Mechanical Vibrations

Tutorial $2\_24$

Figure $1$ shows a model of a diaphragm pump. It consists of a massless bar which is pivoted at one end and has length $L=120mm$ long. An alternating force with a peak value, $F_0$ of $20$ N and frequency $50$ Hz is applied at the other end through a mass, M $,$ of $10$ g $.$ The diaphragm assembly is connected to the centre. The diaphragm can be modelled as a spring with stiffness $4k\frac{N}{m}$ in parallel with a damper with damping coefficient $16N\frac{s}{m}.$

Calculate natural frequency and damping ratio

Calculate the maximum displacement of the diaphragm

If the frequency is doubled calculate the ratio flow from the pump at $100$ Hz to $50$ Hz $.$ Assume flow rate is proportional to frequency times displacement.

Figure $1$ Model of diaphragm pump