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本帖最后由 游龙游龙 于 2014-7-8 14:45 编辑
5 r/ {5 M% \* T/ M) O8 A# r( B+ R+ u" t
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
* P. ~1 n% ?$ Z5 K行列式求不出,画图找不到根. R- V% y8 v( J9 c4 g8 {3 d
(*定义材料常数*)
$ ?$ v$ T7 E' J, [* qSubscript[\[Nu], TL] = 0.25;
0 T N( V7 p6 s9 CSubscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)
- ]& \, G* ]) D$ w# I4 sSubscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)( P3 S8 X" S- p
Subscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)
1 s2 J9 [5 n% A5 R$ h' SSubscript[\[Nu], LT] =
/ g0 T0 T0 Q' Y/ R5 I# N0 m Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];
+ E+ x% B1 q* {- n- ^\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];' O; x0 Y# i5 L
Subscript[C, L] = Subscript[EE, L]/\[Mu];/ p% |0 p( ]8 _5 o: N% S9 f
Subscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];
3 W2 F2 p, p+ gSubscript[C, T] = Subscript[EE, T]/\[Mu];. C3 {" |4 _# e5 P
Subscript[C, LT] = Subscript[G, LT];
5 ~ E$ Z$ V5 d* r: f3 r(*脱层几何参数*)+ @" n5 F) { ~; Y1 {0 P
\[Rho] = 1600;(*脱层密度*)
/ C' Q4 c/ I4 ^5 [, W8 J7 t( pc = 0.06;(*阻尼*)
g0 T+ v( C7 H! M' j6 G2 {% Ot = 0.01;(*t每层厚度*)# Y( l8 A' `, f8 a
h = 0.05;(*h为梁总厚度*)
2 j1 K" y2 _4 s6 U$ p; o/ fl = 1;(*为梁总的长度*)/ X6 h# h; x, E5 U
Subscript[l, 1] = 0.3;(*为梁1区的长度*)
- v- @" x4 @& c+ v- {$ OSubscript[l, 2] = 0.3;(*为梁2区的长度*)
1 A% O: n( {# ]2 Z$ K. PSubscript[l, 3] = 0.4;(*为梁3区的长度*)
) a6 [ v. {- K$ y3 R- hSubscript[l, 4] = 0.4;(*为梁4区的长度*)! D0 N& {; b1 w) k! @
nn1 = h/t;(*nn1为总铺层厚度*)
) G3 y4 v8 o. L& C) a- Jnn2 = 2.0;(*为上子铺层层数*)) \ F# M6 c7 f1 u8 u! N* ~" Z
nn3 = h/t - nn2;(*下子铺层层数*)8 E0 o0 t1 L0 G9 p+ z
Subscript[h, 3] = t*nn2;(*梁的上部子厚度*)+ q- U C; _3 s D6 |8 i9 w3 f
Subscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)
( o9 l+ F. f; Z; P8 k+ F3 M) eSubscript[h, 1] = h;(*梁1区的厚度*)
* z7 M3 _; h- S4 rSubscript[h, 2] = h;(*梁2区的厚度*)
: Z# V/ S' H5 w' C(*求各单层刚度*)
v) D9 \. ~! U+ a. P; ~$ U v7 ]. ?8 [agk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)
; d- B! |# I: H! W, i, n2 \
: m8 T$ U* E0 N
; ]' v( S$ i4 c0 vck = Cos[agk];(*列表求各铺层角度余弦*)( w1 \9 N* G; i* {) z
sk = Sin[agk];(*列表求各铺层角度正弦*)
8 v" V8 N6 H0 q, ls11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +# F& e7 G; n6 T) v; d
sk^4*Subscript[C, T] +
. n0 @- K. w T0 f# P ~5 h; Z9 T 4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)4 R: S. D4 f) _* o4 m: R
A11 = \!\(
( Z2 _! y' y6 n2 V+ I" m\*UnderoverscriptBox[\(\[Sum]\), \(k =
: k$ F% E7 x x" r 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*)* m. @' f" w6 t2 I
A21 = A11
* b( b4 Z( n; d; f; VA31 = (\!\(
( H! \" T! n' Y7 Y9 ?7 w\*UnderoverscriptBox[\(\[Sum]\), \(k =
, s1 O) K+ S4 |/ m, ` 1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*) y/ |1 v; e5 N
A41 = (\!\(
/ I" D& h' k8 j( g! {\*UnderoverscriptBox[\(\[Sum]\), \(k =
* E% r- g) V- C0 w/ O! C A nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)
! H9 p& h( `" N4 }
! H. {+ D1 j; o$ F1 I* v" @
, y" y9 ^4 h) T$ t) q8 P6 R! J' xPrint["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)$ v( u* L1 Y7 b# _5 d
D11 = \!\(
5 ^3 L. z* T7 j2 \ h6 p3 f\*UnderoverscriptBox[\(\[Sum]\), \(k = ! G$ L) [7 O, i' |9 L- K" M
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
0 z0 P2 l, h6 [7 V% K! ?# t\*FractionBox[\(t^3\), \(12\)])\)\)
" g0 }; \5 A! P8 z4 F/ ~2 b8 x. uD21 = D111 D8 K5 [$ w( `' X" @) v6 P
D31 = \!\(, Q2 h/ m& U+ i, l/ L) J: s
\*UnderoverscriptBox[\(\[Sum]\), \(k = 9 b0 U' G( ?% w+ X. j
1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*
( {/ E* W, o4 T3 c* p; ^\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*). J$ t T# P( y1 R
D41 = \!\(
5 x- T. K6 L. I# G\*UnderoverscriptBox[\(\[Sum]\), \(k =
' o" W3 c: y$ g! q1 E; s# |* V @1 A) b nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
* {5 _" i, K4 v. C; h8 D\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)
" K6 ~ @+ S1 Bk1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \5 `9 f* H* O7 }: h
3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;( o+ H* U) `6 z
a1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(
1 _. ]; N q+ i/ ]6 e+ Y' W7 ` DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(
! ~/ B5 K) j; t* j DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);
" E( G/ S, ?8 V; C4 j7 B( U9 q& x+ v" q\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \0 u/ u! T/ K7 m; u( @- |+ b
= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];$ R* z% S2 j" g0 b/ G
