Formulas for deflections and a simplified Dunkerley method for calculating the vibration frequency of a planar truss

Строительная механика

The object of the study is a scheme of a regular statically defined frame-type truss. The lattice of the truss in the crossbar part of the structure is cruciform. The method of induction in the Maple system of symbolic mathematics derives the analytical dependence of the deflection of the truss and the displacement of the movable support on the number of panels in the crossbar. Maple operators are used to generalize solutions for several trusses with a consistently increasing number of panels for a common case. The calculation of the first oscillation frequency of the structure by the Dunkerley method is simplified by replacing the sum of partial frequencies by calculating the product of the maximum partial frequency by the number of degrees of freedom divided by two. Result. The analytical expression for the frequency depending on the number of panels turns out to be noticeably simpler, and the error of the approximate solution is smaller. The analytical results are compared with the numerical solution.