Optimal Design for Maximum Fundamental Frequency and Minimum Intermediate Support Stiffness for Uniform and Stepped Beams Composed of Different Materials 2020-01-5014

The minimum support stiffness that achieves the maximum modal frequencies or critical speed is very important in the design of mechanical systems. The optimal values of the intermediate support stiffness and geometrical parameters of uniform and stepped Timoshenko beams composed of single or two materials are studied in order to maximize the modal frequency and minimize the intermediate support stiffness. Dynamic stiffness matrix (DSM) method and multi-objective particle swarm optimization (MOPSO) algorithm are used together to evaluate new optimal parameters. For single material, the results show that for uniform thick beams, the optimal maximum fundamental frequency and minimum intermediate support stiffness are lower than those of Bernoulli-Euler beams. In addition, the optimal design for stepped beams made of two metallic materials is investigated. For three different metallic combinations, gain factors of 1.561 to 2.745 are obtained for a beam without intermediate support. Comparison with experimental results is carried out. The current study and its results can be applied to improve the dynamic performance of many of industrial applications, such as guyed masts derricks, vertical tube furnaces, and long rotary machines with intermediate support.