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本帖最后由 游龙游龙 于 2014-7-8 14:45 编辑 4 q" _: _2 \. G
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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
+ ]; X! Z, m2 @" C' S6 V/ \, U! D行列式求不出,画图找不到根5 C) I6 g& p) B3 n2 W* |, i6 | P
(*定义材料常数*); p+ z$ T, p8 n4 a$ X" ?6 F( O6 ]
Subscript[\[Nu], TL] = 0.25;) R; o: p* V& ~. O% X2 B
Subscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)0 \- ^% L( {1 u, u& p- T
Subscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)
; I [0 h: q5 G7 b& Z! A# _& USubscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)3 i K( T+ j7 Y; E: M0 _% j
Subscript[\[Nu], LT] =
G. O- q d# Y& t( `; j" r/ R Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];
: s. j/ e. u/ z\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];
' X* W% h" }; b; \; uSubscript[C, L] = Subscript[EE, L]/\[Mu];+ D. M; U7 d9 [6 C) h9 u( b: [
Subscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];0 f& R" Y. P" j
Subscript[C, T] = Subscript[EE, T]/\[Mu];
5 l( d3 a% B& C/ z/ g; v! E5 rSubscript[C, LT] = Subscript[G, LT];
- O: B; @6 {/ _% d" f7 |(*脱层几何参数*)
& h2 ^8 R0 z+ i2 s* ^0 U1 F) e\[Rho] = 1600;(*脱层密度*)
H! K: ^" H9 d8 d- `) c1 M# |c = 0.06;(*阻尼*)4 Y j; T; p$ S
t = 0.01;(*t每层厚度*)& }8 W4 y8 p3 c" u A- O
h = 0.05;(*h为梁总厚度*). V/ R8 c2 X! z' J u8 _, G
l = 1;(*为梁总的长度*)
4 O: K1 p4 v0 i- v* i. pSubscript[l, 1] = 0.3;(*为梁1区的长度*)2 ~( E6 n! l; e4 u# F8 U! V# U
Subscript[l, 2] = 0.3;(*为梁2区的长度*)
3 F- J# T2 m% R+ ~8 iSubscript[l, 3] = 0.4;(*为梁3区的长度*)3 [; x9 O4 J1 `6 ^! u4 q3 L
Subscript[l, 4] = 0.4;(*为梁4区的长度*)
, _- O8 [8 Y6 X& ?+ Bnn1 = h/t;(*nn1为总铺层厚度*)
& ~$ g" F! L9 w0 ^2 B+ }# Onn2 = 2.0;(*为上子铺层层数*)& E* X! y; g8 n# r
nn3 = h/t - nn2;(*下子铺层层数*) X5 G" s) ^! f. L( {
Subscript[h, 3] = t*nn2;(*梁的上部子厚度*)! { m5 N5 m4 {% J0 g
Subscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)
- z5 W5 x4 W9 J- k" Q; W, B0 p. iSubscript[h, 1] = h;(*梁1区的厚度*)
4 I) i) T8 W' CSubscript[h, 2] = h;(*梁2区的厚度*)
6 S' V$ y4 L+ M% T5 s. w(*求各单层刚度*)
+ f0 s* n/ a, Q& aagk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)% x% ]7 x# r' T% V& V0 h
% d& Y' o6 Z" ?: Z r( F2 i
* p- E/ @1 {. e1 _; z: m* M8 `ck = Cos[agk];(*列表求各铺层角度余弦*)
, W- C) Y( O% a) Wsk = Sin[agk];(*列表求各铺层角度正弦*)2 t7 H: l' k1 D7 _
s11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +
$ F8 E4 I( Z8 ~8 C0 E3 [0 y sk^4*Subscript[C, T] + ) j/ z, s! v5 Q+ I: k' k
4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)
, B0 L Y; d* j8 W4 T3 D5 ?' UA11 = \!\($ Q1 H# i8 L- X8 [$ T
\*UnderoverscriptBox[\(\[Sum]\), \(k = # o) P1 E, A/ x, B/ n% I6 u: L
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*)
5 w" x9 Y/ t# c6 X7 O! a# U0 u3 {A21 = A11+ J% T" {6 y0 H- ~
A31 = (\!\(0 l- s! F- n" s) D
\*UnderoverscriptBox[\(\[Sum]\), \(k =
. }( z1 d5 ~+ W) E) c2 { 1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)# j' A, f- T) @9 b# ~# D" ^; O9 l
A41 = (\!\(; o' V3 E" R. D: [7 {' r! a
\*UnderoverscriptBox[\(\[Sum]\), \(k =
5 G$ {5 l/ z2 w8 X$ @: c* N nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)
: ~# b+ `+ K9 G% o+ @6 _/ c9 O& v5 I% D0 `; X
( |* v. ~5 _6 ~/ ^( EPrint["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)
- J* f/ M d, p3 U. U. eD11 = \!\(+ z! b1 `# ]+ G2 t# C( o
\*UnderoverscriptBox[\(\[Sum]\), \(k = " v& c7 @+ M1 d' Z$ E$ J+ J
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
2 P3 ?( V( U! {/ l$ z\*FractionBox[\(t^3\), \(12\)])\)\)
8 T) b8 Y3 f9 I1 aD21 = D11
/ m; f" `( v4 ?9 q- b' E) _( ND31 = \!\(
4 M; Y' v+ g5 ^$ N1 B9 M6 M\*UnderoverscriptBox[\(\[Sum]\), \(k =
) g4 u0 q7 h. T5 i! c% O4 n/ V, L 1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*7 H8 v. n1 m5 q0 k6 F
\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*), R: f) C+ T* o5 ^' r
D41 = \!\(
5 f4 _, b# q& N4 u+ z, z\*UnderoverscriptBox[\(\[Sum]\), \(k =
2 B2 s1 k) G' _2 E nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
( B# b" F5 f- m D\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)2 _2 i3 h1 `, y
k1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \
' {8 E H. e; s3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;
) m8 h' B; h) P0 A3 |, M& v# ga1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(
% @0 Y# I8 g2 s6 ^5 C5 G9 p( C9 ] DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(/ h, x- d0 V( y/ ?* ~
DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);
; z A1 P8 P2 {) ~ J. ?2 c% E\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \
) G# G M. f, W) J8 @= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];' b0 X5 {: u& d# j& j( R, R6 J7 O7 S+ \
b1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \, `& h8 ], X* {& s* K! R2 t8 n2 C
1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \; a; o x C3 ?
