The article presents the process of identifying discrete-continuous models with the use of heuristic algorithms. A stepped cantilever beam was used as an example of a discrete-continuous model. The theoretical model was developed based on the formalism of Lagrange multipliers and the Timoshenko theory. Based on experimental research, the theoretical model was validated and the optimization problem was formulated. Optimizations were made for two algorithms: genetic (GA) and particle swarm (PSO). The minimization of the relative error of the obtained experimental and numerical results was used as the objective function. The performed process of identifying the theoretical model can be used to determine the eigenfrequencies of models without the need to conduct experimental tests. The presented methodology regarding the parameter identification of the beams with the variable cross-sectional area (according to the Timosheno theory) with additional discrete components allows us to solve similar problems without the need to exit complex patterns.

The study investigated the effect of the fill factor, lattice constant, and the shape and type of meta-atom material on the reduction of mechanical wave transmission in quasi-two-dimensional phononic structures. A finite difference algorithm in the time domain was used for the analysis, and the obtained time series were converted into the frequency domain using the discrete Fourier transform. The use of materials with large differences in acoustic impedance allowed to determine the influence of the meta-atom material on the propagation of the mechanical wave.

The study analyzed the influence of materials and different types of damping on the dynamic stability of the Bernoulli-Euler beam. Using the mode summation method and applying an orthogonal condition of eigenfunctions and describing the analyzed system with the Mathieu equation, the problem of dynamic stability was solved. By examining the influence of internal and external damping and damping in the beam supports, their influence on the regions of stability and instability of the solution to the Mathieu equation was determined.

Although the study of oscillatory motion has a long history, going back four centuries, it is still an active subject of scientificr esearch. In this review paper prospective research directions in the field of mechanical vibrations were pointed out. Four groups of important issues in which advanced research is conducted were discussed. The first are energy harvester devices, thanks to which we can obtain or save significant amounts of energy, and thus reduce the amount of greenhouse gases. The next discussed issue helps in the design of structures using vibrations and describes the algorithms that allow to identify and search for optimal parameters for the devices being developed. The next section describes vibration in multi-body systems and modal analysis, which are key to understanding the phenomena in vibrating machines. The last part describes the properties of granulated materials from which modern, intelligent vacuum-packed particles are made. They are used, for example, as intelligent vibration damping devices.