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本帖最后由 游龙游龙 于 2014-7-8 14:45 编辑 ; [; _7 r' t7 ~! k1 N9 `
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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2 X3 ~! u/ j; {- O+ L" m9 Y& R) q
行列式求不出,画图找不到根# p0 ]' B& f; {+ J* Y' Y; @
(*定义材料常数*)
0 ?: O0 i; y+ X/ E3 }* |9 _Subscript[\[Nu], TL] = 0.25;
. N3 G9 j( N& T$ Z% D1 SSubscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)
; w4 H" Q0 C N- ]Subscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)2 V3 g0 T2 \8 z J8 |
Subscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)$ {, U. b1 J3 d4 X* l4 q2 l
Subscript[\[Nu], LT] =
8 w2 K4 A6 U% Z: w8 n; Z Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];
) f+ W" T4 l. ]1 U: o3 @# u8 p\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];
# N# j4 }3 C: bSubscript[C, L] = Subscript[EE, L]/\[Mu];
& V/ [6 J2 P0 g- F( L3 GSubscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];9 M, J7 F% a% g5 L1 R7 r& U
Subscript[C, T] = Subscript[EE, T]/\[Mu];& b2 B+ U+ l; I1 T$ U* ?" S4 r
Subscript[C, LT] = Subscript[G, LT];; H7 H: i& @- a, f: g8 R5 ~
(*脱层几何参数*)
: m" Q8 R& t6 J/ s. Z5 }- X\[Rho] = 1600;(*脱层密度*)
" v$ K0 q% J6 J' Ac = 0.06;(*阻尼*)
- d! I6 Z. ^4 g/ e' v2 A4 a k+ Yt = 0.01;(*t每层厚度*)
6 F& Q/ L3 e# q9 B( ~h = 0.05;(*h为梁总厚度*)
$ N$ X+ f. p# q0 Il = 1;(*为梁总的长度*)
* o$ `3 v& C4 hSubscript[l, 1] = 0.3;(*为梁1区的长度*)
3 S6 B2 X9 ?1 R9 hSubscript[l, 2] = 0.3;(*为梁2区的长度*)
7 G/ W4 C$ J4 X# k1 X) f- Q2 A kSubscript[l, 3] = 0.4;(*为梁3区的长度*)
& S& w, ` i( [2 T xSubscript[l, 4] = 0.4;(*为梁4区的长度*)
9 a6 _0 o) a3 K; p3 L2 S/ i; `5 hnn1 = h/t;(*nn1为总铺层厚度*)( c7 E& @# g2 F9 o/ V( `1 j" \: ~
nn2 = 2.0;(*为上子铺层层数*)
1 |- K$ z% e3 Hnn3 = h/t - nn2;(*下子铺层层数*)
8 e" S3 A' c# M# aSubscript[h, 3] = t*nn2;(*梁的上部子厚度*)
+ M0 @: O) e% F* E1 S% x4 B$ ^Subscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)0 j! |( J% f" k3 i. h4 r
Subscript[h, 1] = h;(*梁1区的厚度*)- ?9 l0 q1 ^/ Y7 T2 b8 D, s
Subscript[h, 2] = h;(*梁2区的厚度*)
! o T9 ]% f5 A) S3 Q. L- l" c(*求各单层刚度*)) m& F% d: _+ g5 K% F! a5 f
agk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)0 W+ G% D# X7 x9 w7 p& s/ j) D
$ W' F" P2 E4 c8 y, F
, E5 _. \# D" n) F1 a
ck = Cos[agk];(*列表求各铺层角度余弦*)' L3 t7 Y! P/ U+ X1 \8 P9 {5 Y
sk = Sin[agk];(*列表求各铺层角度正弦*)! e) u0 X! g6 E3 _, U, |
s11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +* U# d! g# I' r- D2 I B8 ?
sk^4*Subscript[C, T] + " g4 U" N' a4 \1 t
4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)" z! z3 H- m% K3 \7 w B
A11 = \!\(/ d) Q' o$ \. v
\*UnderoverscriptBox[\(\[Sum]\), \(k =
* i% a5 ^. P7 B 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*)* I6 M5 f1 ]% a4 o V
A21 = A11) I# G" p) U, |2 Z
A31 = (\!\(
1 j( O6 \& t. _% x' r0 ?\*UnderoverscriptBox[\(\[Sum]\), \(k = ' X; O9 N$ r, Q) B2 ]# I
1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)
' u8 O1 d! y% d9 P* s9 ^" FA41 = (\!\(; k5 d% x( \4 O' K( p
\*UnderoverscriptBox[\(\[Sum]\), \(k = ! a! ? g" G5 n. a, L. T9 e: y
nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)
& V( v3 M0 ]" b' R& c5 I
* s2 Q& _; ~. x, H
( f r( Y& t7 R4 _6 qPrint["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)5 c3 I+ ~, F7 L; d
D11 = \!\(. | J! R) |! x! j) j. @6 _3 F
\*UnderoverscriptBox[\(\[Sum]\), \(k = . V8 [. H, ~$ J Q# z" ?) C F
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
- M2 M0 T2 }9 Y' A\*FractionBox[\(t^3\), \(12\)])\)\); G. b, b3 s+ ?
