The Analysis of Vibrations in a Floor Plate With Two Sources of Vibration

This article presents a mathematical model of vibrations in a floor slab with two sources of vibration (rotors with unbalanced masses). The equations of the motion of a system of bodies are obtained using Lagrange equations of the second kind. An analytical solution to the system of differential equations is obtained under the assumption that the angular velocities of the vibration sources are constant. The vibrations of the floor slab consist of three components: a damped vibration, which has its own frequency, but is caused by the action of driving forces, and two forced vibrations. The results are presented using the example of vibrations of a 3 m long I-beam with several vibration sources with unbalanced masses. It was found that in some cases deflections may exceed permissible values. A structural model of systems with moving loads and vibration protection has been constructed, which visually represents the object under consideration, abstracting from its specific content. As practice shows, all kinds of vibration sources can be represented by a system with moving loads. The results of the study indicate the relevance of a more in-depth study of the influence of moving loads on the dynamics of building structures and the development of special vibration protection measures during the design, construction, and operation of buildings. Particular attention should be paid to simultaneous exposure to multiple vibration sources.