Frequency and stress optimization of an engineered wood portal frame suporting a rotating machine

Resumo

We consider a portal frame with 3 prismatic bars. The horizontal beam, of length L, is articulated at the top of the vertical columns, of height h, embedded in the base. The cross sections are rectangular with thickness b, constant, and width d, which can be different in the beam (dv) and in the columns (dc), always greater than or equal to the thickness. The material is considered linear and homogeneous elastic, with given modulus of elasticity (E) and density. In the middle of the beam span, a motor of mass M is mounted, rotating at a frequency of N rpm.
Considering only the Service Limit State, we present the minimization of the mass of the structure so that the motor rotation frequency is always at least 20% above any of the first 2 undamped free vibration frequencies of the frame.