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FROM:
Jan Ravinger (Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovakia),
“Stability and vibration in civil engineering”, Building Materials and Structures, Vol. 57, (2014, 2(3-17)
INTRODUCTION: Taking into account the stiffness and inertia forces, dynamic behaviour of structures can be investigated. Dynamic investigation usually starts with an example of free vibration. It means to evaluate the natural frequency. The simplest stability problem of structures is buckling of a column. This problem can be arranged preparing the equilibrium conditions on a deformed structure. In general, however, for the evaluation of the stability problems strains should be evaluated for a deformed differential element what means to apply geometric non-linear theory.
Combination of dynamics and stability yields in a lot of problems: dynamic buckling, dynamic post buckling behaviour, parametric resonance, etc. Introduction example – vibration of a column loaded in compression is simple but its investigation still represents a lot of problems.
The natural frequency can be measured by using rather simple equipment. The comparison of frequencies measured experimentally and evaluated numerically is the basis of non-destructive methods for investigation of structure properties. Generally, it can be said that in structural design stability effects have to be taken into consideration. These two ideas are the reason for our investigation of the combination of vibration and stability.
Leonard Euler was probably the first scientist who had analyzed stability problems. The former solutions are supposed to be the linear stability. It means that we suppose an ideal structure. The differences between theory and reality inspired researchers to search for more accurate models. Especially the slender web as the main part of thin-walled structure has significant post-buckling reserves and it is necessary to accept a geometric non-linear theory for their description. The problem of the vibration of the non-linear system was formulated by Bolotin [2]. Burgreen [3] analysed the problem of the vibration of an imperfect column in early 50's. Some valuable results have been achieved by Volmir [7]. Combination of dynamics and stability is still a subject of research all over the world.
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