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本帖最后由 游龙游龙 于 2014-7-8 14:45 编辑 3 v+ B4 ~' S$ x
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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
w) r6 M; R5 Y' n) q行列式求不出,画图找不到根8 d7 a0 p* \' M
(*定义材料常数*)
9 N% b( M4 P* Z) `Subscript[\[Nu], TL] = 0.25;3 S- O$ S& G( O" }, E. D" }$ u: M2 J! A
Subscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)0 w" B& |4 v& }, Y! v+ p
Subscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)0 l5 n5 ^2 x7 \
Subscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)
& @# d6 j3 w/ T8 H$ cSubscript[\[Nu], LT] =
8 s0 s# l2 Y: k0 v/ q/ D5 I, N Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];- H( d. W3 n2 E7 X8 B3 F( z
\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];1 e, B* E4 }( Y, h8 `) Z0 d
Subscript[C, L] = Subscript[EE, L]/\[Mu];& U5 K! A& E( J# l' F/ Y' p; g
Subscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];
. V& d( Y! `0 {: o& ]# s/ e0 ?, t# `Subscript[C, T] = Subscript[EE, T]/\[Mu];
3 n7 a4 ]- d5 P2 H, n. o4 [) u3 J& c( d6 bSubscript[C, LT] = Subscript[G, LT];
7 o8 ~) [, N% k# n5 @( ](*脱层几何参数*)
& r) V* C( c$ K* U8 m4 p( I\[Rho] = 1600;(*脱层密度*)
0 d8 a" h; M+ D5 R6 T& Tc = 0.06;(*阻尼*). |. w; r1 X p1 @
t = 0.01;(*t每层厚度*)
, N# e1 w& C7 F Ah = 0.05;(*h为梁总厚度*)
# r: k7 Q3 L! Y6 Dl = 1;(*为梁总的长度*)
9 K( D" s1 P/ T& w8 P1 [Subscript[l, 1] = 0.3;(*为梁1区的长度*)
/ m. U9 N) A4 N7 u/ X6 KSubscript[l, 2] = 0.3;(*为梁2区的长度*)( U5 s, A: m' A: J z' k G+ S: |/ J
Subscript[l, 3] = 0.4;(*为梁3区的长度*)
* o& f2 |: o, m# ]& \0 ASubscript[l, 4] = 0.4;(*为梁4区的长度*): t! v) I% t% c, o& E5 Z7 }2 Z
nn1 = h/t;(*nn1为总铺层厚度*)( m( v# O- B1 k5 n; G, G6 W
nn2 = 2.0;(*为上子铺层层数*)0 v9 n' [& M7 _) z! M
nn3 = h/t - nn2;(*下子铺层层数*)
! T2 T' R' D" NSubscript[h, 3] = t*nn2;(*梁的上部子厚度*)- `4 G& Y* `7 P2 F ^. r! R
Subscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*), O# {2 _/ i/ M! @0 N! j0 T2 T
Subscript[h, 1] = h;(*梁1区的厚度*)
% F# D& j L( C' _8 bSubscript[h, 2] = h;(*梁2区的厚度*)
4 n0 A. m% n9 ?0 H. y, l(*求各单层刚度*)
" I* H( l1 W: S; lagk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)* o* R2 V# a; F
2 y8 R2 M' T- L6 e* K
8 f# m. k( i2 {; }; L( k- \3 w
ck = Cos[agk];(*列表求各铺层角度余弦*)
) a5 C! U9 U0 `" k! k, ^3 Y$ a+ Xsk = Sin[agk];(*列表求各铺层角度正弦*)
Z; t. G( H3 \* A$ g$ k/ Zs11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +3 [3 L* @2 G: W
sk^4*Subscript[C, T] +
- W E5 O) f x6 ~; e 4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)' I- n% H* N! q y
A11 = \!\(
) e0 W9 l* O0 x- [0 w, ~\*UnderoverscriptBox[\(\[Sum]\), \(k =
5 @4 P8 \% p& L' L# x 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*)
@; x$ {+ V5 n7 XA21 = A11
: v0 n9 S1 O% f& f9 c, |A31 = (\!\(
9 m6 G, B h8 A. j$ T\*UnderoverscriptBox[\(\[Sum]\), \(k =
8 z7 c' y6 _3 C1 G+ T7 G" b8 M 1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)
( Y) \" m! W4 Y; U! J2 G" A& ?A41 = (\!\(( `; E! M( P% }+ ^* c% \) @
\*UnderoverscriptBox[\(\[Sum]\), \(k =
: N1 W# U# g4 g- E- j3 D) j+ f nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)
9 N! s3 M- z$ q6 _( W) Y: T3 v2 A( L. U8 g! H2 z: p# P2 v
+ L* ~ B. _# g3 N% H3 x/ m2 JPrint["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)* q# t0 G9 X6 n( q3 V
D11 = \!\(
! S! e$ i2 ]# T7 _4 V\*UnderoverscriptBox[\(\[Sum]\), \(k =
; n; S8 r* L2 s- I 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*0 G$ [0 U% s: U8 L' D& o% r
\*FractionBox[\(t^3\), \(12\)])\)\)
$ E! G# D2 u+ A- r1 ND21 = D11& g( W9 b& l7 F$ F9 z
D31 = \!\(
* `% T, ^7 r v& k6 Z\*UnderoverscriptBox[\(\[Sum]\), \(k = - w4 W8 A- _' Z* \# p
1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*. F9 x6 E' N* z( i
\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)
6 z$ o' ~ _* | [) SD41 = \!\(
( e% ^% i1 p+ v) Z3 b\*UnderoverscriptBox[\(\[Sum]\), \(k = . D4 C" h( [; X& {
nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*! p! \# Z p& I& y/ S, I+ j
\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)" C5 t" u4 ?6 F# o1 B( D
k1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \
$ [# [7 o2 @* W# |1 a8 y3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;
: x* o, s1 X; d: Fa1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(
2 F( \& |7 l; x* ?# n DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(
5 c+ C% E0 a8 d( l9 q2 u DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);" Z. t3 ~: ]. [; O
\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \
6 R- P2 s' z: m8 @/ u) W( p= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];/ _9 t: i3 Y( @: C
