The analysis of publications and the results obtained in the field of dynamic behavior of inhomogeneous beams and rods based on foreign press materials is performed. The work consists of an introduction and six sections. The introduction discusses the relevance of the problems associated with the study of inhomogeneous beam vibrations. The second part is devoted to highlighting the achievements in the development and application of analytical methods. The next paragraph deals with various aspects, reflecting the variety of dynamic phenomena arising in geometrically heterogeneous beam structures. Results related to modeling of conical, stepped beams and rods having different types of geometric features are discussed. The fourth section considers the state of the art for dynamic problems for physically inhomogeneous beams. It is shown that structural heterogeneity can be associated not only with material properties, but also arise due to external influences, such as inertial and temperature loads. Considerable attention is paid to questions related to the effective use of structurally heterogeneous beams in the field of architecture, construction, robotics, aeronautics and other innovative fields. The sixth and seventh paragraphs give an overview of the existing numerical approaches for an approximate and reliable description of the dynamic processes taking place in inhomogeneous beams. Different industrial software packages are discussed that allow solving dynamical problems of beams with varying physical and geometric properties within a reasonable time and with a high degree of accuracy. In the seventh, the final part, much attention is paid to the application of the finite element method.

Keywords: dynamics, a beam with a variable cross-section, eigenvibrations, numerical methods, structural inhomogeneity, finite element method, functionally graded materials