A mixed finite element method for free vibration analysis of multilayer composite beams

In this paper，a two-dimensional analytical model for composite beams is first proposed through the equivalent transformation of the cross-section. Based on the mixed variational principle，the dynamic state equations are derived through finite element meshing and interpolation along the length of the beam，with frequency contained nodal displacements and their energy-conjugated stresses as element nodal variables. The differential quadrature method（DQM）is introduced to discretize the equations along the height of the beam，and natural frequencies of composite beams under different axial forces and boundary conditions are obtained. This method was verified by numerical examples about natural frequencies of three beams，i.e. a concrete-wood composite beam，a concrete beam with a corrugated steel web and steel-concrete composite beam. Since the proposed method is based on the two-dimensional theory，it can provide benchmarks for beam theories and error analyses. © 2024 Nanjing University of Aeronautics an Astronautics. All rights reserved.