1 MIDTERM EXAM REVIEW 2 m 081.SLDASM REVIEW Excitation force 50N normal to face k=10000N/m m=6.66kg Modal damping 5% 3 4 Natural frequency with the equations of motion method 5 Natural frequency with the energy method 6 What angular and linear damping will give us 5% modal damping? 7 Steady state displacement amplitude at load application; excitation with resonant frequency 8 Natural frequency m 081.SLDASM 9 Steady state displacement amplitude at load application; excitation with resonant frequency m 081.SLDASM 10 Problem 1Vibration isolation 11 Problem 2Vibration isolation 12 Problem 3 Oscillating load 10N Base m = 10kg k = 1000N/m c= 5Ns/m Calculate amplitudes of displacement, velocity and acceleration at resonance 13 Problem 3 Solution method 1 Method of undetermined coefficients 14 Problem 3 Solution method 2 Using the formula Inman p. 116 15 Problem 3 Solution method 3 SW Simulation Amplitude of displacement at resonance 0.2m 16 Problem 4 2 excitation Total massm = 450kg modeled as a distributed mass Material custom with very low density Dynamic unbalancem 0 e = 0.35kgm Each spring 8.85kN/m Damping = 30% Find the amplitude of displacement = 100rad/s 17 Problem 4 Solution method 1 Method of undetermined coefficients 18 Half amplitude of vibration for >> n Even though 100rad/s is not much large than the natural frequency) Problem 4 Solution method 2 Using the formula = m 19 Problem 4 Solution method 3 Using SW Simulation washing_machine.SLDASM 20 Problem 5 A 45kg machine is placed at the end of a 1.6m cantilever beam: E=200,000MPa, b=0.1m, h=0.1245m We assume that the beam is weightless (questionable assumption) As it operates it produces a harmonic force of magnitude 125N. At what operating speeds will the machines steady state amplitude be less than 0.2mm? 125N 21 Problem 5Analytical solution Inman p. 119 22 /228 < 0.85 < 194 rad/s f < 30.8 Hz /228 < 1.13 < 257 rad/s f < 40.9 Hz Problem 5Numerical solution 23 Problem 6 24 at least So we need to add at a mass of at least 171kg to the turbine Problem 7