Solving Problems in Dynamics and Vibrations Using MATLAB ...

More documents

Recommendations

Info

40 Assignment 4r a) Solve the differential equation given in the example for m = 10 Kg; e = m; r = 0.2 m. Plot 3π ‘β’ with respect to time. Compare the result with that obtained in the example and comment on the result. b) Determine the equilibrium value of ‘β’. c) Linearize the differential equation for small motion about the equilibrium value and determine the natural frequency for the small motion. Also plot the value of the ‘β’ with respect to time. Note that for plotting the value of ‘β’, you have to solve the linearized differential equation. d) Compare the natural frequency of the linearized model to that produced by the non- linear model.
41 7. A bar supported by a cord Derive the governing differential equation of motion of a swinging bar supported at its ends by a cord. Calculate the eigen values and the eigen vectors. Solve the derived differential equation and plot the initial response of the system for the following initial conditions: a) Arbitrary initial condition b) Initial condition vector proportional to the eigen vector. Choose l 1 = 1m; l 2 = 1m; m 2 = 5Kg φ l 1 θ l 2 , m 2 The differential equations of motion for the above system when represented in a matrix form is ⎡ ⎢ ⎢ ⎢m2l1l ⎢⎣ 2 m l 2 1 cos( θ 2 −φ) m2l2 cos( θ 2 2 m2l2 3 ⎧ −φ) ⎤ .. ⎪ ⎥ − ⎪ ⎧ ⎪ ⎫ w φ ⎪ ⎥⎨ .. ⎬ = ⎨ ⎥⎪⎩ θ ⎪⎭ ⎪− w2l ⎥⎦ ⎪ ⎩ 2 2 . 2 ⎫ m2l2 θ sin( θ − φ) sinφ + ⎪ 2 ⎪ . 2 ⎬ sinθ + m sin( − ) ⎪ 2l1l2 φ θ φ ⎪ 2 ⎭ Eliminating the second order terms in the above equation gives the linear equation ⎡ ⎢ m2l1 ⎢ ⎢m2l1l ⎢⎣ 2 2 2 m2l2l1 ⎤ .. 1 2 ⎥ ⎡ ⎪ ⎧ ⎪ ⎫ l w φ ⎢ 2 ⎥⎨ .. ⎬ + m2l2 ⎥ ⎢ 0 ⎪⎩ ϑ⎪⎭ ⎣ 3 ⎥⎦ 2 0 w2l 2 2 ⎤ ⎧φ ⎫ ⎥⎨ ⎬ = 0 ⎥ ⎦ ⎩θ ⎭ Note that the inertia matrix has been made symmetric via a multiplication of the first row by l 1 .
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 and 36: 35 Open a new m-file and type the f
Page 37 and 38: 37 Assignment a) Solve the followin
Page 39: 39 y0=[0.5233;0]; [t,y]=ode45('tofr
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
show all

Solving Problems in Dynamics and Vibrations Using MATLAB ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?