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Influence of constant compressive axial force on free transverse vibrations of uniform beams is considered. Three technical beam theories are applied and appropriate analytical solutions are obtained. Hamilton's variation principle is utilized for derivation of well -known differential equations of motion of Timoshenko beam, while Bernoulli-Euler and Rayleigh theories are considered as special cases. Furthermore, simple two-dimensional plane stress finite element with drilling degree of freedom is employed for numerical analysis. Appropriate code is developed and verified via comparison with commercial finite element software Abaqus, as well as with analytical results. Parametric analysis of influence of the axial force on the modal characteristics of considered beams is performed and discussed in detail.

This paper presents brief dynamic analysis of one typical steel bridge orthotropic plate. Geometry and load data are adopted according to recommendations from the literature. Calculation is preformed using the Finite element method where the commercial software package Abaqus is used. Dynamic load due to vehicle crossing is modeled via six weighted rigid plates with dimensions equal to the contact surface between the wheel and the plate. Obtained results suggest that the main impact on the structural response comes from the speed of the vehicle. Influence of the crossing of the second vehicle was negligible in presented analysis.

Paper deals with bifurcation stability of stiffened thin plates using the compound finite strip method. Using this method it is also possible to introduce point supports into plate which allows modeling of columns. Thin plate is obtained by simple addition of column and beam stiffness properties into finite strip via deformation energy. According to bifurcation stability theory, critical load is obtained from the standard eigenvalue problem. This approach allows efficient computation of stiffened plates without the need for additional degrees of freedom. Program code is written in software package Wolfram Mathematica. Verification of the model is done through comparison with the analytical solutions and the one obtained from commercial software packages.

Development of simple classroom demonstration device and software for visualization of structural normal modes is presented. Device is made of parts of old speaker, controlled with personal computer, where the harmonic motion of solenoid is used as an excitation for beam and plate models. Simple code for finite element free vibration analysis of plates is written in Wolfram Mathematica. Good agreement of results and attractive visual patterns of normal modes attracted attention of students. Results are confirmed using modern modal testing methods. Presented approach is complementary to standard teaching of structural dynamics.