- 在线时间
- 3 小时
- 最后登录
- 2014-7-16
- 注册时间
- 2014-7-7
- 听众数
- 2
- 收听数
- 0
- 能力
- 0 分
- 体力
- 7 点
- 威望
- 0 点
- 阅读权限
- 10
- 积分
- 3
- 相册
- 0
- 日志
- 0
- 记录
- 0
- 帖子
- 1
- 主题
- 0
- 精华
- 0
- 分享
- 0
- 好友
- 3
升级   60% 该用户从未签到 - 自我介绍
- 游龙
 |
本帖最后由 游龙游龙 于 2014-7-8 14:45 编辑 5 C' R3 {) o6 `
- @" G# f- r+ {- n
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3 J, [' O* a) H" T0 Y
行列式求不出,画图找不到根
9 _/ ]' i0 O' h f( P7 b(*定义材料常数*)2 I0 m( k- s/ o3 y
Subscript[\[Nu], TL] = 0.25;5 ~6 D8 Q; K0 {
Subscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)2 `) R" U9 p3 @; \9 y3 A% ?" k
Subscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)
- U7 T4 m: P. `6 w* pSubscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)5 B( {' [2 y+ b% e8 y' \: y* e
Subscript[\[Nu], LT] =
! Q* Z3 j, x+ g Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];* |; u5 C8 E$ {# X6 `
\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];
5 h- y3 i0 u$ X4 a, p/ nSubscript[C, L] = Subscript[EE, L]/\[Mu];
7 k# f- L+ N- e, D- w! @! X$ J% P& CSubscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];
: o8 O9 F, A& ~; ]Subscript[C, T] = Subscript[EE, T]/\[Mu];
5 I _/ c9 H+ y1 g: p: dSubscript[C, LT] = Subscript[G, LT];% Z8 h: j% |3 `
(*脱层几何参数*)
H+ c1 w, H/ {$ L1 j5 i0 P\[Rho] = 1600;(*脱层密度*)+ w& g, g" b2 p
c = 0.06;(*阻尼*)
) k0 B! W) Q" B8 X# C! mt = 0.01;(*t每层厚度*)
! t) U+ N2 f7 i& Z( r2 Fh = 0.05;(*h为梁总厚度*)3 m# M, F1 @3 a9 a
l = 1;(*为梁总的长度*)
% Q8 Z+ Y# Q$ ^Subscript[l, 1] = 0.3;(*为梁1区的长度*)
1 J( v( [( c5 z1 Z1 @Subscript[l, 2] = 0.3;(*为梁2区的长度*)
) v9 Z$ n1 B1 ~, ]) ESubscript[l, 3] = 0.4;(*为梁3区的长度*)
5 e( d7 Z+ c. O& G2 l6 j* PSubscript[l, 4] = 0.4;(*为梁4区的长度*). ~ ]3 c4 V' p" w1 n% N6 v
nn1 = h/t;(*nn1为总铺层厚度*)7 }: R) ~6 w9 p7 `
nn2 = 2.0;(*为上子铺层层数*)$ e9 u9 M/ @ d- b$ c! b8 D
nn3 = h/t - nn2;(*下子铺层层数*)* q2 b. X1 h1 U" |' ]0 m
Subscript[h, 3] = t*nn2;(*梁的上部子厚度*)# g9 p3 }" O! L( d
Subscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)3 F& V, @6 s, t6 h7 C
Subscript[h, 1] = h;(*梁1区的厚度*)
$ O; m" `3 p4 |, t& VSubscript[h, 2] = h;(*梁2区的厚度*); E7 E7 U9 [3 F8 X2 H
(*求各单层刚度*)
4 \1 n) S# U2 Y" ?/ qagk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)( a! y* B1 k8 G( q' c1 }
7 m+ o" _+ {8 b+ i
. g. i4 K6 p& j* h2 s6 [3 Uck = Cos[agk];(*列表求各铺层角度余弦*)
5 J& _; _. z+ R0 ask = Sin[agk];(*列表求各铺层角度正弦*)
+ M4 P1 Z& M9 k! Y9 }& Ls11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +. u- J) y4 C6 I; d0 j7 p! v
sk^4*Subscript[C, T] + / O$ U$ D8 g* F E9 b9 f* [0 i
4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)
4 K2 t6 o! `3 f) _( ?- f, mA11 = \!\(! {. x, G. T: E+ t
\*UnderoverscriptBox[\(\[Sum]\), \(k =
e/ h" a( G) X% y7 P5 b 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*), N$ U$ T8 I2 t' }* z
A21 = A11
; u6 S4 Q5 {- }# C- @ {A31 = (\!\(1 ^& \+ G1 Z2 F, Y+ w: T4 t w
\*UnderoverscriptBox[\(\[Sum]\), \(k =
8 M3 n6 U3 P# |- b5 ^ 1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)
4 m: Q/ A! k8 h5 CA41 = (\!\(
9 L% q# T& D3 ^( p3 y' n4 X\*UnderoverscriptBox[\(\[Sum]\), \(k =
