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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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- J) H' m) L1 ]- ?4 H4 W6 B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 D2 j9 d( _8 e" e8 a9 x9 U行列式求不出,画图找不到根
& [' Q1 B3 Y: x8 B' f9 c y! r t6 q(*定义材料常数*)3 p3 Z* g8 l- n& F
Subscript[\[Nu], TL] = 0.25;4 [, ?; Y: s6 ~8 n; K( F, f
Subscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)8 j7 U% O5 u# P$ A0 m6 v R
Subscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)
0 J( h* C9 x8 ^& O6 a% YSubscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)% g& Z; x7 K6 i( S0 f
Subscript[\[Nu], LT] =
( M: l# ?7 |/ L, b Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];
+ x/ ]! K g* n8 m; p\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];
- H/ S9 l" x" v6 R0 D$ r- E) C. USubscript[C, L] = Subscript[EE, L]/\[Mu];% x0 a5 i3 _- {5 D8 z; e+ \
Subscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];; a4 \1 ^. t4 d; O- ~. n
Subscript[C, T] = Subscript[EE, T]/\[Mu];7 c3 V. O' i9 B6 p$ a
Subscript[C, LT] = Subscript[G, LT];
0 t' G; R7 l/ C! B4 t5 i# F* d(*脱层几何参数*)( L5 G2 P1 N( ` }5 Z+ h
\[Rho] = 1600;(*脱层密度*)
0 v6 D; |+ E& @ Y4 I0 M# u7 ]c = 0.06;(*阻尼*)* O% x3 C2 z% N( g' a! P( D
t = 0.01;(*t每层厚度*)- K. F+ ?3 D% N" b5 Q4 Y0 h
h = 0.05;(*h为梁总厚度*)) |9 r5 i6 ? J- c
l = 1;(*为梁总的长度*)
, u' Z2 r8 C! K' V+ \3 ^1 MSubscript[l, 1] = 0.3;(*为梁1区的长度*); O& k' B% K% v2 [3 q
Subscript[l, 2] = 0.3;(*为梁2区的长度*)
6 T* H& a7 I9 F; zSubscript[l, 3] = 0.4;(*为梁3区的长度*)( n }$ w, M% f+ s
Subscript[l, 4] = 0.4;(*为梁4区的长度*)/ F4 m0 Y5 y5 E* k, W1 R( r ?
nn1 = h/t;(*nn1为总铺层厚度*)
1 w$ T9 j( G7 ^; C& tnn2 = 2.0;(*为上子铺层层数*)
! w8 h8 M) F enn3 = h/t - nn2;(*下子铺层层数*)3 O- p7 J- d% F; d- ~
Subscript[h, 3] = t*nn2;(*梁的上部子厚度*)
" ]" `0 O6 p& ^2 rSubscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)2 h2 w9 E' A9 h1 c2 L- I# {% O |1 V# o1 M
Subscript[h, 1] = h;(*梁1区的厚度*)9 t4 o( z4 C" \4 G) I L8 M
Subscript[h, 2] = h;(*梁2区的厚度*)
9 H7 s! X; S: n* q(*求各单层刚度*)4 f0 `& a) d! `4 n* _
agk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)
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' H& `5 Q- |' ~0 t; y) h
8 b' O3 {' P" y& g1 f. pck = Cos[agk];(*列表求各铺层角度余弦*)
& S! `% P& u( X" @sk = Sin[agk];(*列表求各铺层角度正弦*) |' z6 R) n( h) p/ S
s11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +6 n n& ~: I# W; Q `+ ~/ y
sk^4*Subscript[C, T] + 7 x' {/ K" H k$ d# ^% J g
4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)
" [$ c% a3 h) `2 \" n0 n5 vA11 = \!\(
5 ~' o: G) x4 o3 G( Z; `# t\*UnderoverscriptBox[\(\[Sum]\), \(k =
$ [, E2 [+ r8 B& N 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*)
5 |- O' O4 n2 v9 `! yA21 = A11
; V- N8 K7 B& C/ d# IA31 = (\!\(
3 ^ z0 L! A, f1 @9 Y\*UnderoverscriptBox[\(\[Sum]\), \(k =
! Z( ?$ i* R( ?+ @6 T `& ` 1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)( O1 J0 M4 E3 _$ H9 g# g
A41 = (\!\(
! ~* l4 o) J% i! J8 u\*UnderoverscriptBox[\(\[Sum]\), \(k =
7 ^5 t/ y. s+ P. P# m+ s) s$ \ nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)
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R* y5 `: b2 g+ |2 [Print["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)
; {7 b- a5 L( r B# U r& |D11 = \!\(3 [ P3 {! d. s
\*UnderoverscriptBox[\(\[Sum]\), \(k =
& }& Q: x2 W+ f7 D0 {& M 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*& b. `7 a3 I, c
\*FractionBox[\(t^3\), \(12\)])\)\)
7 h" h' \2 o- X6 ID21 = D110 w0 @& Y+ w# x6 z; `; \% W; F
D31 = \!\(
2 R$ U) ?+ V& T1 P/ L) \\*UnderoverscriptBox[\(\[Sum]\), \(k = ( P, v; w' k8 ]2 n# d
1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*9 G7 L X4 Z( e- T
\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)
, `2 d& [; P6 l. t i4 FD41 = \!\(
5 i2 l! P) c( f( M\*UnderoverscriptBox[\(\[Sum]\), \(k = 5 B, X& z) e, H$ S" o( E
nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*6 b9 ^" b8 W, x$ e f
\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)
& Z7 `8 c# V, ~6 U% q4 qk1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \$ X# {5 G$ Y h9 f+ n
3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;
% y2 x, k/ J6 j) H& }a1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(% i* q: h9 P1 }6 I" [
DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(! r, I# S% c$ f8 P4 A. d& |$ {
DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);
; M0 h8 y) T. C9 b\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \5 Q+ g) N* v1 D# b. Z
= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];( K9 C9 T; t& P y" X7 b
