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本帖最后由 游龙游龙 于 2014-7-8 14:45 编辑
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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4 F% s( V3 V5 B
行列式求不出,画图找不到根
. |5 M* G0 a1 |1 x/ B(*定义材料常数*)
% W. _9 p! M i0 C8 q( NSubscript[\[Nu], TL] = 0.25;
# }& y, d5 V" S3 B' [- S; q7 zSubscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)4 ~4 Z. a* h- \. ^6 _2 ^0 O
Subscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)
D! n4 t, C: n$ `- _8 j. @8 ]Subscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)
4 m, s0 Z- L: K; _2 ~Subscript[\[Nu], LT] =
9 A# B. r" p9 e' N W3 l6 [ Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];
* c0 M8 R. `1 w\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];4 s1 J0 y: H% L- Z c
Subscript[C, L] = Subscript[EE, L]/\[Mu];
4 A" J6 i* C% R7 _; m+ ]" v3 H) ySubscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];5 C, u( i+ P! T3 Z+ r# I4 Y
Subscript[C, T] = Subscript[EE, T]/\[Mu];
W, ^; }9 o' w' ]! y5 N: `Subscript[C, LT] = Subscript[G, LT];
5 y6 P" d' n6 I(*脱层几何参数*)
2 h. t! b' r1 L9 H9 I\[Rho] = 1600;(*脱层密度*)
; h4 _5 I, U4 Y' f& A% Mc = 0.06;(*阻尼*)$ \8 S4 l4 }: x
t = 0.01;(*t每层厚度*)% b2 u; o) c, g3 R# i+ K% V/ L
h = 0.05;(*h为梁总厚度*)
! S/ Q' x+ i2 b0 j4 K' `$ jl = 1;(*为梁总的长度*)
" M# B2 h( B. E& `: I# ~" kSubscript[l, 1] = 0.3;(*为梁1区的长度*)' M0 V. ]4 ^0 m5 J" t9 `) D" `* u
Subscript[l, 2] = 0.3;(*为梁2区的长度*)& V9 j& z2 E/ z8 V' L( p0 |
Subscript[l, 3] = 0.4;(*为梁3区的长度*)
& x' m0 ]3 M) y3 ?9 t( eSubscript[l, 4] = 0.4;(*为梁4区的长度*)
! S7 f, D+ }# |$ d0 U6 W$ Unn1 = h/t;(*nn1为总铺层厚度*)
* O$ c+ b+ ?6 inn2 = 2.0;(*为上子铺层层数*)
`: p4 ~ e+ T0 Lnn3 = h/t - nn2;(*下子铺层层数*)
5 a! P3 a& U# X& @% z9 PSubscript[h, 3] = t*nn2;(*梁的上部子厚度*)% P& O w5 [: a/ C
Subscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)6 D9 v6 G; P+ i& D6 R
Subscript[h, 1] = h;(*梁1区的厚度*)/ R$ f8 t. f- I; {. i- t
Subscript[h, 2] = h;(*梁2区的厚度*)
4 a! G& H4 `4 H) K2 `# ~8 A5 }) P2 H(*求各单层刚度*)
: m( B2 k& o5 ]7 h: L# Jagk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)" }' l( J1 f \0 e( h- v( g
+ {6 h+ j+ y l: Z4 e+ ?8 Y/ T7 }; q! n# O3 o4 ~
ck = Cos[agk];(*列表求各铺层角度余弦*)5 o9 S. l o+ C
sk = Sin[agk];(*列表求各铺层角度正弦*)! t6 X* E& ?4 e5 k" p' Y1 Y) W
s11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +% \1 U% i8 f( u+ [' T& U( y
sk^4*Subscript[C, T] +
1 I9 P% W7 ^7 K1 \ u 4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)& [# z9 D$ J5 N3 h7 b
A11 = \!\(
0 B2 C, I5 A- _: s) I0 C9 t\*UnderoverscriptBox[\(\[Sum]\), \(k =
8 q3 w2 d* ~ q h 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*)
, r/ C( ? A7 J+ ]2 r& j. LA21 = A11
* z/ m& X: Y$ P3 \- k GA31 = (\!\(* _3 E% y: F* o- { b( O
\*UnderoverscriptBox[\(\[Sum]\), \(k = 3 i" d* T! w! v9 @
1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)
6 L1 i" L4 v7 R9 ZA41 = (\!\(" j1 i$ G, r3 |) {0 Y9 w
\*UnderoverscriptBox[\(\[Sum]\), \(k =
9 W5 i2 T+ n- s) c nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*) M6 b8 B0 ^- h N( e+ ^, F0 d0 B
: Q- d% {# l. [3 m+ _" e J7 i- z. j8 d2 l: }0 L3 w
Print["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)# g+ ]. N4 _) Q: \$ |$ r
D11 = \!\(" C0 m/ o. b% h* f
\*UnderoverscriptBox[\(\[Sum]\), \(k = ( @: J: c1 n2 N4 ~7 y* \1 ^
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*. E* p" u; X, @$ v2 Y- U$ f
\*FractionBox[\(t^3\), \(12\)])\)\)$ [. I8 O: Y8 A( T* r/ _ `; ]2 y" n
D21 = D113 g- W& ~ U: J
D31 = \!\(
9 f# ?7 g: A' o$ X6 ?\*UnderoverscriptBox[\(\[Sum]\), \(k = # o; i+ w% R* L1 x. c; m( b
1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*
3 w" ?7 D. J( b& q\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)
* i* G# x3 f t$ AD41 = \!\(0 s, `; E- i3 M# s7 o
\*UnderoverscriptBox[\(\[Sum]\), \(k = , Q) i4 c- h8 B. V
nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
3 L: L: U# A: s, A1 i" q\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)
" u3 Z6 r! c. i+ rk1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \
4 Z _' o+ {! e* Q3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;
7 d9 ~4 \; O0 X6 x* K* [a1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(
+ q3 N, @3 p0 Q! t* ~7 d3 G DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(
/ L3 j8 h! w7 `+ d DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);: v& N" h- |' N% Y
\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \/ g: j! ?3 @; H, Q: m
= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];
