Dynamic analysis of 3-DOF systems: Optimizing vibration control with shape memory alloy and stainless steel springs

This research delves into the intricate dynamics of 3-DOF (Three Degrees of Freedom) systems, emphasizing their capacity for independent movement in three dimensions. Unlike single-DOF systems, these configurations necessitate three coordinates & equations of motion, incorporating mass, damper, and stiffness matrices. The study focuses on the nuanced effects of introducing a damper to the vibration absorber, specifically investigating its influence on the system’s natural frequencies. Two distinct cases are examined, each involving unique arrangements of springs and dampers. And, the arrangements integrate the Shape Memory Alloy (SMA) as well as the Stainless Steel (SS) springs, with the over-arching aim of improving the vibration governing through the tart-up of system. Also, in case (1), a thorough test of a massless spring and the damper preparation in parallel among (3) masses in a system with a 3-DOF is commenced. The motion equations being derived and the non-trivial solutions are determined for revealing the 1st, 2nd, and 3rd natural frequencies. As well, case (2) presents an arrangement with kSMA, in parallel with a damper between the second and third masses, further exploring the system’s dynamic behavior. In addition, the motion’s equations being expressed, as well as the natural frequencies being determined throughout the equations of non-trivial solution. Furthermore, the investigation includes the spring constants computation for the Nitinol and the SS springs, integrating the physical characteristics explained in the tables. Moreover, the analysis of MATLAB works as a complete study into the conduct of natural frequency of the system with 3-DOF. The tables showing the relation between the natural frequencies and the values of stiffness give an obvious description of the sensitivity of system to the changes in the factor of stiffness. The present work provides important visions into the intricate dynamics of systems having 3-DOF, giving a basis for more examination in the vibration governing realms and the engineering uses. Moreover, the results underscore the planned modifications significance in stiffness of spring for the natural frequencies optimization in the applied scenarios.