Influence of the damping in the sandwich bar on the dynamic stability

In the paper influence of the damping in the sandwich bar on its dynamic stability is studied using analytical methods. This paper presents an analysis of dynamic buckling of a sandwich bar compressed by a periodically variable force. In order to determine the dynamic stability of the bar equations of its transverse vibration were formulated. From the equations of motion, differential equations interrelating of the dynamic deflection with space and time were derived. The partial differential equations were solved using the method of separation of variables (Fourier’s method). Then the ordinary differential equation describing the bar vibrations was solved. An analysis of the solution became the basis for determining the regions of sandwich bar motion instability. Finally, the value of the compressive force at which dynamic stability occurs have been calculated.