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本帖最后由 游龙游龙 于 2014-7-8 14:45 编辑
0 `2 }4 r' o& x* r, ]' {
/ w% z. ?: B7 g5 C' f麻烦大家帮忙看下这个程序,不知道哪里出错了,小弟是刚入门,请高手指教
1 C! [/ ?7 S5 v. V/ @行列式求不出,画图找不到根6 ?: N& g3 ?+ T" }/ g7 B
(*定义材料常数*)6 ]) _6 ?! s. {% \$ }3 T( ?
Subscript[\[Nu], TL] = 0.25;
5 t/ \! ?% n, cSubscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)
' m/ a$ ^* c3 L' _Subscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)
. z6 f( r! N0 H/ @Subscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)4 Q) X8 o' x2 m# H: O
Subscript[\[Nu], LT] =
+ R' t; K9 C( ?! D8 N% W& Y Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];
0 `, [' {/ u( P9 r# |7 N" N\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];, b; n3 N8 P) |, L/ ~: Z0 Y5 a
Subscript[C, L] = Subscript[EE, L]/\[Mu];/ G0 y6 n5 u1 }7 D
Subscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];
4 m0 P1 G) `+ |8 ~0 G9 n- {Subscript[C, T] = Subscript[EE, T]/\[Mu];5 U" N4 m1 N& }, `. w0 l9 {
Subscript[C, LT] = Subscript[G, LT];
' e0 D4 O1 A- x9 m(*脱层几何参数*)1 ?- l8 }$ {2 ]
\[Rho] = 1600;(*脱层密度*)
8 h' j, D* b/ C5 G; ?c = 0.06;(*阻尼*)9 [1 u' y5 [: d
t = 0.01;(*t每层厚度*)' t8 q0 W* a' ]6 k1 m J
h = 0.05;(*h为梁总厚度*)
. W% ?( Z& {$ V3 _# N% c( S" fl = 1;(*为梁总的长度*)
! U! [8 G, B% H- P4 Z/ i1 cSubscript[l, 1] = 0.3;(*为梁1区的长度*)) M' X9 _; `$ p& M0 f
Subscript[l, 2] = 0.3;(*为梁2区的长度*); h7 ?# S" ^0 G! o+ ]; w5 Y4 D
Subscript[l, 3] = 0.4;(*为梁3区的长度*)
4 H+ z8 A6 E& `: j( pSubscript[l, 4] = 0.4;(*为梁4区的长度*)* N" f2 y3 c2 r3 H
nn1 = h/t;(*nn1为总铺层厚度*)
: ^0 [5 n2 b6 n5 tnn2 = 2.0;(*为上子铺层层数*)
, f& r; Q8 p, }; G( C+ X( |/ W0 Inn3 = h/t - nn2;(*下子铺层层数*)' m. A; S* \! `6 W; z6 I0 }6 Y c
Subscript[h, 3] = t*nn2;(*梁的上部子厚度*)
" c6 w5 ^/ l- {! o$ v9 Z' fSubscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)% y0 ?2 E* u: l
Subscript[h, 1] = h;(*梁1区的厚度*)
" Z" x& [* u) B) E2 j9 TSubscript[h, 2] = h;(*梁2区的厚度*)8 X/ c! L4 J" W* {3 V) N' N# M; }
(*求各单层刚度*)
# G+ p$ \5 H7 G% [6 g4 l( hagk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)
/ n4 k7 z, W2 C7 H. J( \
" K; T! y2 \- V: z1 |' c: J2 W" a# W- a+ e& `$ I! v
ck = Cos[agk];(*列表求各铺层角度余弦*)6 R3 K5 [0 G7 K) u$ ?
sk = Sin[agk];(*列表求各铺层角度正弦*)% p' {8 O2 _- o$ r: F' w
s11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +2 W4 u3 t7 R! L- \5 ?5 s7 Y
sk^4*Subscript[C, T] + 6 m5 G. p" B: ]8 `. p) z
4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)
$ F9 u% l- {' CA11 = \!\(
6 Z( H& I4 _ {2 `\*UnderoverscriptBox[\(\[Sum]\), \(k = 4 |5 r- N# I0 D4 n9 O, G- H1 M
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*)2 d) h3 ?& { m; Y1 q7 w
A21 = A11
- O% m; X% O. C3 Q# VA31 = (\!\(7 B ^: ?% n" H y" g' E
\*UnderoverscriptBox[\(\[Sum]\), \(k = . r3 f0 m4 D4 F7 @
1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)( e6 r! c0 r- R& I% ^/ {
A41 = (\!\(
4 [+ N* Z# {5 |1 |$ F\*UnderoverscriptBox[\(\[Sum]\), \(k =
$ v& {& a7 J; L/ F nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)
K9 q9 \6 i: Z3 f3 U
* x" E- P4 z; B- g1 t4 N
x4 ]0 h; y3 s2 g; T; cPrint["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)
& v4 C: M$ c9 X. C$ Y1 o- E1 yD11 = \!\(- ~. |1 x6 G% k
\*UnderoverscriptBox[\(\[Sum]\), \(k =
0 M0 \& f) I ^0 w0 V 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
7 c" I' ?$ J6 s7 g2 H. s' H$ l7 }\*FractionBox[\(t^3\), \(12\)])\)\)
( j+ Z2 a* Z1 ]9 {' @3 Y, ?+ vD21 = D11 A; Q# g; ]/ i. Q) |
D31 = \!\(
& O3 k \( {( Z1 R* e+ E* A) l7 A0 p\*UnderoverscriptBox[\(\[Sum]\), \(k =
1 b' U5 R) i$ I& M0 G9 {' |: c 1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*
3 K$ M T+ m# E- S) f3 i* j/ K\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)
. j6 N F# p- f3 |1 w" m4 Z' \1 z6 c+ XD41 = \!\(! H. ?/ g+ A! x4 O6 g/ T# n
\*UnderoverscriptBox[\(\[Sum]\), \(k =
2 M: }8 A/ w9 |8 H! I; F% Q% Z nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
- \+ N% P& H+ h3 o8 R5 \, H\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)* }* ?: l. \3 m& B6 q
k1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \
) e/ G, Z& b' X+ b9 j. s0 g3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;
* g2 l5 B' R& B- `! ca1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(
, W& w. ?8 w: x. Q DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(
1 a0 A- ~/ ^( ~. X9 L& z' E DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);
0 ]5 F" I. `" }; [9 `: i\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \/ h d& ]" H& }# t8 M
= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];( v0 P0 Y) ^! t1 |- g( y: M
