Vibration of Structures

the repeated reciprocating or rotational motion of structural members as a result of elastic deformation under forces that change very rapidly over time. During vibration of structures, structural members are displaced with respect to their stable position of static equilibrium (vibration of bridges, tall structures, and machine foundations) or of general motion (vibration of aircraft, railroad cars, and motor vehicles). The vibration of structures is classified according to several features. With respect to deformations, a distinction is made among longitudinal vibrations (tension-compression), transverse vibrations (flexural and shearing vibrations), torsional vibrations, and mixed vibrations; with respect to the character of the displacements over time, a distinction is made between periodic and nonperiodic vibrations.

Large vibrations are dangerous to the strength and stability of structures. An example is the extensive destruction of buildings and structures during earthquakes, the breaking of engine shafts, and the failure of the Tacoma suspension bridge, which was built in 1940 in the USA, as a result of vibrations caused by wind. Even moderate regular vibration of structures that are safe for the structure itself may have a harmful effect on human health and on the quality of precision production processes. Therefore, control of the vibration of structures by taking vibrations design into account and by implementing measures to reduce the vibration of structures is of great importance. The problems of designing structures for vibrations and the methods of reducing the vibration of structures are considered in the theory of the vibration of mechanical systems.