Use the transfer function approach and a lumped-parameter model to determine a relationship between the geometrical and material parameters of the nanobridge shown in Figure 9.31 so that the natural...

Use the transfer function approach and a lumped-parameter model to determine a relationship between the geometrical and material parameters of the nanobridge shown in Figure 9.31 so that the natural frequency corresponding to the y translation is twice the one corresponding to the ix rotation. The rigid plate has a mass m and a moment of inertia J about the longitudinal axis. The identical side rods are flexible and massless; they have circular cross-sections and their length is l; the material has a Poisson’s ratio n. Hint: Apply separate adequate input for each of the two motions (a force for the y translation and a moment for the ix rotation).