69439 AlfaBuild AlfaBuild 2658-5553 3 10.57728/ALF.38.3 The first natural frequency and deflection of a two-hinged truss arch The first natural frequency and deflection of a two-hinged truss arch 0000-0002-8588-3871 16412815600 H-9967-2013 Kirsanov Mikhail Nikolaevich mpei2004@yandex.ru Moscow Power Engineering Institute 16 02 2026 38 2 38 3803 3803

The object of research is a statically determinate model of a planar, regular, arched truss on two fixed, hinged supports. Using the induction method in a computer mathematics system, calculation formulas for the structure's deflection under a uniform vertical nodal load on the lower or upper chord are derived. An approximate analytical dependence of the truss's first natural frequency of oscillation on the number of panels is found. The forces in the rods are calculated for an arbitrary number of panels. Method. The truss's inertial properties are modeled using concentrated masses at the nodes. The truss's natural frequency of oscillation is calculated using the Dunkerley method and its simplified version. Vertical node oscillations are assumed. Results. A comparison of the analytical calculations with numerical results, performed taking into account all degrees of freedom of vertical mass oscillations, shows good agreement between the methods.

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