تعیین فرکانس طبیعی خرپای دو بعدی با ارتعاش آزاد به روش المان محدود با متلب

تعیین فرکانس طبیعی خرپای دو بعدی با ارتعاش آزاد به روش المان محدود

در این بخش پروژه تعیین فرکانس طبیعی خرپای دو بعدی با ارتعاش آزاد به روش المان محدود با نرم افزار متلب به همراه سورس کد آماده کرده ایم که در ادامه توضیحاتی در مورد پارامترهای ورودی و خروجی پروژه آورده ایم.

تعریف فرکانس:

فرکانس یعنی اندازه گیری تعداد تکرار اتفاقی یک عمل در واحد زمان را گویند.

تعریف فرکانس طبیعی:

فرکانس طبیعی به فرکانسی گویند که سیستم به طور طبیعی و بدون دخالت نیرو های خارجی تمایل به انجام آن دارد.

مفروضات مسئله:

طول عضو های خرپای دو بعدی:

L1 = 1.2 m; L2 = 2.68 m; L3 = 2.4m; L4 = 1.2 m;

زاویه عضو قطری خرپای دو بعدی:

θ = 63.43°

مدول الاستیسیته اعضای خرپای دو بعدی:

E = 2 × 1011N/m2

سطح مقطع اعضای خرپا:

A =0.04m2

چگالی اعضای مربوطه:

ρ = 7600 kg/m3

تصویر مسئله:

مود شیپ خرپای مورد نظر:

خروجی پروژه:

