Question

A 50 kg machine is mounted on a viscoelastic foundation. During operation, the machine is subject to a harmonic excitation with a frequency of 140rad/s. For this viscoelastic foundation to isolate the vibrations, determine the allowable range of its stiffness.

Answer 1

The allowable range of stiffness for the viscoelastic foundation to isolate vibrations can be determined using the equation k <= 2*m*gamma*w, where k is the stiffness, m is the mass of the machine, gamma is the damping constant of the foundation, and w is the angular frequency of the harmonic excitation.

Step-by-step explanation:

The allowable range of stiffness for the viscoelastic foundation to isolate the vibrations can be determined using the equation:

k <= 2*m*gamma*w,

where k is the stiffness, m is the mass of the machine, gamma is the damping constant of the foundation, and w is the angular frequency of the harmonic excitation.

In this case, the mass of the machine is 50 kg and the angular frequency is 140 rad/s. The value of gamma depends on the specific design and properties of the viscoelastic material used for the foundation. Therefore, you need to determine the value of gamma from the specifications or experimental data of the material to calculate the allowable range of stiffness.