b1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \( D& c. k4 q& N- h, O
1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \' P- [5 ?" x" y/ y) s
Subscript[l, 2]/Subscript[l, 4];0 V* Y. I( c: h
DD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);
1 c5 U; h! C9 R- d; Z5 QDD4 = D41/(A11*h^2);- q; h/ X1 ?1 k1 u( P! h, q
r11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[
8 C2 W5 `+ v" A! S2 x$ r" R G a2*\[Omega]^2, (4)^-1]; r13 = Power[
9 X: _0 F, [ h3 ~ a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];" p5 q1 e* d* E- r* _2 j
BB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},2 O7 W, ?, Y, b# l8 h
{0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},& `1 X% @& M W
{0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0, 8 Y) _6 G. h b# ? a: x) N
Sin[r12], 0, 0},9 D3 i/ N. ?* l* H
{0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0,
1 m7 |! ^7 F# g& k' \9 i2 e8 X/ T2 f Cos[r12], 0, 0},
4 |% G! I/ y# b+ y \/ u K5 f/ i {-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11], # t. d: T, Z+ X( n. W2 o
0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,4 E9 k, k( J* B8 u
-(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0, & V- A4 g1 G9 ~- i
0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11],
" q0 m+ O2 ]2 U! o- S4 f" {4 Z 0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*( w o7 k, e8 c+ K
DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},6 S* ~% M; H( }7 w3 M
{-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0, 9 I3 Z- X) i+ s: a) {* v
0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11],
% V: R T6 ]" A* C3 L 0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*8 B. l! K- s; d% b
DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,. p' N6 M- U: D6 D3 @+ t- b
(r11)^3*DD1*(\[Beta]1)^3*Cos[r11], 4 h2 E: o$ `3 @: j' X, Z( Z
0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3}," G) U6 o; G O6 u2 ?' r: p7 E
{0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*4 P9 _( S4 ~" Y6 S9 Q' D; K' h
Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14]," K2 ]" C5 S7 m$ f% B( f
0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*
' @0 T1 z( P! x( i' S9 ] Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,# S* A; r, O, ]$ Y; }' j
-(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*
% S0 U( s& |2 I V Cos[r14], 0, 0,3 O# C6 f8 q0 l9 O* a$ X5 _1 Y, j% |
-(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*
. L+ x! \1 H9 E: {7 S Sin[r14]},% y5 B6 A+ c/ s3 S. n1 R$ t
{0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*
0 _5 G2 n) J/ G" D* f; k9 f Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,8 M7 l; x! V0 ?0 J) K
(r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*% p1 D& ~) F# F: O+ \
Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],! Y' e& C+ ~2 ^
(r14)^3*DD4*(\[Beta]4)^3*Sin[r14], 5 F% h) d. z$ S; p
0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],
; [; a b! }9 Z -(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},3 B3 c5 o" u! s# f( x: L
{Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0, 3 N: ~& ?+ W2 c; W
Sin[r11], 0, 0, 0},& { u) a- o( k. c
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1, ! b$ R1 v8 C2 I- D
0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],2 d; g! E0 z& I5 f, Z0 y( |: t
0, -r13*b1},3 l3 B" Q) l8 F+ n# h1 D# a
{Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1,
% k3 q. }% \* T w' l) t Sin[r11], 0, 0, 0},6 p& l! L8 o# d `
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, 7 G( a6 l, ~' k
0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
6 t4 P7 ^2 O( i" E* a5 z& _ Y 0, 0, -r14*b2},& m4 K: i8 _2 b5 L' Q Y' T, X& D
{0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,
* v- i: Y8 [; p0 J' p# w; _5 a 0, -Sin[r13]},2 j, t3 k' j7 h0 Q
{0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0,
! B/ h3 ?- m# G r13*b3*Sin[r13],3 c8 G# r/ y3 ~% p8 v
0, 0, r12, -r13*b3*Cos[r13], 0},
. ]% E# v" H4 x4 R; n8 q {0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,
" j; a; l) M& @! y. N+ B 0, -Sin[r14]},
. y7 N) ]. j9 m) I2 M {0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0,
) l! G% u0 ?& i! h4 P r14*b4*Sin[r14],
5 B7 Z% G( Y- W 0, r12, 0, -r14*b4*Cos[r14]}}
/ x( [$ f% G, x7 f& g* @0 Kaa1 = Det[BB]
( @; E5 x/ O) a( }) {Plot[aa1, {\[Omega], -10, 10}]# p! q: x2 K3 x* s& @2 H
ss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]
0 n% b, @- l( X e; d, s2 g; D5 m$ S. r6 E0 k0 K. E2 O p. q
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