Shape Memory Alloy Based Actively Tuned Undamped Mass Absorber

Tuned Undamped Mass Vibration Absorber

The combination K, M is the schematic representation of the system under consideration, with the force, Fsinωt acting on it as show in Figure 1. The vibration absorber consists of comparatively a small vibratory system k, m attached to the main mass M as shown in Figure 1. The natural frequency of the attached absorber is chosen to be equal to the frequency, ω of the disturbing force. It will be shown that the main mass, M does not vibrate at all, and that the small system k, m vibrates in such a way that their spring force are equal and opposite to Fsinωt. So there is no net force acting on main mass M and therefore that mass does not vibrate.

Figure 1.

Equivalent lumped mass representations

Equations of motion of the combined system are,

The response of forced vibration of this system will be in the form, (2) where a₁ and a₂ are the amplitudes of main mass and absorber mass respectively Division by sinωt transforms the differential equations into algebraic equations the result.

For simplification the equations are converted into a dimensionless form and for that purpose the following symbols are introduced.