the transverse fibers. It investigates the free oscillations of the macro-beam and explores aeroelastic phenomena. The cellular structure is immersed in a steady wind flow producing velocity-dependent aerodynamic forces.