b1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \: w( W$ F- k8 e% G* `. N4 Z, R& P
1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \
4 r# D/ A2 q; D' V/ q0 TSubscript[l, 2]/Subscript[l, 4];
/ Y. S; o# A- C" XDD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);" X o9 A N/ |$ }
DD4 = D41/(A11*h^2);- n/ T0 t) H; o' ?% S" g3 Y
r11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[* [5 ^9 N2 d" P' d
a2*\[Omega]^2, (4)^-1]; r13 = Power[
! E2 _8 u* V1 O; k9 l a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];6 { {* @& z0 i' \+ E
BB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},3 T1 V1 ?( H2 Z) `( w3 b6 L7 m% m3 p0 z) Z2 E
{0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},- J% g1 R& U3 w( d
{0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0, 3 C; q( }3 q0 O; ^8 n
Sin[r12], 0, 0},, i0 E6 B; Y# y8 J* J6 P
{0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0, ) [# F- O% I1 h! V
Cos[r12], 0, 0},
- v) {- J# P0 V& v" ~! Q7 D {-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11], 1 u5 t' O# Z; m& ]
0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,
8 n- S& Y3 @: x& B/ n e4 N -(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0, ! m& m8 P. W' e N2 z, X
0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11],
7 D2 x, C* n6 e4 ^+ \5 M 0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*$ W( [" n- _; S: \. Z
DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},
; _# t2 K/ j: c2 k9 k+ A8 W' U2 { {-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0,
7 v$ G- V0 C" a9 N. ?; ^ 0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11], * u% n7 F2 ~& I- @
0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*9 b5 _0 M9 M1 W2 k- x5 @9 ]6 `$ ] v
DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,
# j6 Z6 k0 z7 b0 f (r11)^3*DD1*(\[Beta]1)^3*Cos[r11],
2 ~. P5 h: w! r: S6 B8 N' g; N 0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3},
, |3 F% j# c% p5 N. v6 y {0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*$ ~3 ?6 d2 P3 N1 |
Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],- z# m9 v9 d( E9 @* O. ^% C! R
0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*
6 v0 m" \% s7 h Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,
8 J4 F- }3 x$ d% R2 Z- l -(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*
, V) v: a4 l" D Cos[r14], 0, 0,% j1 e4 V" o0 F5 t- E% |
-(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*
& G0 n9 X- h4 n' f Sin[r14]},
( D3 F+ ^8 L5 n5 n/ O% x" h9 H {0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*8 J2 s" d: q9 x3 O- u( O0 n* e
Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,
& n% o, A0 _ @; e$ h# Q (r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*
4 p/ x) F, H$ a3 L Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],
9 V0 K& N5 P: U3 N (r14)^3*DD4*(\[Beta]4)^3*Sin[r14], / R: p( ]1 D' y+ L
0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],0 d7 v$ ]+ l* P
-(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},; a0 p. B6 O) K9 }$ p# B2 G
{Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0,
+ r1 \( y2 W Q7 b Sin[r11], 0, 0, 0},
; Q) j/ b5 x0 b. S {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1, ' @2 u" S+ I' K: \6 _4 v
0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
- e' r; i9 g( n! D 0, -r13*b1},$ |$ D1 g2 z0 [6 D8 @
{Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1,
. F1 ^: R! c& s- l) z Sin[r11], 0, 0, 0},
% ^0 ?9 A2 n) K {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0,
% p7 E. S0 X5 _2 U) g; v" _ 0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
- i0 j8 p2 r9 x 0, 0, -r14*b2},, Y/ y& x4 P; I" S u
{0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,5 H o7 Q) N0 n* Z( T
0, -Sin[r13]},3 s8 y% F- { {* J6 A
{0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0, * `& k/ a/ A: [7 d! Q4 h
r13*b3*Sin[r13],
1 c; z% d) Q4 O1 |, x 0, 0, r12, -r13*b3*Cos[r13], 0},
+ T' R* @4 x9 ^# ^0 e+ N {0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0," f) T7 e, M6 U! P% s( n1 d O
0, -Sin[r14]},9 U& L3 k& n6 v0 |/ G/ I _+ z# ^
{0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0,
! a0 c, h: Y9 j' a8 t r14*b4*Sin[r14],
4 C& d4 ]; P3 Y' H- j$ n; T9 s# s 0, r12, 0, -r14*b4*Cos[r14]}}, D1 R- I; Q- j2 j _/ r
aa1 = Det[BB]
9 T8 i( }3 J9 n! _6 V8 _, ?Plot[aa1, {\[Omega], -10, 10}]& c) t$ x5 X6 v- q. S! U
ss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]- y6 }2 @" r' V! @: T# ?
$ Y! o; X9 I2 Z1 j |
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