Krzysztof Sokół

The Bernoulli-Euler and Timoshenko theories in the context of research on the characteristic curves of column with different boundary conditions

In this paper the boundary problem taking into account the shearing effect and rotational inertia of cross-section (Timoshenko theory) has been presented. The column is loaded by external Euler’s force with constant line of action. The results of numerical calculations of characteristic curves on the plane external load – vibration frequency obtained on the basis of Bernoulli-Euler and Timoshenko theories have been compared. Calculations have been performed for different slenderness parameter magnitude and types of support. It has been shown that the type of support has great influence on the difference in the obtained results on the basis of both considered theories.

Stability of a Hydraulic Telescopic Cylinder Subjected to Euler’s Load

In this paper the stability of a hydraulic telescopic cylinder subjected to Euler’s load is discussed. The boundary problem of stability has been formulated on the basis of the static stability criterion. The presented results of numerical simulations are related to the piston rod to make the easiest comparison of real life object to the disused one. The results can be used by the designers of the hydraulic telescopic especially in the case when the possibility of the damage due to buckling can be present.

Linear and nonlinear vibrations control of a two member column by means of piezoceramic element

The results of numerical studies on linear and non-linear transverse vibrations control of a two member column subjected to Euler’s load by means of piezoceramic element have been presented in this paper. The investigated column is composed of two members. The external member is a single element and the internal one consists of two rods (the one of them is a made of piezoceramic material). The connection of elements of the internal member has been modeled by means of a pin and a rotational spring of stiffness C. The boundary problem has been formulated on the basis of Hamilton’s principle. Due to non-linearity of the column, the perturbation method was used to solve the problem. An influence of the residual force generated by the piezoceramic element on natural vibration frequencies, maximum loading and amplitude - vibration frequency relationship have been discussed in this paper.