Solving Problems in Dynamics and Vibrations Using MATLAB ...

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36 and the vector ‘y(:,2)’ gives the values of the angular velocity. To plot the angular velocity, change the variable ‘y(:,1)’ in the plot command line to ‘y(:,2)’. From the plots it can be seen that, quadratic damping causes a rapid initial amplitude reduction but is less effective as time increases and amplitude decreases. Whereas, linear damping is less effective initially but is more effective as time increases.
37 Assignment a) Solve the following non-linear differential equation with aerodynamic damping .. 2 g C . . a θ + sinθ + θ sgn( θ) = 0 (1) l ml and compare it with the following linearized differential equation with viscous damping .. . cd g θ + θ + θ = 0 (2) m l . m = 5 g; l = 10 cms; C a = C d = 140; θ (0) = 0.5233; θ(0) = 0. Show the results in the same plot. b) Comment on the results obtained. Assuming a harmonic motion, i.e., θ = A cos(ω n t), for what amplitude ‘A’, are the linear and the non-linear damping moments equal? Also confirm the result from the plot obtained.
Page 1 and 2: Solving Problems in Dynamics and Vi
Page 3 and 4: 3 An Introduction to MATLAB Purpose
Page 5 and 6: 5 x + 2y = 6 x − y = 0 There are
Page 7 and 8: 7 p = ‘x + 2*y = a + 6’ q = ‘
Page 9 and 10: 9 Suppose one wants to change the c
Page 11 and 12: 11 1. Spring Mass Damper System - U
Page 13 and 14: 13 MATLAB Code In order to apply th
Page 15 and 16: 15 Assignment Solve for six cycles
Page 17 and 18: 17 For our convenience, put x = y (
Page 20 and 21: 20 Assignment Plot the response of
Page 22 and 23: 22 When the values of ‘theta’ a
Page 25 and 26: 25 Assignment a) Compute and plot t
Page 27: 27 tspan=[0 2] y0=[0;0] [t,y]=ode45
Page 30 and 31: 30 4. Trajectory Motion with Aerody
Page 33 and 34: 33 Assignment Solve the following d
Page 35: 35 Open a new m-file and type the f
Page 39 and 40: 39 y0=[0.5233;0]; [t,y]=ode45('tofr
Page 41 and 42: 41 7. A bar supported by a cord Der
Page 43 and 44: 43 MATLAB Code In this type of a pr
Page 45: 45 tspan=[0 30] y0=[0.5233;0;1.0467
Page 50 and 51: 50 8. Double Pendulum Derive the go
Page 52 and 53: 52 yp(1)=y(2); yp(2)=-(w1+w2)*sin(y
Page 55 and 56: 55 Assignment 1.) For the double pe
Page 57 and 58: 57 2 ⎡−ω [ M ] + [ K] ω[ C]
Page 59: 59 figure(1) plot(f,x(1,:));grid xl
Page 63 and 64: 63 10. A Three Bar Linkage Problem
Page 65: 65 xlabel('alpha') ylabel('gamma do
Page 70 and 71: 70 11. Slider-Crank Mechanism Examp
Page 72: 72 To calculate the angular acceler
Page 77 and 78: 77 12. A Bar supported by a wire an
Page 79 and 80: 79 end To store the right hand side
Page 81: 81 t1=t'; figure(3) plot(t1,theta);
Page 85 and 86: 85 The above model involves second
Page 87 and 88:
87 l=1; L=1.5; m=5; M=5; g=9.81; w=
Page 91 and 92:
91 Assignment: Three bar linkage as
Page 93 and 94:
93 where ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
Page 95 and 96:
95 ⎡kx1 ⎤ ⎢ ⎥ ⎢ 0 ⎥ ⎢
Page 97 and 98:
97 m = 0.002; k = 175000; M1 = m*ey
Page 99 and 100:
99 cnt = cnt +1; end end end % To p
Page 101 and 102:
101 plot(vect3(:,i),c(i)) hold on;
Page 103 and 104:
103
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Solving Problems in Dynamics and Vibrations Using MATLAB ...

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