Читать книгу Engineering Acoustics - Malcolm J. Crocker - Страница 56

Solving the system of Eq. (2.43) simultaneously, we obtain that

(2.44)

(2.45)

and the ratio

(2.46)

where and .

It is noted from Eq. (2.44) that the steady‐state amplitude of the mass m₁ will become zero when r₂ = 1, i.e. when the excitation frequency is . Thus when the stiffness and mass of the secondary mass‐spring system are chosen correctly, the main mass theoretically does not move. At this frequency the secondary mass is exactly 180° out‐of‐phase with the force applied to the primary mass and the mass has an amplitude A₂ = −F₀/k₂. This is the concept of the dynamic vibration absorber (also called neutralizer) used in machinery vibration control applications [11, 13]. The applied force is canceled by an equal and opposite force from the secondary spring. The dynamic vibration absorber was invented in 1909 by Hermann Frahm. This technique works when the excitation is at a fixed frequency at or close to resonance. Since the total system has two natural frequencies (one either side of the excitation frequency), a change in the frequency of the excitation force could excite the modified system at one of these frequencies, making the vibration absorber ineffective.