Nonlinear transient vibrations of an orthotropic silo longitudinally stiffened considering the charging/discharging of the grains

Resumo

The type of structure most used for the storage of grains are the cylindrical metallic silos, being slender
structures in shell, which have great capacity to withstand the axial loads and the lateral pressures that are
submitted. This paper aims to develop a low-dimensional model, with a reduced number of degrees of freedom,
capable of analyzing the behavior of orthotropic and longitudinally stiffened silos subjected to static and dynamic
axisymmetric actions. The nonlinear Sanders-Koiter theory is used to model the silo and Chebyshev polynomials
are used to simulate the cantilever at the base and the free end in which these types of structures are commonly
built. Grain pressures are determined according to the Janssen model, including the Heaviside function to simulate
charging, and discharging inside the silo. In addition, the Heaviside function is also applied to the kinetic energy
and the natural frequency of the system, to compose the variation of mass and damping generated by the grains
over time. The motion equations are obtained by applying Hamilton's Principle and the Rayleigh-Ritz method and
using the 4th order Runge-Kutta method, the maximum axial and transverse displacements during charging, and
discharging are found, noting that an increase occurs when compared to the static values of grain storage, which
generates greater efforts being applied to the silo structure.