A novel semi-active TMD with folding variable stiffness spring

An innovative variable stiffness device is proposed and investigated based on numerical simulations. The device, called a folding variable stiffness spring (FVSS), can be widely used, especially in tuned mass dampers (TMDs) with adaptive stiffness. An important characteristic of FVSS is its capability to change the stiffness between lower and upper bounds through a small change of distance between its supports. This special feature results in lower time-lag errors and readjustment in shorter time intervals. The governing equations of the device are derived and simplified for a symmetrical FVSS with similar elements. This device is then used to control a single-degree-of-freedom (SDOF) structure as well as a multi-degree-of-freedom (MDOF) structure via a semi-active TMD. Numerical simulations are conducted to compare several control cases for these structures. To make it more realistic, a real direct current motor with its own limitations is simulated in addition to an ideal control case with no limitations and both the results are compared. It is shown that the proposed device can be effectively used to suppress undesirable vibrations of a structure and considerably improves the performance of the controller compared to a passive device.