Subscript[l, 2]/Subscript[l, 4];" U* ^; ^/ q' V; C& O: x2 ?
DD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);8 Q% C0 C, i8 [0 T
DD4 = D41/(A11*h^2);; g# T- s: Z0 t _" Q
r11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[; f% e/ g5 }0 A; c
a2*\[Omega]^2, (4)^-1]; r13 = Power[
" F" `7 D0 X8 k+ Q9 b a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];
" ~" s3 |! g: G. n6 x2 a) vBB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},8 n# v& I0 S, |- s* J& I
{0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},
( _/ [/ n* q3 o+ D* I% u& _2 [ {0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0,
4 R; m: _$ k/ v Sin[r12], 0, 0},
. z8 E4 y$ C6 F) A, v7 L) H* p {0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0,
3 O" p7 z' |9 | Cos[r12], 0, 0},
& m2 Z3 y5 \4 I: b {-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11], 2 s- K* ^ M5 L% G6 Y: t5 X' R
0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,$ R1 n, G$ Q9 \
-(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0,
) ?5 m$ O1 ]6 y, }! T- a) U% z& Z) E 0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11], ! U- b. @6 S1 M( V! F
0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*0 _* P; B# v( k3 ^0 a' e
DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},- `$ A& D* u& e6 J& a5 I. P
{-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0,
/ T: j9 D3 z) N6 e 0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11], 1 b! @8 R% V" [+ L
0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*
; \7 \% q8 t+ G( b' R DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,
; w( {) \3 b8 `$ W) W (r11)^3*DD1*(\[Beta]1)^3*Cos[r11], 5 g9 a1 A! w9 @
0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3},
- F9 S5 i, Y3 O3 N/ t. s( @& D {0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*$ O; [) Z; o: s B
Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],1 L$ t5 a! c) t2 c3 ^. ^
0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*
6 A4 L5 G4 f. S, _( d Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,
0 j0 p" N' K1 h y -(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*; n. y/ x& ^' V
Cos[r14], 0, 0,9 J, @2 N- _; {! h& C% w% I
-(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*
9 F# b' X G: i- X1 x& v7 M5 n! U Sin[r14]},
1 ~/ l$ A3 ?0 K% r; R {0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*
! }3 |+ l9 X) ` Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,
4 I4 ~2 H' F( s4 |6 m& N (r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*
! g" b; o' F7 L! H$ s+ [8 t! m0 Q$ K Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],9 c8 g F/ L5 I" A& O- K0 i
(r14)^3*DD4*(\[Beta]4)^3*Sin[r14],
( j* O9 f* L* L9 J0 ?5 S8 T f 0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],; V1 B/ D( ?+ A4 S( r- _6 [7 q; a
-(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},
: V8 Z7 m" |/ k7 w% ? {Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0,
* d: Y5 o: h7 h# @! ^ Sin[r11], 0, 0, 0},' I% s; }% _, ?1 ]5 R2 k& R0 ^
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1, ( V4 e* |2 S6 q6 A# h
0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],% A9 c* J" u4 ~8 _( m; n
0, -r13*b1},
9 `2 x6 ], ]9 [+ @2 p: j- E {Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1,
3 [. d' l+ X" P+ w Sin[r11], 0, 0, 0}," v( [; o8 |. o; H2 [
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, ; q3 d: b( H7 {% |& c
0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
' q- u3 k' Z9 _, W: t9 _ s. s 0, 0, -r14*b2},
. W" z: {. ^" W/ I# X& j' d {0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,
* h+ P7 l! N/ I: {! M. R' G 0, -Sin[r13]},. H4 ~3 X! O' @4 F
{0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0, 2 {# [4 I& l1 h# ~% _
r13*b3*Sin[r13],
3 i% E1 }; B7 `2 o& z8 `$ S 0, 0, r12, -r13*b3*Cos[r13], 0},. n- e" H; e5 b" n6 g
{0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,
3 p* Z" ~; ]; K0 Y+ W1 ]# r 0, -Sin[r14]},
6 l. X6 C1 w+ Z& j {0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0,
- j- i, D. c3 \- G r14*b4*Sin[r14],: F5 z9 i4 L- C0 v
0, r12, 0, -r14*b4*Cos[r14]}}
# b2 n2 ?; X! Aaa1 = Det[BB]3 r2 c9 c d9 X/ ~
Plot[aa1, {\[Omega], -10, 10}], M# j1 ~& g& _1 ]1 w4 q
ss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]
* q1 c2 V! A& O6 w7 y
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