Procedure

This experiment deals with the process of design of a tuned vibration absorber. Read the text provided on the screen opened on clicking tab 'Background'.

On opening the screen of simulator by clicking the tab 'simulator' and following the hyperlink 'click here to open the simulator', you will see graphics of main system having mass M₁ and stiffness K₁ (divided in two springs, each having stiffness K₁/2) attached with an auxiliary system with mass M₂ and stiffness K₂. A representative rotating mass is seen inside M₁. The values of mass and stiffness of the main system and the unbalance mass and its rotational speed are fixed i.e. the natural frequency of the main system before attaching the auxiliary system and the forcing frequency are fixed (cannot be changed) and their values are close to each other ω = 0.95 ωn.

The values of mass and stiffness of the auxiliary system can be selected by the user, i.e. natural frequency of the auxiliary system as an independent and separate system can be changed. You are supposed to input different values of the mass and stiffness of auxiliary system (M₂ and K₂) and observe the responses of this and the primary system. You are also supposed to note that when the value of natural frequency of the auxiliary system is equal to the excitation frequency, the response of the main system is reduced to minimal. It is the value of natural frequency (the ratio K₂/M₂) of the auxiliary system that is important and not the individual values of M₂ and K₂. The design of a dynamically tuned vibration absorber is governed by the permissible response of the mass of auxiliary system, M₂, which is given by the ratio of amplitude of the forcing function and stiffness of the auxiliary system (X₂ = F₀/K₂). Higher values of K₂ keep the response X₂ low but demand greater values of mass M₂. Usually, the value of the mass ratio, M₂/M₁, is kept between 0.05 and 0.25.

Follow these steps to work with the simulator:

1. Input values of mass, M₂, and stiffness, K₂, of the auxiliary system in the suggested range. Select the value of M₂ around 0.1 times the mass M₁ and the value of K₂ such that the ratio K₂/M₂ is very nearly equal to the ratio K₁/M₁.
2. Run the simulation.
3. On stopping the simulation automatically, observe the values of responses of X₁ and X₂. Note that when ω= ω₁ = ω₂, X₁ = 0 and X₂ = F₀/K₂.