Studying forced oscillations of a single-span cantilever beam using the analytical method (Journal of Mathematics Mechanics and Computer Science, 2025)
This article deals with the "dynamics" of a rod system (a two-support beam with two cantilevers) with three point masses located along its length that simulate the distributed mass of the structure under the action of a vibratory dynamic load applied to the corresponding mass; this load models the kinematic disturbance that occurs in the chassis structure of vehicles when they move along uneven road surfaces.Dynamic forces and displacements were obtained by an accurate analytical method of forces based on modal and vibration analysis of the structure operation. Unit and load coefficients of canonical equations were determined by the Mohr formula using the Vereshchagin rule.A comparative analysis of the parameters of the beam stress-strain state was carried out for absolutely rigid and elastic-pliable support points of the chassis structure.As a result of the study, the necessary unit and final moment and deflection diagrams were presented. For the comparative analysis of the results of dynamic and static calculations, the values of dynamic coefficients for bending moments in characteristic nodes along the beam length were calculated.
Keywords: two-support cantilever beam; point masses; external vibration load; kinematic disturbance; dynamic displacements and forces; force method; displacement diagrams; elastic pliability of supports; dynamic coefficient; circular frequencies; frequency spectrum.