Maurice Tutor

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Teaching Since: May 2017
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Education

  • MCS,PHD
    Argosy University/ Phoniex University/
    Nov-2005 - Oct-2011

Experience

  • Professor
    Phoniex University
    Oct-2001 - Nov-2016

Category > Management Posted 02 Jan 2018 My Price 10.00

radius of the inner cylinder

2.39  Given the following system of equations

 

16s + 32u + 33p + 13w = 91 5s + 11u + 10p + 8w = 16

 

9s + 7u + 6p + 12w = 5 34s + 14u + 15p + w = 43

 

determine the values of s, u, p, and w, the value of the determinant, and the inverse of the coefficients of s, u, p, and w (Answer: s = - 0.1258, u = - 8.7133, p = 11.2875, and

w = - 0.0500. Determinant = 7,680).

 

               Consider two long cylinders of two different materials where one cylinder just fits inside the other. The inner radius of the inner cylinder is a, and its outer radius is b. The inner radius of the outer cylinder is also b, and its outer radius is c. The Young’s modu-lus and Poisson ratio of the inner cylinder are E1 and n1, respectively, and those of the outer cylinder are E2 and n2, respectively. The radial stress srr, hoop stress suu, and radi-al displacement ur are given, respectively, by,

srri(r) =

 

Ai

+ Bi

 

 

 

 

 

r

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

suui(r) =

 

- Ai

+ Bi

i = 1, 2

(a)

 

 

 

 

 

 

r2

 

 

 

 

 

 

 

uri(r) =

- (1 + yi)

Ai  +

(1 - yi)

rBi

 

 

 

 

 

 

 

 

 

 

 

 

rEi

 

Ei

 

where i = 1 refers to the inner cylinder and i = 2 to the outer cylinder.

 

     Szabo, Linear Algebra, p. 265.

 

      Ibid., p. 266.


 

 

 

If the outer surface of the outer cylinder is subjected to a compressive radial dis-placement Uo and the inner surface of the inner cylinder has no radial stress, then the following four boundary conditions can be used to determine Ai and Bi, i = 1, 2:

srr1(a) = 0

 

srr1(b) = srr2(b) (b) ur1(b) = ur2(b)

 

ur2(c) = - Uo

 

Substituting Eqs. (a) into (b), the following system of equations in matrix form is obtained:

 

 

          1

1

   (1 + n1) 0

 

 

 

a2

0

 

0

T d

A1

t

 

d

0

t

b2

- 1

 

- b2

B1

=

0

(1 - n1)b2

(1 + n2)E1/E2

-

(1 - n2)b2E1/E2

A2

0

0

- (1 + n2)

(1 - n2)c2

B2

 

- UoE2c

 

Determine the hoop stress in the inner and outer cylinders at r = b when n1 = n2 = 0.4, E1 = 2.1 * 109 N/m2, E2 = 0.21 * 109 N/m2, Uo = 0.25 mm, a = 5 mm, b = 6.4 mm, and c = 8 mm (Answer: suu1(b) = - 6.301 * 107 N/m2 and suu2(b) =

   1.179 * 107 N/m2)

 

               For the electric circuit shown in Figure 2.10, the governing equations for the three loop currents are given by

 

V1 - 6Ri1  + 4R(i2 - i1) = 0

V2  + 2R(i3 - i2) - 3Ri2 - 4R(i2 - i1) = 0

- V3 - Ri3 - 2R(i3 - i2) = 0

Use solve from Symbolic toolbox to show that the three currents are given by

 

 

 

i1  =

1

 

 

(12V2 - 8V3  + 23V1)

 

 

 

 

 

 

 

182R

 

 

i2  =

1

 

 

(6V1  + 15V2  - 10V3)

 

 

 

 

 

 

 

 

 

 

91R

 

 

i3  =

1

 

 

(4V1  + 10V2  - 37V3)

 

 

 

 

 

 

 

 

 

 

91R

 

 

 

i2

 

 

 

 

 

 

 

 

 

 

6R

 

 

 

 

 

 

 

 

V2

 

 

 

 

 

 

 

 

 

 

V

 

 

 

 

 

 

 

 

 

 

 

 

 

 

i1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3

 

 

 

 

 

 

 

 

 

 

 

 

4R

 

 

i3

 

 

 

2R

 

 

 

 

V1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

R

 

 

 

3R

 

 

Figure 2.10  Electric circuit.

 

 

 

 

 

 

 

 

               An ac electric circuit with resistors R and capacitances C is described by the following set of equations in the Laplace transformed domain:

 

C

2s + to

- s

0

S c

 

1(s)

s =

c

 

 

 

s

V

sU

(s)

0

- s

s + to

 

0

V3(s)

 

- s

2s + to

- s

 

V2(s)

 

 

0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

where s is the Laplace transform parameter, to = 1/RC, Vj(s), j = 1, 2, 3, are the trans-formed nodal voltages, and Uj(s) is the transformed applied voltage. Use the Symbolic

toolbox to solve for Vj(s).

 

 

 

 

Answers

Maurice Tutor
(5)
Status NEW Posted 02 Jan 2018 10:01 PM My Price 10.00

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