Free vibration of a steel-concrete composite beam with coupled longitudinal and bending motions

Free vibrations of steel-concrete composite beams are analyzed by using the dynamic stiffness approach. The coupled equations of motion of the composite beams are derived with help of the Hamilton's principle. The effects of the shear deformation and rotary inertia of the two beams as well as the transverse and axial deformations of the stud connectors are included in the formulation. The dynamic stiffness matrix is developed on the basis of the exact general solutions of the homogeneous governing differential equations of the composite beams. The use of the dynamic stiffness method to determine the natural frequencies and mode shapes of a particular steel-concrete composite beam with various boundary conditions is demonstrated. The accuracy and effectiveness of the present model and formulation are validated by comparison of the present results with the available solutions in literature.