Natural Frequency Optimization of 2D and 3D Truss Structures Using a Discrete Sensitivity Analysis

Controlling and optimizing natural frequencies of structures is an important issue in mechanical, aerospace and civil engineering. In this paper, some new problems for cross-section area optimization of 2D and 3D truss structures considering different frequency objective functions are introduced and investigated. Three algorithms are developed in order to 1- increase the difference of the first two natural frequencies, 2- increase the first natural frequency and 3- increase of the second natural frequency with a limited change of the first natural frequency. Using a discrete sensitivity analysis, the cross-section area of the truss members are changed while the total mass of the structure is maintained fixed in order to achieve optimum natural frequencies. Modal analysis, sensitivity analysis and optimization process are performed by a developed APDL code in ANSYS software. Several two and three dimensional truss optimization examples are presented to demonstrate the efficiency of the methods. The presented examples show that natural frequencies of a truss structure can be optimized significantly by using the proposed methods.