- b* I' b( ^% i6 X% vb1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \5 A, M+ P- p* X( Y5 ]
1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \
1 w) @. h( V. G$ L' ]Subscript[l, 2]/Subscript[l, 4];. w8 F w4 p' a
DD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);4 g' k, B5 ~' |' s+ C
DD4 = D41/(A11*h^2);
, I$ y" Z8 ]6 q% M6 J1 y( Qr11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[, g7 _7 C: I1 z- N
a2*\[Omega]^2, (4)^-1]; r13 = Power[, b) A. W' B3 R
a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];# `+ D" E, ]9 a g2 B/ g4 i; P
BB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},
% T5 S& q3 K6 { {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},- [2 }& L4 d% x, i4 l. V
{0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0, $ S* F4 g/ w1 j8 l ~4 f
Sin[r12], 0, 0},6 F1 A, a" [$ N: ?
{0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0,
& C8 P0 k+ p$ Y; k1 f Cos[r12], 0, 0},; [* ^. U2 ?2 k
{-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11], $ }$ w# e4 F; K9 L8 O6 }3 A
0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,& d9 f8 x/ O2 z7 d V
-(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0, g: s; g6 _/ P& q
0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11], ' R/ a: {5 @3 d+ `& h$ J
0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*
2 H8 y+ u# [" |# n0 @9 @ DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},
: C6 W) B8 ~5 c {-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0,
* G8 H; Y. F8 I! X& T, S' m6 N% e) q 0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11],
+ {$ J* s* h4 }" L) U 0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*
1 ?7 h5 I- D# H! f" O& l DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,& ?, V; M, W. ^
(r11)^3*DD1*(\[Beta]1)^3*Cos[r11], 6 x }/ v6 k1 z3 j3 Y4 M1 y
0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3},
3 H7 v. |$ Y- F" }* L {0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*" F6 `( H) r: [ q0 D
Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],
. h S0 R" A* {) i# b, l1 b+ ~ 0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*& M- w8 F+ Q A) h* W; }
Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,% x4 W: v1 {1 k
-(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*
! f( q4 }! o ?" ^- l6 n5 W! {2 p0 [ Cos[r14], 0, 0,
. [3 _ s7 u, k- J -(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*
, @ i; T, ~) u: U( j+ O) ^. I" s Sin[r14]},8 s7 ?/ m( {8 I4 |8 i
{0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*; z) m9 B" D8 \7 n4 K" O
Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,
9 |) {" n0 y" G- H+ m+ C4 z* J (r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*6 N* g! W( r9 X6 {5 T
Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],
) z4 g; G& a: F! y" O4 y (r14)^3*DD4*(\[Beta]4)^3*Sin[r14], 3 I! v3 d: w' B$ S7 g* e# A) g
0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],. U0 L( F7 n: [- q8 i
-(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},% @1 I7 m+ Q7 k3 x, h
{Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0,
" b+ {+ A, C# E: i; f' J* i( { Sin[r11], 0, 0, 0},3 I& V8 } R5 A9 v
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1, & |) }( }/ \* \+ x! A
0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
- L: P3 ^% x M/ i7 c 0, -r13*b1},
; u' y* X+ L5 Y& m% c% D x3 u5 l {Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1,
/ p1 A w. C |8 ?3 M Sin[r11], 0, 0, 0},
8 _ f. y; b# u# g {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0,
" H ~' z1 x5 m }! W& L' i 0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
4 A. Q9 W' k7 E4 M9 |2 Z. D 0, 0, -r14*b2},! J) q8 _' t1 d6 u4 X+ F, y
{0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,
; l" P- v ?3 v+ E 0, -Sin[r13]},
) u% E5 }7 L& X/ ^5 W+ V0 x {0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0, * s1 y7 g! y7 v6 @& h
r13*b3*Sin[r13],* L6 o' \+ e2 F
0, 0, r12, -r13*b3*Cos[r13], 0},
1 K* ^: W% a8 l4 r* q {0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,: t) ~3 E" w+ m' P7 \
0, -Sin[r14]},- @# S! k7 ?1 q8 `0 I
{0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0,
6 q* ^" G/ O: l r14*b4*Sin[r14],- M7 M2 Z9 P1 Q% z
0, r12, 0, -r14*b4*Cos[r14]}}3 X* t1 j9 c6 V0 {% I
aa1 = Det[BB]
. \) O1 b8 F9 m$ nPlot[aa1, {\[Omega], -10, 10}]
+ | |& T" q$ S8 v' Z/ g( P2 d- Lss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]& h4 m0 e" e$ k/ X- i/ K
( a2 {* o& s: B( g/ F6 j |
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