Need the solution to 8.16
8.15. Consider the machine punch of Figure P8.15. This punch is made of two materials and is subject to an impact in the axial direction. Use the finite element method with two elements to model this system and estimate (calculate) the first two natural frequencies. Assume E1 = 8 x 101 Pa, E2 = 6000 Pa, P1 = 2, P2 = 0.5, A1 = 0.008 m, A2 = 0.002 m, L = 0.5 m.
Figure P8.15 A bar made of two materials of two sizes used for a punch. Material passes around the rollers. At appropriate points on the material, the roller stops and the toolhead is actuated in the x direction and impacts the bar, causing a hole to be punched in the material. The punch itself (E) is made of hardened steel while the base is made of cast iron (E2).
8.16. Recalculate the frequencies of Problem 8.15 assuming that it is made entirely of one material and size (i.e., E1 = E2, P1 = P2, and A1 = A2), say steel, and compare your results to those of Problem 8.15.