Question

Homework 8: Modal and Direct Solution Approaches Figure 1 shows a system with two masses. The two coordinates of which the origins are set up at the unstretched spring positions are also shown in Fig. 1. The system is excited by the force f(t) 1. (a) Draw the FBDs for the system and show that the EOMs can be written as (b) Find the undamped, natural frequencies and the corresponding mode shapes of the system for the given system parameters of ki-k2-50 kN/m and m 4m2-12 kg (c) Normalize the mode shapes with respect to the mass matrix. (d) Using the light damping approximation, state the modal differential equations (including the definition of modal forces). The damping coefficients are given as c12c2-20 N sec/m (e) Using the modal solution approach and the light damping approximation, determine the steady-state vibration responses of the two bodies with the excitation force of f(t) fo sin(wt) where f75 N and 130 rad/sec. Plot the steady-state responses from 0 to 0.2 sec (f) Solve Problem 1(e) using the direct solution approach. Compare the steady-state responses obtained by using the direct and modal solution approaches. For this comparison, plot the steady-state responses from 0 to 0.2 sec. m2 Figure 1: 2-DOF System

Answer 1

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No 3 3.35 0.53 nd Hoclet Analysis: 200 O 20 kitk 300 150 0

dt e odol di

Slate spa 3 0