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The free vibrations and optimization of the shape of a column subjected to a load by a follower force directed towards the positive pole applying the variational method

100%

Szmidla J. , Yatsenko D.

tom Vol. 25

393--398

The results of numerical computations and theoretical research into optimization of the shape and the free vibrations of a cantilever column subjected to a load by the follower force directed towards the positive pole are presented in this paper. The systems of equations: of motion and of cross-sectional area of the considered column were determined on the basis of the total mechanical energy and Hamilton’s principle. Taking into account the formulated boundary conditions, optimized shapes of the systems were determined for the chosen values of geometrical parameter of a head subjected to a load. The values of natural frequency of the considered system were obtained taking into account distribution of flexural rigidity along the column length while the values of critical load of optimized column were obtained on the basis of curves of changes in the basic natural frequency in relation to external load. The results of numerical computations were presented in the case of one from three classes of the systems – versatile uniformly convergence column for the assumed criterion of constant volume of the system.

Influence of the specific load on stability and vibrations of the multimember column with internal cracks

80%

Sokół K. , Kuliński K.

tom Vol. 71, nr 4

art. no. e146408

Slender systems are mostly studied when Euler’s load or follower load is considered. The use of those types of external loads results in well-known divergence or flutter shape of the characteristic curve. In this study, one takes into account the specific load which allows one to obtain an interesting divergence – pseudo flutter shape of characteristic curves on the external load–vibration frequency plane. The curves can change inclination angle as well as one can observe the change in vibration modes along them. The shape of those curves depends not only on the parameters of the slender system but also on loading heads that induce the specific load. In this study, one considers the slender multimember system in which cracks are present and weaken the host structure. The results of theoretical as well as numerical simulations are focused on the influence of the parameters of the loading heads on vibrations, stability, and loading capacity of the investigated system as well as on the possibility of partial reduction of unwanted crack effect.