0 A$ S1 i8 m1 a) e nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)
0 U& F0 h; | z9 T& `! F* l5 e( s/ \" D8 ^ N' b* ~8 m6 o( v
' M& M. d- Z H$ k$ k8 J u+ IPrint["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)
' t% C2 e1 H8 Y5 t+ y: Z$ gD11 = \!\(1 C2 E: I ~( i6 D( z4 l) V
\*UnderoverscriptBox[\(\[Sum]\), \(k = 3 z4 ]# J$ F4 I' w; j
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
( @) o% Q3 n/ ^; Q) ~\*FractionBox[\(t^3\), \(12\)])\)\)8 |% ~4 g. w, c( l
D21 = D11* @$ Y" x& R1 u3 I5 n- q3 r o: x
D31 = \!\(
3 U- \$ G! i6 i1 y8 Z1 i! M1 }\*UnderoverscriptBox[\(\[Sum]\), \(k = $ y* ]8 p8 k, s, A$ x" f
1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*
2 g& c0 M# E0 |; B! {; [7 E' A- B7 p\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)/ y/ a! M8 s1 i
D41 = \!\(! l0 E7 H1 M: o
\*UnderoverscriptBox[\(\[Sum]\), \(k =
- l8 g- x( S# h& C' N9 @* V nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*+ R. J; I- Z6 g6 Q3 q
\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*). I# ~; H U( H
k1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \1 L7 }- o# q2 v! \( o
3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;
3 v. h4 \$ b4 X5 _/ E# t0 y; w; Va1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(
& y9 D! t& J. W$ O2 ?# u DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(
- ~1 x; E" D4 u; J' {: m" n DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);
: L( O6 Q: D$ [2 k! ]$ H) u" j5 O\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \& e8 x. d" z9 Z
= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];
. A3 c+ L6 Q5 d7 `+ q. Ab1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \/ B4 V* j. ]* t2 I
1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \. x, Z# Z! S) k7 L9 m' J7 ^- c
Subscript[l, 2]/Subscript[l, 4];- j) N3 ^7 T' _. v
DD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);9 f; n# B* O+ E1 X; M8 U
DD4 = D41/(A11*h^2);" u8 V/ v. C' Y- b, a
r11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[
; ^- s" `* I$ l. D9 n+ O a2*\[Omega]^2, (4)^-1]; r13 = Power[% O" s* _1 v9 U6 b$ D a9 e: ~2 U
a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];
, a! `9 U2 K$ bBB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},' p' X, J8 m) k, v2 h9 G1 L
{0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},
8 G ^' b$ S6 l+ K; v3 u, I6 h, _ {0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0, + {" N* j+ `3 r! E9 c
Sin[r12], 0, 0},3 Z" W% ?2 v- q/ R; ]6 n2 M" U+ [
{0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0, 7 x3 Y& I& q U# y& F
Cos[r12], 0, 0},
$ h* j4 v8 R% v2 h/ t3 Y {-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11], & i# J2 j3 B0 D+ l9 u
0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,
- f$ x# f2 J3 _+ m8 m8 N -(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0,
1 Q( B: ]/ L& w 0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11],
1 ]/ ^* G5 S! ?7 ?% V. E1 W 0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*
; B( c# w1 ] a3 c5 s4 m& [ DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},0 r1 j- P& K8 ^0 |
