Dynamic Buckling of a Sandwich Bar Compressed by Periodically Variable Force

The paper presents an analysis of dynamic buckling of a sandwich bar compressed by a periodically variable force. In order to determine the stability of the bar transverse motion equations of its transverse vibration were formulated. From the equations of motion, differential equations interrelating of the bar 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 an ordinary differential equation (Hill’s equation) describing the bar vibration was solved. An analysis of the solution became the basis for determining the regions of sandwich bar motion instability. Finally, the critical damping coefficient values at which parametric resonance occurs have been calculated.