Natural frequencies in rad/sec (فرکانس طبیعی) :
1.0e+03 *
0.001000000000000 + 0.000000000000001i
0.001000000000000 + 0.000000000000000i
0.001000000000000 + 0.000000000000005i
1.251059697285805 + 0.000000000000000i
3.234745189867316 + 0.000000000000000i
4.531894283691921 + 0.000000000000000i
4.713083345959323 + 0.000000000000000i
4.713083345959323 + 0.000000000000000i
4.713083345959323 + 0.000000000000000i
4.713083345959323 + 0.000000000000000i
4.713083345959323 + 0.000000000000000i
4.713083345959323 + 0.000000000000000i
normalized modal vector (بردار مودال عادی شده):
Columns 1 through 2
-0.000000000000000 - 0.000000000000000i   0.000000000000000 + 0.000000000000000i
0.000000000000000 + 0.000000000000000i   0.000000000000000 + 0.000000000000000i
-0.000000000000000 - 0.000000000000000i   0.000000000000000 + 0.000000000000000i
0.000000000000000 + 0.000000000000000i   0.000000000000000 + 0.000000000000000i
-0.000000000000000 - 0.000000000000000i   0.000000000000000 + 0.000000000000000i
0.000000000000000 + 0.000000000000000i   0.000000000000000 + 0.000000000000000i
0.000000000000000 + 0.000000000000000i   0.000000000000000 + 0.000000000000000i
0.000000000000000 + 0.000000000000000i   0.000000000000000 + 0.000000000000000i
0.082866851281265 + 0.000000000000000i   0.000000000000000 + 0.000000000000000i
0.004913261537653 - 0.000001351102874i    0.000000000000000 + 0.000000000000000i
-0.007300880614994 + 0.000001305557560i  0.083333333333333 + 0.000000000000000i
0.000293943747742 - 0.000000156592487i 0 .000000000000000 + 0.000000000000000i
Columns 3 through 4
-0.000000000000000 - 0.000000000000000i  -0.000000000000000 + 0.000000000000000i
0.000000000000000 + 0.000000000000000i  -0.000000000000000 + 0.000000000000000i
-0.000000000000000 - 0.000000000000000i  -0.000000260427963 + 0.000000000000000i
0.000000000000000 + 0.000000000000000i   0.000055844026585 + 0.000000000000000i
-0.000000000000000 - 0.000000000000000i  -0.000008341065740 + 0.000000000000000i
0.000000000000000 + 0.000000000000000i   0.000043778871676 + 0.000000000000000i
0.000000000000000 + 0.000000000000000i   0.000000000000000 + 0.000000000000000i
0.000000000000000 + 0.000000000000000i   0.000000000000000 + 0.000000000000000i
0.017868947817806 + 0.000000344870250i  -0.027927079130739 + 0.000000000000000i
0.076555712747130 - 0.000000000000000i   -0.069705663397814 + 0.000000000000000i
-0.027554078722646 + 0.000002108980364i  0.036035442696086 + 0.000000000000000i
0.002267318957497 - 0.000000179728071i   -0.002661757098521 + 0.000000000000000i
Columns 5 through 6
0.000000000000000 + 0.000000000000000i   0.000000000000000 + 0.000000000000000i
-0.000000000000000 + 0.000000000000000i  -0.000000000000000 + 0.000000000000000i
-0.000042882418570 + 0.000000000000000i  -0.000215409834780 + 0.000000000000000i
-0.000025420146306 + 0.000000000000000i    0.000145766701363 + 0.000000000000000i
-0.000096037851027 + 0.000000000000000i   0.000071211884392 + 0.000000000000000i
0.000002670111066 + 0.000000000000000i   -0.000103972149098 + 0.000000000000000i
1/14/17 11:23 PM MATLAB Command Window 2 of 2
0.000000000000000 + 0.000000000000000i   0.000000000000000 + 0.000000000000000i
0.000000000000000 + 0.000000000000000i   0.000000000000000 + 0.000000000000000i
0.048155175998573 + 0.000000000000000i   0.077308870155084 + 0.000000000000000i
0.011522249122856 + 0.000000000000000i   0.013210020935473 + 0.000000000000000i
0.067027779117940 + 0.000000000000000i  -0.027445098024882 + 0.000000000000000i
-0.000162342768338 + 0.000000000000000i  0.006321506972978 + 0.000000000000000i
Columns 7 through 8
-0.000000000000000 + 0.000000000000000i   -0.000000000000000 + 0.000000000000000i
0.000000000000000 + 0.000000000000000i     0.000000000000000 + 0.000000000000000i
-0.000241567503614 + 0.000000000000000i   -0.000241567503614 + 0.000000000000000i
-0.000245420177498 + 0.000000000000000i   -0.000245420177498 + 0.000000000000000i
0.000128486770305 + 0.000000000000000i     0.000128486770305 + 0.000000000000000i
0.000193996127138 + 0.000000000000000i     0.000193996127138 + 0.000000000000000i
0.000000000000000 + 0.000000000000000i     0.000000000000000 + 0.000000000000000i
0.000000000000000 + 0.000000000000000i      0.000000000000000 + 0.000000000000000i
0.055852585404651 + 0.000000000000000i     0.055852585404651 + 0.000000000000000i
-0.039180521461746 + 0.000000000000000i   -0.039180521461746 + 0.000000000000000i
-0.046373763659922 + 0.000000000000000i   -0.046373763659922 + 0.000000000000000i
-0.011794965060997 + 0.000000000000000i    -0.011794965060997 + 0.000000000000000i
Columns 9 through 10
-0.000000000000000 + 0.000000000000000i   -0.000000000000000 + 0.000000000000000i
0.000000000000000 + 0.000000000000000i     0.000000000000000 + 0.000000000000000i
-0.000241567503614 + 0.000000000000000i   -0.000241567503614 + 0.000000000000000i
-0.000245420177498 + 0.000000000000000i   -0.000245420177498 + 0.000000000000000i
0.000128486770305 + 0.000000000000000i     0.000128486770305 + 0.000000000000000i
0.000193996127138 + 0.000000000000000i     0.000193996127138 + 0.000000000000000i
0.000000000000000 + 0.000000000000000i     0.000000000000000 + 0.000000000000000i
0.000000000000000 + 0.000000000000000i      0.000000000000000 + 0.000000000000000i
0.055852585404651 + 0.000000000000000i      0.055852585404651 + 0.000000000000000i
-0.039180521461746 + 0.000000000000000i    -0.039180521461746 + 0.000000000000000i
-0.046373763659922 + 0.000000000000000i    -0.046373763659922 + 0.000000000000000i
-0.011794965060997 + 0.000000000000000i    -0.011794965060997 + 0.000000000000000i
Columns 11 through 12
-0.000000000000000 + 0.000000000000000i   -0.000000000000000 + 0.000000000000000i
0.000000000000000 + 0.000000000000000i     0.000000000000000 + 0.000000000000000i
-0.000241567503614 + 0.000000000000000i   -0.000241567503614 + 0.000000000000000i
-0.000245420177498 + 0.000000000000000i   -0.000245420177498 + 0.000000000000000i
0.000128486770305 + 0.000000000000000i     0.000128486770305 + 0.000000000000000i
0.000193996127138 + 0.000000000000000i     0.000193996127138 + 0.000000000000000i
0.000000000000000 + 0.000000000000000i     0.000000000000000 + 0.000000000000000i
0.000000000000000 + 0.000000000000000i     0.000000000000000 + 0.000000000000000i
0.055852585404651 + 0.000000000000000i     0.055852585404651 + 0.000000000000000i
-0.039180521461746 + 0.000000000000000i  -0.039180521461746 + 0.000000000000000i
-0.046373763659922 + 0.000000000000000i  -0.046373763659922 + 0.000000000000000i
-0.011794965060997 + 0.000000000000000i  -0.011794965060997 + 0.000000000000000i