The paper is devoted to a review of recent achievements in the field of dynamic analysis of structures and structural elements, such as beams and plates, with embedded viscoelastic (VE) dampers and/or layers. The general characteristics of VE materials, their rheological models, and methods of parameters identification are discussed. New formulations of dynamic problems for systems with VE elements are also reviewed. The methods of determination of dynamic characteristics, together with the methods of analysis of steady-state and transient vibrations of such systems, are also discussed. Both linear and geometrically non-linear vibrations are considered. The paper ends with a review of the methods of sensitivity and uncertainty analysis, and the methods of optimization, for structures with VE elements.

The paper presents an analysis of the rheological properties of a selected viscoelastic material, which is dedicated to the reduction of vibrations in structures subjected to dynamic loads. A four-parameter, fractional Zener model was used to describe the dynamic behavior of the tested material. The model parameters were identified on the basis of laboratory tests performed at different temperatures and for different vibration frequencies. After proving that the material is thermoreologically simple, the so-called master curves were created using a horizontal shift factor. The Williams–Landel–Ferry formula was applied to create graphs of the master curves, the constants of which were determined for the selected temperature. The resulting storage and loss module functions spanned several decades in the frequency domain. The parameters of the fractional Zener model were identified by fitting the entire range of the master curves with the gradientless method (i.e., Particle Swarm Optimization), consisting in searching for the best-fitted solution in a set of feasible solutions. The parametric analysis of the obtained solutions allowed for the formulation of conclusions regarding the effectiveness of the applied rheological model.

The subject of this study was the complex structure of a wooden historic church, which consisted of several segments that differed in the material used, the structural system employed, and the degree of wear of the elements. Particularly examined were the multi-branched columns located at the junction of different segments. The main objective of the analyses was to determine the degree of bonding of the column branches and the effect of this bonding on the operation of the entire structure. To evaluate the degree of bonding of the column branches, it was proposed to use experimental modal analysis. Based on the results of the experiment, it was found that the column branches are connected, but their cooperation is limited. Several computational models of the analyzed structure were also created, differing, for example, in the degree of bonding of the column branches. The effect of bonding the column branches on the values of stresses in the nave columns and on the values of extreme wind-induced displacements was studied.