b1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \! F( r B; Y3 G! m% J" a8 c
1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \
1 R) ~2 @6 k- z7 l9 lSubscript[l, 2]/Subscript[l, 4];
( u3 B5 l- s! j r tDD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);" O! q0 F( m4 O
DD4 = D41/(A11*h^2);
7 N8 e& Q7 C- B0 ^) vr11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[
+ v1 n/ Y b7 O) c a2*\[Omega]^2, (4)^-1]; r13 = Power[ o% ]8 ]* q3 ~4 P
a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];+ m. V& Q% G! h
BB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},
1 q: Z8 Q$ \! r6 z5 ]- w- l6 v8 ^ {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},$ H' \2 I K$ P7 D) m1 j
{0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0,
/ W4 f5 y! d8 c+ e e, q Sin[r12], 0, 0},
8 u; h, U% J* w1 y {0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0,
3 d5 ?- U% K( B, D) n2 N$ C2 a Cos[r12], 0, 0},1 [) F1 ]& s$ x; E
{-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11],
9 D# O' t/ @6 A3 }& n0 a$ \ 0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,
0 e; V8 B$ q; x4 c5 f* l -(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0, 5 _% K9 }5 q1 g! u9 D7 w
0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11], ; B0 V7 F" N# W; H! V8 ?/ |# `- N
0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*1 l+ d, o- {% H# y6 P M
DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0}," a; T9 l0 ?3 D! Z+ |( s
{-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0,
& Z$ I! ]) t' s8 X; i4 U 0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11], . [1 W; M+ U- n4 {0 @- X8 a8 s' ?; o4 u
0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*/ p: N. W8 q8 w {
DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,
3 q5 o* Q, f7 [0 | (r11)^3*DD1*(\[Beta]1)^3*Cos[r11], 6 `! X7 J. U% S, s
0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3},
5 z3 }! G8 A2 |2 [1 _ {0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*
+ f0 R% q, ^1 O n Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],8 F2 R I* Q/ e/ o, U- L$ L& U
0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*7 k: t2 ]+ J: r: ~5 w" S; F7 v& k0 H
Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,
" Z% x! L5 R% F# Q# {, N3 q -(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*
7 E6 {; c1 _, z, g N- d6 j Cos[r14], 0, 0,
; e, }* _9 }0 O M) @9 f -(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*& K- @" u5 H" e8 U& W8 ~
Sin[r14]},
) y. k) _$ D* U2 x; P {0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*
- _# X* f9 w0 E1 u/ D Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,9 u7 U. L7 @7 J# O) U' x
(r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*
$ H9 T! Y4 u; F* z3 S' d Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],6 C5 z! b. n( V% o* |
(r14)^3*DD4*(\[Beta]4)^3*Sin[r14],
/ @8 P* K1 c" K; ?% J 0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],3 t' n% L3 k( |' [0 N
-(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},
# m8 ~/ B2 J1 I6 l; T {Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0,
; F3 {. i. T8 {6 x9 h9 S, @: V Sin[r11], 0, 0, 0},1 o- s p; p2 T7 M) s/ [
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1,
8 E3 c) L2 ~7 G, V- K' ]% t 0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
; [+ Z0 y7 r i 0, -r13*b1},
5 x( o- p; J" @5 D5 x {Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1, 0 O" u, G! b" o4 R
Sin[r11], 0, 0, 0},
9 |' l9 q! Z, X3 G& {1 v! x {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0,
" o6 Z; a$ _5 g3 _$ i 0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
! k( ?( n1 v( `1 n- i" X+ ~$ N+ y 0, 0, -r14*b2},
! y5 W% U J4 J* J {0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,
9 Q: {/ |* n) [) o$ T 0, -Sin[r13]},
. n2 L# X* Y# {* e4 m- g% S {0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0, ( i; M$ Z- b$ n G6 f9 x4 b
r13*b3*Sin[r13],
9 L- {+ j6 w% x$ H: ]- ~ 0, 0, r12, -r13*b3*Cos[r13], 0},
* B0 n: a3 j. R. u3 Q {0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,
+ b. J( v9 @' h( h* C: d 0, -Sin[r14]},
3 m1 X2 L$ }% {6 w1 F2 r) L {0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0,
3 E5 Y5 R2 [6 Z. \! o r14*b4*Sin[r14],; W4 _/ w+ a3 ~0 J5 q, B ` a9 w5 R J
0, r12, 0, -r14*b4*Cos[r14]}}4 `( L! |( E+ c& h: Z1 i
aa1 = Det[BB]
6 k7 H/ x3 K$ F/ N4 X: `$ QPlot[aa1, {\[Omega], -10, 10}] i6 p) G& u% b1 D1 s
ss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]
( f2 F- ]+ `) ^
4 O7 q8 D$ u: M" P( Z5 \ |
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