Clamped Column Research Articles

Liapunov Stability Criteria for Continuous Systems Under Parametric Excitation

A Liapunov direct method is developed here to derive stability criteria for continuous systems under parametric excitation. The method makes use of time-dependent Liapunov functionals and the extremal properties of Rayleigh quotients of self-adjoint operators. The application of the method entails solving an eigenvalue problem with the variable t appearing in the problem strictly as a parameter. As examples of application the method is applied to (a) a clamped column under the action of periodic axial load, and (b) the panel flutter problem with the panel also subjected to periodic in-plane load. The calculated results for the first example show improvement over those obtained previously.

Stability of Heated Elastic Plastic Column

It is shown analytically and confirmed experimentally that the buckling strength of a clamped column can be significantly reduced by partial yielding caused by a transverse temperature gradient. The behavior of the column is of the Shanley type. An initially straight column can begin to bend at any load between two characteristic loads. The classical buckling load lies between the characteristic loads. Below it a load deflection curve initially rises, and above it falls. For a real column the lowest critical load is the most significant. The maximum load the column can carry (smaller than the classical buckling load) when it starts to buckle at this load was determined numerically for some typical cases. From a design point of view the best value to use for a critical load is probably the lowest buckling load. This use of the lowest buckling load was confirmed by the experimental investigation which showed the maximum load the columns carried to group closely around this value.