📄 cantbeam_ss_freq.m
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echo off
% cantbeam_ss_freq.m plotting frequencies for Block Lanczos
% and Reduced with different number of elements. Compares theoretical
% frequencies for the first 16 modes for example beam with Matlab and
% ANSYS model results.
% beam dimensions, material properties from cantbeam_ss.inp
% 0.075 thick x 2 wide x 20mm long steel cantilever
% steel properties:
% ex,1,190e6 ! mN/mm^2
% dens,1,7.83e-6 ! kg/mm^3
% nuxy,1,.293
% calculate theoretical resonant frequencies from Chang/Craig paper
% beta^4 = rho*w^2/(EI), rho is mass per unit length
I = 2*0.075^3/12;
E = 190e6;
l = 20;
dens = 7.83e-6;
mass = 0.075*2*20*dens;
rho = mass/l;
% table of beta*l for modes
betal = [ 1.875104068712
4.694091132974
7.854757438238
10.99554073488
14.13716839105
17.27875953209
20.42035225104
23.56194490181
26.70353755552
29.84513020910
32.98672286269
36.12831551628
39.26990816987
42.41150082346
45.55309347705
48.69468613064 ];
beta = betal/l;
freq16 = (1/(2*pi))*sqrt(beta.^4*E*I/rho)
% results from above calculations for reference
%
% freq16 = 1.0e+005 * [ 0.00149202964605
% 0.00935039018305
% 0.02618136326318
% 0.05130502265734
% 0.08481087856779
% 0.12669276700411
% 0.17695105607145
% 0.23558572547420
% 0.30259677627882
% 0.37798420843106
% 0.46174802193380
% 0.55388821678682
% 0.65440479299011
% 0.76329775054368
% 0.88056708944752
% 1.00621280970164 ];
% 2bl
freq2bl = [149.27
942.94
3189.1
9254.8];
% 2red
freq2red = [149.45
945.38];
% 4bl
freq4bl = [149.20
936.09
2638.2
5204.5
9679.5
15544.
24640.
40411.];
% 4red
freq4red = [149.21
937.56
2672.0
5242.1];
% 6bl
freq6bl = [149.20
935.24
2622.8
5163.0
8607.2
12878.
19855.
27269.
37258.
50389.
66259.
91281.];
% 6red
freq6red = [149.20
935.44
2627.9
5211.7
8830.4
13060.];
% 8bl
freq8bl = [149.20
935.08
2619.6
5141.5
8528.9
12817.
18041.
23966.
33691.
42729.
54195.
68300.
85497.
0.10564E+06
0.12586E+06
0.16212E+06];
% 8red
freq8red = [149.20
935.13
2620.8
5152.8
8594.4
13079.
18684.
24389.];
% 10bl
freq10bl = [149.20
935.04
2618.6
5134.9
8501.2
12735.
17866.
23934.
30943.
38463.
51186.
61830.
74940.
90431.
0.10864E+06
0.12991E+06
0.15414E+06
0.17990E+06
0.20254E+06
0.25288E+06];
% 10red
freq10red = [149.20
935.05
2619.0
5138.4
8521.2
12820.
18152.
24677.
32229.
39191.];
% 12bl
freq12bl = [149.20
935.02
2618.3
5132.4
8490.4
12701.
17781.
23756.
30660.
38523.
47308.
56363.
72336.
84544.
99354.
0.11642E+06
0.13596E+06
0.15826E+06
0.18359E+06
0.21187E+06
0.24224E+06
0.27211E+06
0.29602E+06
0.36340E+06];
% 12red
freq12red = [149.20
935.03
2618.5
5133.8
8498.0
12732.
17888.
24067.
31426.
40050.
49418.
57435.];
% 16bl
freq16bl = [149.20
935.01
2618.1
5130.8
8483.3
12678.
17721.
23620.
30392.
38054.
46633.
56157.
66653.
78116.
90392.
0.10234E+06
0.12559E+06
0.14078E+06
0.15901E+06
0.17944E+06
0.20208E+06
0.22711E+06
0.25474E+06
0.28518E+06
0.31858E+06
0.35490E+06
0.39371E+06
0.43390E+06
0.47324E+06
0.50797E+06
0.53276E+06
0.64268E+06];
% 16red
freq16red = [149.20
935.01
2618.1
5131.1
8484.9
12685.
17742.
23683.
30552.
38429.
47436.
57720.
69354.
82036.
94511.
0.10415E+06];
% 32bl
freq32bl = [149.20
935.00
2618.0
5130.0
8480.0
12667.
17692.
23555.
30255.
37796.
46178.
55403.
65475.
76398.
88178.
0.10082E+06
0.11433E+06
0.12873E+06
0.14401E+06
0.16020E+06
0.17731E+06
0.19535E+06
0.21435E+06
0.23431E+06
0.25525E+06
0.27718E+06
0.30011E+06
0.32399E+06
0.34873E+06
0.37406E+06
0.39907E+06
0.42044E+06
0.48375E+06
0.50878E+06
0.53973E+06
0.57371E+06
0.60995E+06
0.64825E+06
0.68857E+06
0.73095E+06
0.77545E+06
0.82216E+06
0.87118E+06
0.92261E+06
0.97655E+06
0.10331E+07
0.10923E+07
0.11543E+07
0.12190E+07
0.12865E+07
0.13566E+07
0.14291E+07
0.15037E+07
0.15799E+07
0.16569E+07
0.17337E+07
0.18090E+07
0.18812E+07
0.19484E+07
0.20082E+07
0.20584E+07
0.20964E+07
0.21202E+07
0.24844E+07];
% 32red
freq32red = [149.20
935.00
2618.0
5130.0
8480.1
12667.
17693.
23556.
30259.
37803.
46193.
55432.
65530.
76498.
88352.
0.10111E+06
0.11482E+06
0.12950E+06
0.14521E+06
0.16202E+06
0.18002E+06
0.19929E+06
0.21993E+06
0.24203E+06
0.26561E+06
0.29060E+06
0.31670E+06
0.34330E+06
0.36928E+06
0.39297E+06
0.41227E+06
0.42498E+06];
% 64bl
freq64bl = [149.20
935.00
2618.0
5130.0
8479.8
12667.
17690.
23550.
30246.
37778.
46145.
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