{-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0,
4 U$ t, l1 K$ P" p) ] f 0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11], ' B9 `3 g% \" j& I8 z
0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*
( T2 k# z$ q( F+ U2 G9 Y4 d DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,: f U z6 i$ v, |8 W7 ^9 \
(r11)^3*DD1*(\[Beta]1)^3*Cos[r11],
2 L: @/ P1 p+ I7 O% G0 f. p 0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3},( d( L% p) P: p _' A3 ~) X
{0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*4 _6 Y$ G6 w: \4 C! f
Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14], [# Y- q: R7 D7 L3 ?# y
0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*
" a- B8 y8 K3 E f* Q# {. W5 h" `; p! G: j Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,
4 w' E. F( t; x6 q4 {5 G -(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*% H8 ?% M, ]; K. k$ i
Cos[r14], 0, 0,
" @: T2 M' b$ @4 L -(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*# `2 }0 v6 u4 C" Z
Sin[r14]},5 ~+ W, O6 ^. ]- |8 T1 R
{0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*
) N T" z: |6 [, ] Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,
' v% L/ \3 m! I/ { (r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*4 e2 [- S+ z; c- F
Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],
, S, k( B3 l2 x+ h% y9 O (r14)^3*DD4*(\[Beta]4)^3*Sin[r14], 0 z s! g, J* y) K3 D Y
0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],
& }# Z/ _7 p# \ -(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},) U- v- s3 v! _2 ]
{Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0,
% q9 E9 T$ J: T$ ^ Sin[r11], 0, 0, 0},
2 C" r0 d6 M( d( c/ H {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1,
) ?' S# z2 P" N) v k& `. Z( ]8 T 0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
% P! p7 G7 i. B+ q. L+ B 0, -r13*b1},* f4 a$ K1 d# E4 N7 Y
{Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1, " H! S4 ~' F8 z3 W2 _
Sin[r11], 0, 0, 0},1 E" H" l- b" f! h: c# j
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0,
& M- |( m5 F3 ~% L7 |2 ^ 0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
! y. K% ?9 n9 e& v 0, 0, -r14*b2},
$ l" m0 t2 C4 N$ S {0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,
2 g$ l4 R- h9 E, r0 @2 Z 0, -Sin[r13]},/ d1 X- P: j% E! W6 y
{0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0, ( Y$ B; p3 H0 b; h* h
r13*b3*Sin[r13],% Q5 B1 B: @9 R0 e7 ~+ U
0, 0, r12, -r13*b3*Cos[r13], 0},. e$ v2 \* a: ?/ Y
{0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,
- p- j5 Z! ? _0 t8 l9 K8 C 0, -Sin[r14]},
) y/ B2 e0 A, f {0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0, 1 `; |1 N6 {8 L N7 f% w X2 X) q
r14*b4*Sin[r14],) c% y8 Z; a' W' `5 I8 j- D
0, r12, 0, -r14*b4*Cos[r14]}}) Y/ x) G, y0 V: N1 W1 v
aa1 = Det[BB]
0 i/ a. u b8 K/ X. ~Plot[aa1, {\[Omega], -10, 10}]
. I1 _) }$ Y" z$ G( s$ wss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]' Q+ |5 ~0 C9 r: ]& D
8 v/ A1 j/ x: I; B' |& x/ D7 T |
zan
|