Engineering Transactions, 55, 3, pp. 217–227, 2007

Dynamic Buckling of a Sandwich Bar Compressed by Periodically Variable Force

Wrocław University of Technology Wrocław, Poland

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.
Keywords: sandwich bars, stability
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