D21 = D11# q5 A% f" r/ Y8 f( V9 g" E
D31 = \!\(
: |9 x2 H' g3 F$ y' s+ @\*UnderoverscriptBox[\(\[Sum]\), \(k =
, M0 F! j4 a+ P2 O i 1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*; r* o& Y5 K/ d3 K5 z
\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)! A% J9 b7 A, Q$ n9 ]
D41 = \!\(
/ Q( L4 b, m3 Z( s h\*UnderoverscriptBox[\(\[Sum]\), \(k = / T4 w( \2 Y9 r6 X
nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
4 h7 _" n3 f5 ?* u2 e9 D& N* `\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)
# G& _ Y. ?, \+ L' }7 Ck1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \/ ~, C/ i! F* ^/ B5 j
3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;
1 \ j1 A. ~9 e8 S/ j8 sa1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(
1 I2 ?7 r6 |7 } DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(
3 b; U; w8 o) e+ f4 q) @) } DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);
2 s( a- n" `" H& P9 z\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \% Z" O# I& n, v% }. Y' ~& T) N6 o/ B
= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];; Z& p4 ~5 q+ W N: X7 F
b1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \3 U/ P- g1 ~' J
1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \* U9 @4 n& k- A. ^. g
Subscript[l, 2]/Subscript[l, 4];
1 }: p! d) f: r% ODD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);; B+ [9 v4 ~( e- `4 n% z
DD4 = D41/(A11*h^2);
6 Q3 Y6 f' M H5 C* |# ir11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[
& t3 F8 x. M5 ]) P9 b* d8 i5 ^0 L a2*\[Omega]^2, (4)^-1]; r13 = Power[' O6 \% z8 G8 q7 h" \1 N
a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];. Y2 `+ }. |/ f2 u( L
BB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},
+ z4 |+ N C& a {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},
% u3 v! |, i A {0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0,
; _3 p$ R. {* q0 w$ \* a Sin[r12], 0, 0},
+ h9 z( X, C5 N+ h4 w {0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0, 4 Q/ y4 e% g3 @ ?1 z/ ]6 H; k
Cos[r12], 0, 0},2 O# u7 h0 w. _6 D. k" `
{-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11],
5 p- A- N3 X# [) B2 w 0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,: n) M% a; ]3 g; j$ p
-(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0,
0 m2 ^1 v3 I1 V& r2 ?5 O2 Y3 | 0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11], 6 `; o9 T, z* d5 L% C
0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*
5 u. V1 m/ S' J4 ]. T DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},
! @0 S5 ]8 F& y {-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0, & [$ n$ Z7 s; r
0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11], u( h6 G) |, w5 o- W* j" J
0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*
, U x& V1 e1 r( H$ x* v DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,' h* u! B0 n* s
(r11)^3*DD1*(\[Beta]1)^3*Cos[r11], " X5 \% ^; i) q/ t
0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3},
b8 D1 d6 K( F0 A {0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*: E$ \1 X' e/ w8 [6 k
Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],( s& w( T" M! V0 K4 H
0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*. P, [( p9 q* D; A, E7 |/ U$ _
Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,5 q8 u: h! z5 L
-(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*+ x8 ]/ V' n( S* J1 |
Cos[r14], 0, 0,9 _! W' \" q! F4 W
-(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*
7 w: {" g- j$ k, a) l Sin[r14]},+ w3 o1 W* V5 o% n2 }( [8 `
{0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*' }( D9 D" N" u
Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,
8 U4 }' b- ~3 u5 S: ` (r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*4 H+ v/ H% T& C& G/ u
Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],
# q# n+ M: B5 x# { (r14)^3*DD4*(\[Beta]4)^3*Sin[r14],
7 o" n, e4 c, P% G7 R0 [7 ? 0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],; B1 r U" o; d& Y
-(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},
5 e6 Z, b+ r, h" i. W% T {Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0, 5 x5 p2 ]+ Z$ |; S0 J2 i' z2 e
Sin[r11], 0, 0, 0},
& _' J0 X2 }6 c/ v" c- B2 Q/ e: x5 _ {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1,
, `# c0 Z1 W+ R3 G' p" E V 0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
- m9 `+ R/ @) O% Z0 C1 L 0, -r13*b1},
* q, Y' z, e4 g7 g2 T, c {Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1,
3 c; o- N$ B$ G! l( u* U Sin[r11], 0, 0, 0},; T6 T, a$ f& q! V# P% | @$ [8 ?
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0,
* z* F& r+ O* x 0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
6 @8 V, B/ ~: L+ f" V8 Z7 K, \5 ` 0, 0, -r14*b2},& t/ O+ p. I5 W4 e' S
{0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,8 [/ \# w( D/ b% k( H& {
0, -Sin[r13]},2 O& c' A; f2 ?3 o$ f
{0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0, - ]4 q7 l" w; l4 V; Q
r13*b3*Sin[r13],
7 p P+ b$ t2 v; }" K7 j 0, 0, r12, -r13*b3*Cos[r13], 0},# }1 w5 F$ M: K! \, o5 V' N
{0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,
" |# |0 E5 j' J* b5 M% g 0, -Sin[r14]},
# O; |1 y" H% v+ L! u7 @% h {0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0, % A# r4 O5 e3 ~( D$ Q' ]7 ?
r14*b4*Sin[r14],, d- P `) Q& V$ A) ~" V
0, r12, 0, -r14*b4*Cos[r14]}}
7 N3 W8 N4 B, J. `/ Z* `4 eaa1 = Det[BB]
3 F' ]& @9 K* R7 h7 Y4 x* `0 \5 W: W APlot[aa1, {\[Omega], -10, 10}]$ ]% P& W6 H* Q, P
ss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]! r( A* c& M3 a' M
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