b1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \
) c- l6 r9 ^# ?$ w& h1 x/ ?1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \8 O3 T9 X# H" {
Subscript[l, 2]/Subscript[l, 4];' J6 s. C3 q6 T" N
DD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);
3 s3 Y* I8 T/ P7 xDD4 = D41/(A11*h^2);$ M" l3 k1 R: R& |0 s5 n" Q( E
r11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[' Z0 \- _& o; d
a2*\[Omega]^2, (4)^-1]; r13 = Power[
, f- ^. A+ ^* p% N) }! P a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];+ l* N7 [3 d* ^
BB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},
0 O) @4 ?7 G' j7 r# e" D" _ {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},. m8 a8 y3 \1 U0 m$ k+ R% L) j
{0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0,
7 M) [, C/ y) s' M Sin[r12], 0, 0},7 ]% F7 Q, w. K" ^: p% @( a
{0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0, % o9 U; X" v6 C% n# Q' X9 q/ z
Cos[r12], 0, 0},
* R8 L& Y* ]" Z4 Z {-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11],
0 ~, W* v6 b5 p) e; B 0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,- X8 K& m. @! u$ E8 N4 Q: m' q
-(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0, 2 j) {/ K* A' F. E
0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11],
! p) N" R. |& z 0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*5 F2 g X6 \$ a4 {# H, O
DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},3 L2 L3 V! H( N3 e) D0 O2 k
{-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0, / \+ o: h" i7 ?0 U6 e7 J/ g; {8 S
0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11],
' e; `* `2 P: M# i* e2 t 0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*3 w& ?2 {* z) J; y. \5 u; ]9 x' p3 r
DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,
: ~- `$ Q) w' j$ ~- n) t; {$ i- U (r11)^3*DD1*(\[Beta]1)^3*Cos[r11],
7 D3 A. e, _1 Q& A) R" s3 x5 @ 0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3},# ]; t4 w/ R6 A, ?
{0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*+ \' k* h M0 F# g, ]/ z' w7 C2 _
Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],. N& [% D! s; m: v' V7 j' F6 B
0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*
9 E; [1 X/ h# q) `' Y) ~ Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,* O2 H! G4 y2 Q& E$ y
-(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*
) d2 C+ s; }8 a! h" r Cos[r14], 0, 0,( f3 f; b8 L: a3 x0 T
-(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*0 u( M# d7 B& Y' y6 X) c" D8 k
Sin[r14]},
! Z/ \" n# ?& M9 H- Q5 P8 u. _ {0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*
* y3 F7 h) t3 f Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,% K/ b3 o& j% m" f1 U6 }* z ~- O8 F
(r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*; N& h5 K6 {5 v% G, u- }8 S/ l, k
Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],
0 w0 }' P% M3 F1 W& t' @: \& A9 u9 v8 E (r14)^3*DD4*(\[Beta]4)^3*Sin[r14], ; |' p% U' _- c' z+ d) H4 ] b
0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],
; {( ~& P5 {6 O, L -(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},2 w3 J+ Z4 ~( K w
{Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0, 2 P1 | Y \8 @" S
Sin[r11], 0, 0, 0},
* n6 S2 f* {7 C" y% D {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1, * o5 |+ j# L2 H: L
0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],0 k0 M3 J3 ~0 K6 r( B. L ~
0, -r13*b1},
. J4 [9 O8 U! {6 g {Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1, ' Y) n" P) n. \3 M
Sin[r11], 0, 0, 0},& c0 b( F3 ]9 M/ @4 J t( @, q
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0,
2 E0 b4 |' v5 K 0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11], b: e8 g# ~! W0 R& F6 p( p
0, 0, -r14*b2},) K/ R$ B1 c# _7 U ?
{0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,
. W: i0 @/ m- q 0, -Sin[r13]},% R* [4 C2 A$ [7 R
{0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0, $ N& T1 X6 g; x/ i" y
r13*b3*Sin[r13],! v K0 P; S% o* z6 t
0, 0, r12, -r13*b3*Cos[r13], 0},# G+ V/ i8 O! R
{0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,8 r* ]% h8 n( ^7 v( d
0, -Sin[r14]},
* c* H% A) o8 x' _" N6 ? {0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0,
7 h+ }* B' r$ U+ ^, q& Z r14*b4*Sin[r14],6 t1 D" k% T/ t2 p1 p6 Q& I
0, r12, 0, -r14*b4*Cos[r14]}}3 @1 l0 k/ @; p9 w N
aa1 = Det[BB]) p$ g" s# _5 m# B8 H; ?
Plot[aa1, {\[Omega], -10, 10}]
1 {3 q, [( X0 _3 T, F% wss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]
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