Generalized variational principle of dynamic analysis on naturally curved and twisted box beams for anisotropic materials

Abstract

An incomplete generalized variational functional for naturally curved and twisted composite box beams with complete constrained boundaries at two ends is established by means of Lagrange multiplier method. The equations of motion governing the dynamic behavior of the beams and corresponding boundary conditions are derived from the stationary condition of the functional. The non-classical influences relevant to the beams are those due to transverse shear deformations, torsion-related warping and several elastic couplings that can arise in composite beams. In order to demonstrate the correctness of the theory developed the natural frequencies and normal mode shapes of the beams under in-plane free vibration are evaluated and compared with the results using PATRAN’s beam elements.