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本帖最后由 游龙游龙 于 2014-7-8 14:45 编辑 $ g% v2 E( f8 g( t" w& H
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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( S E& \, }! n& h5 t5 [2 V
行列式求不出,画图找不到根; m5 ]- b, L l; z7 s! l) A
(*定义材料常数*)
9 E+ Z: i9 S/ {. l% aSubscript[\[Nu], TL] = 0.25;! Z0 X5 T% `. k, H* p( M
Subscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)
) X- S+ w6 _. r @" @Subscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*), c2 b) x4 b h& C
Subscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)& l* B: k0 M q1 [9 o
Subscript[\[Nu], LT] = : E: Q) r# K0 n" j, P- `
Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];
2 ]& I9 F% Y- l8 ?& l4 p\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL]; [- c1 S% B7 U6 {9 H( Z# l5 N
Subscript[C, L] = Subscript[EE, L]/\[Mu];
5 w' _7 N9 o+ F: V) k* tSubscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];0 X' M' K) g3 _( J$ [+ w; e' V6 K
Subscript[C, T] = Subscript[EE, T]/\[Mu];9 R0 J% A/ q9 v
Subscript[C, LT] = Subscript[G, LT];& T$ \$ D e/ y9 S. i+ s, ^( }
(*脱层几何参数*)1 Z% B' _, i1 e1 v T$ V
\[Rho] = 1600;(*脱层密度*)4 u) t" @& E' W9 J C1 e
c = 0.06;(*阻尼*)
7 B" x1 b; ?+ A' Jt = 0.01;(*t每层厚度*)
! ~" p% H! A- H8 [, G( @h = 0.05;(*h为梁总厚度*)
* a, i6 J6 I! u! y% i# v0 Yl = 1;(*为梁总的长度*)1 k& [2 g% F; Q) Z7 g
Subscript[l, 1] = 0.3;(*为梁1区的长度*)* A( r2 |3 R8 g0 K
Subscript[l, 2] = 0.3;(*为梁2区的长度*)
/ P- U6 k6 M, Y. }: b0 WSubscript[l, 3] = 0.4;(*为梁3区的长度*)) U2 T" q; \5 g) ?9 e
Subscript[l, 4] = 0.4;(*为梁4区的长度*)
# ~9 R, E% P# t N/ B% |nn1 = h/t;(*nn1为总铺层厚度*)/ @/ @1 d% C" c7 w# ~
nn2 = 2.0;(*为上子铺层层数*)
! y6 |9 J. N; h. L" fnn3 = h/t - nn2;(*下子铺层层数*)
* q+ J& J9 x, p4 WSubscript[h, 3] = t*nn2;(*梁的上部子厚度*)0 P! x+ y8 @9 F- K1 B3 t; v
Subscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)( J& L( m- ]+ I1 K8 I8 c1 D
Subscript[h, 1] = h;(*梁1区的厚度*)
- f5 I" e% |3 b( OSubscript[h, 2] = h;(*梁2区的厚度*)! X; q+ D0 M" F" K+ P
(*求各单层刚度*)
( m. S- J$ `! z3 _agk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)8 M2 z$ z" o7 u Q( m
' W( B4 u8 w A, S/ K
5 ]7 B- ~5 i% s" F7 K% L8 x
ck = Cos[agk];(*列表求各铺层角度余弦*)
" D, y( H- ]2 u, ?" Wsk = Sin[agk];(*列表求各铺层角度正弦*)7 l, I' F0 v( l! s" q
s11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +
0 R. J, o0 k# O sk^4*Subscript[C, T] + ) u, j5 r$ r, \, D* o7 ?! P
4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)3 ]! s7 u1 _% D) `* m+ z
A11 = \!\(0 n8 t: M1 I6 q6 T
\*UnderoverscriptBox[\(\[Sum]\), \(k = 0 ]+ i4 B+ Z, J" X$ \
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*)
8 M# V% h9 Q8 bA21 = A11
$ I7 T/ Z. d2 [4 W2 } YA31 = (\!\(
6 s* A; X) E& E2 t1 k- e\*UnderoverscriptBox[\(\[Sum]\), \(k = & N9 a- K+ u [ V; v
1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)
0 v/ }- \! _$ v A0 e* LA41 = (\!\(
: R) S% }8 h: O# f: |\*UnderoverscriptBox[\(\[Sum]\), \(k = ! n9 f" P3 z4 {8 {( F+ y9 O7 g& ~
nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)& O! c) m) y$ |1 O; [1 J
# w0 P2 f. | o
7 `. N% h) }* y. U. Q) {Print["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)7 D7 r j3 f) p4 ~0 s& \
D11 = \!\( F& ~/ S4 S" s, z, u8 I. x
\*UnderoverscriptBox[\(\[Sum]\), \(k = , l) l7 c' w! x1 i" _; P5 n
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*/ p' E+ p8 D* u. |8 [' y, F9 }
\*FractionBox[\(t^3\), \(12\)])\)\)
* [' w% Q% u7 u. D3 {5 ]! e$ ED21 = D119 ~1 ^4 s) s0 }
D31 = \!\(
6 _1 ~7 a1 D0 H6 I% Z" w/ U\*UnderoverscriptBox[\(\[Sum]\), \(k = $ ^0 `3 [% ^ Y) x
1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*. C: K6 Q* \1 W2 g
\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)
% z( G- R, H# A. i5 X$ o) XD41 = \!\() G+ o6 F" p: Z, o/ X* @( e
\*UnderoverscriptBox[\(\[Sum]\), \(k = . e& i, r; r+ A2 Z
nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
0 A S& u; e! E9 t\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)/ V7 y, N5 g; P, H- Y: p0 n0 m
k1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \
* D) v% N$ D) ?3 [7 G3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;8 o: L$ J6 i4 @% T& O
a1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(- g4 ~% { z& m
DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(" p3 i+ J0 f" X( r! C4 W
DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);
, t# e8 k/ S$ o* c2 | R3 J: Q7 k, Z\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \9 k1 C6 N8 L) W% V
= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];
- ]& Q3 U( T1 [( Zb1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \
