Desenvolvimento de um programa computacional para análise modal de estruturas reticuladas planas

Abstract

This study develops a Python based computational program for the modal analysis of planar reticulated structures, with emphasis on determining natural frequencies and the corresponding mode shapes. The formulation is based on the Direct Stiffness Method, incorporating the plane frame element and assembling the global stiffness and mass matrices with a consistent mass formulation. After the enforcement of boundary conditions, the modal problem is cast and solved as a generalized eigenvalue problem using the reduced submatrices associated with the free degrees of freedom. The structural model is defined via spreadsheet input files, which standardize data entry and facilitate the organization of output results. Program validation is carried out by comparison with Autodesk Robot Structural Analysis Professional, adopted as a commercial reference, using two planar frame examples with distinct layouts. For the first three vibration modes, close agreement is obtained between the computed natural frequencies, with relative errors on the order of 1%, indicating consistency in the implementation of the matrix assembly routines, constraint handling, and numerical solution of the modal problem. The resulting program constitutes a reproducible and pedagogical tool, suitable for preliminary studies of the dynamic behavior of planar structures under the assumptions of linear response and undamped free vibration.