Question

2. The natural frequency coefficient of a cylindrical shell clamped at one end and restrained by an attached stiff circular plate at the other end is given by: (20 pnts) (1 – 1²) 1 (h) . Inm = 12 + 12 + 1.78nºx? :) (n + n4 + 1.78m24%) Where m and n are positive integers and )(4m + 1) 4 Show that when n=2, m = 1, h/R = 0.05, R 1 = 0.1 and y = 0.3, 21 = 7.51587 x 10-3

Answer 1

solution:

Given data:

2.

MATLAB CODE

clc; clear all; format long g % Defining variables syms n m h_by_R R_by_l v del_m = (pi / 4) * (R_by_l) * (4 * m + 1); OHM_nm = (1 - v*v)*(del_m^4) / (del_m^2 + n^2 + 1.78*n^2*del_m^2)... + (1/12)*((h_by_R)^2)*(del_m^4 + n^4 + 1.78*m^2*del_m^2);    vars = [n, m, h_by_R, R_by_l, v]; values = [2, 1, 0.05, 0.1, 0.3]; OHM_21 = subs(OHM_nm, vars, values) OHM_21 = sprintf('%.5e', double(OHM_21))

OUTPUT

Command Window OHM_21 = (89*pi-2)/15360000 + pi 4/19660800 + (91*pi^4)/(409600* ((203*pi-2)/1600 + 4)) + 1/300 OHM_21 = 7.51587e-03 fx >>

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