+ ~/ b" Z9 T0 d+ m1 k8 T5 M) k1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \
7 H* {, y1 [$ s/ ^% A2 ySubscript[l, 2]/Subscript[l, 4];# \4 R7 J% D" [6 |0 F; t
DD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);0 a' X! M! E/ \2 W) A6 @
DD4 = D41/(A11*h^2);
5 p" g* s4 n" o4 R0 W1 i) ^r11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[
% s9 i9 s. V% H a2*\[Omega]^2, (4)^-1]; r13 = Power[
$ S# @- ^; L S& C" ` a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];
! _/ m8 z/ o8 o& ]9 XBB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},8 W. ^, z4 G% i7 F# y+ T
{0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},; H# m$ p2 r; o& K
{0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0,
3 L1 A5 S6 f" E) F Sin[r12], 0, 0},. S( D, F, e4 n6 t( g% C
{0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0,
5 |$ |" K% H+ b. |$ c* L! r Cos[r12], 0, 0},
9 b" Y; q2 Q O' o0 S6 a5 I {-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11], ( s) o1 v7 S. f6 f& i: B
0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,/ [% [0 U$ b5 d. Z. t8 t
-(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0, ; K8 A% S7 `. u3 _
0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11],
, G; w$ V4 K8 e! m6 y. D* W& Y+ } 0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*
; g- o3 o# u j( J; t$ X4 Q DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},) D7 i: a& Y. ]5 K% X; k8 o+ ?
{-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0, " n1 H4 n/ G h& x8 B
0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11], - r0 C/ B( e, t# i$ c3 @
0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*
. s Q) J7 U: h" O- B, Z DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,1 ]) d7 p* S* J g9 U" g
(r11)^3*DD1*(\[Beta]1)^3*Cos[r11], ! N8 A. R; ~, {7 X0 ~& y" J- U
0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3},
& W& j4 w, p- _; S7 H# b/ c* W {0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*
" A- M) { t5 h+ M6 i) e% i2 w Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],
8 e7 L& X; V( _- {9 T- S& v 0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*1 _- X) |: H9 w; B) U5 f* e. s6 O
Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,
" |8 b8 E4 L; g3 G" }4 _ -(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*
3 @6 y2 m5 b8 ?, I Cos[r14], 0, 0,0 \! z# q N+ ?( L& U7 n# S6 l- S% w0 j
-(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*
' A# z; B( D. D( _9 C( ~; G" | Sin[r14]},
; f) `8 p( |1 h: m {0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*
1 w3 n! a3 [7 @- ~& ?) V Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,
" ?, z$ k% W, Z2 k0 y0 ?! @; a (r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*( Y3 f; C9 |0 D% F2 Z
Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],0 D( D0 z" M; g; j! c8 G
(r14)^3*DD4*(\[Beta]4)^3*Sin[r14], , Y6 g4 B+ }: ~% \0 q) O. c
0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],
+ Y- }) O, }4 A- X3 p# U -(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},
5 X6 j+ ]. N; c* p, N {Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0,
; t1 ^2 { W4 r: O1 k: N Sin[r11], 0, 0, 0},
: ?! S" T. `# V6 m8 J {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1, : Q) w( D/ T2 ^# o1 z# T& `3 Z9 g b( C
0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],: h$ |3 _8 ~: H, L( T0 o
0, -r13*b1},4 x2 ^) s r2 k; e; X9 G% [$ _, d7 u9 c
{Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1,
4 W! i. }7 A: L' M" F7 B# A- I8 a Sin[r11], 0, 0, 0},% r2 v, k% ]; [* o
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0,
& u! @/ E2 t- h6 y8 m( D# B4 T 0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
0 N% i" G0 V m, E( ~+ }2 s 0, 0, -r14*b2},$ c& Z& G6 K, f9 j8 M/ K
{0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,
; B8 n' E# r! x5 e 0, -Sin[r13]},
" K1 w8 `- }% M {0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0,
5 D' u$ o/ Q1 t: g8 ]0 f r13*b3*Sin[r13],' r0 ^; U( h- c3 v+ ?: @7 m- }
0, 0, r12, -r13*b3*Cos[r13], 0},
! { N1 U9 i& u! ^1 w7 R0 b {0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,
, A* ~# ?9 p! }5 p 0, -Sin[r14]},
. v" r/ v0 X" w5 b {0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0,
; H; e4 y' b! b3 P( G r14*b4*Sin[r14],
7 G9 D9 l r& F1 d 0, r12, 0, -r14*b4*Cos[r14]}}2 @- x' t6 R' u1 W4 `( m3 Y
aa1 = Det[BB]
0 I. W7 o0 H# I) E0 I( o! ]Plot[aa1, {\[Omega], -10, 10}]
" o6 f' j$ L, d9 z& ?2 xss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]) j& o, m" v, P) [9 I4 ?- z& x* |. G
0 @0 x# H/ ]9 m& | j
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