A reciprocating engine of mass \(m_{1}\) is mounted on a fixed-fixed beam of length \(l\), width \(a\), thickness \(t\), and Young's modulus \(E\), as shown in Fig. 5.55. A spring-mass system \(\left(k_{2}, m_{2}\right)\) is suspended from the beam as indicated in the figure. Find the relation between \(m_{2}\) and \(k_{2}\) that leads to no steady-state vibration of the beam when a harmonic force, \(F_{1}(t)=F_{0} \cos \omega t\), is developed in the engine during its operation. \({ }^{3}\)

Figure 5.55:-

Transcribed Image Text:

F(t) = Fo cos tot x1(t) mi m2 X2(1) FIGURE 5.55 Reciprocating engine, beam and mass system.