Free vibrations of the partial-interaction composite members with axial force

The governing differential equations of motion are derived for the partial-interaction composite members with axial force and the solutions of free vibrations are presented under common boundary conditions. An exact analytical solution for a simply supported case is obtained. If the slip at the interface of the composite member is ignored, both the equations and the solution can be degenerated to those corresponding to the elementary beam theory as they should be. An approximate simple expression is also proposed to predict the fundamental frequency of the partial-interaction composite members with axial force, which is of practical interest. Finally, numerical results and the effects of the axial force, shear connector rigidity and other parameters upon the frequencies are presented and discussed in detail.