Rapid step response with limited ringing and light damping.

Abstract

The time domain step response of an underdamped simple harmonic oscillator can be characterized as having two parts. The first is a transition from the initial position where the structure is accelerated toward a target position by a step force that introduces energy to the system. The second is a ringdown process, involving decaying oscillations about the target position as energy is removed from the structure. This study reports how an array of substantially smaller subordinate oscillators attached to the primary structure can dramatically reduce the time constant of the ringdown (the settling time) without slowing the first phase (rise time) in the way added classical damping does. In addition to having a more rapid initial response, a lightly damped oscillator with such an array of attachments requires less energy to change states than a more heavily damped structure. The approach is based on the concept of apparent damping, where vibration energy is transferred into and trapped by the set of attachments. Numerical results show that the distribution of the individual masses, isolated natural frequencies, and quality factors Q of the attachments, referred to as a subordinate oscillator array, can be tailored to achieve the rapid step response.