- 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
- F" S2 ~/ K/ {6 a; G
2 F4 Q7 x, Q8 x2 g/ \ J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
" X6 c! q& ]7 U- z9 L行列式求不出,画图找不到根
9 ?1 w5 L- N/ _3 g3 d# h2 H4 t(*定义材料常数*)
5 ]; U& F) }) n# T7 aSubscript[\[Nu], TL] = 0.25;+ E+ u3 C E! \ E
Subscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)
( Q9 Y# T% h$ l; l; `+ R. \Subscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)
7 I( i3 O% K2 y% C/ TSubscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)
9 O0 C2 c! q) V+ I B4 tSubscript[\[Nu], LT] = 7 {# T% Y i- E$ {. ?( q1 t
Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];
. F$ b/ |" N2 }7 N7 e. u# n; A/ @\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];& j3 M. W4 ]+ \. k. Y/ G; _( L( V
Subscript[C, L] = Subscript[EE, L]/\[Mu];
2 A o5 C( g( i ^" tSubscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];
) I2 J9 m) Z) X9 B) qSubscript[C, T] = Subscript[EE, T]/\[Mu];8 X: H! Q8 q% M' d- h' F# n9 ]
Subscript[C, LT] = Subscript[G, LT];
: @1 t& C" \4 M% j- \' q( y(*脱层几何参数*)9 U$ l: `% b1 k8 o
\[Rho] = 1600;(*脱层密度*)( o: K8 u) `% i; u3 L! ]
c = 0.06;(*阻尼*)0 a, v7 E2 r. O' {1 s/ R) r+ R
t = 0.01;(*t每层厚度*) E: M- C: X# O: I: _: q
h = 0.05;(*h为梁总厚度*). |6 |/ `! ]+ S8 U( g
l = 1;(*为梁总的长度*)' n' D7 R1 \+ A3 P2 L0 M2 M
Subscript[l, 1] = 0.3;(*为梁1区的长度*)& N6 k( m4 }# a7 r1 v$ p
Subscript[l, 2] = 0.3;(*为梁2区的长度*)
/ W) {1 b$ P. k2 S$ z/ dSubscript[l, 3] = 0.4;(*为梁3区的长度*)) R, g) O0 k2 E4 `
Subscript[l, 4] = 0.4;(*为梁4区的长度*)) n4 @" y K( p
nn1 = h/t;(*nn1为总铺层厚度*)
" w/ H* ]1 D i, U: R- a, mnn2 = 2.0;(*为上子铺层层数*). t8 g$ T% U9 D7 ~3 g
nn3 = h/t - nn2;(*下子铺层层数*)# I1 P* X/ H1 q4 N0 s W
Subscript[h, 3] = t*nn2;(*梁的上部子厚度*). {4 [0 H6 J/ ]2 H5 d
Subscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)
: s+ S6 {& d' o9 jSubscript[h, 1] = h;(*梁1区的厚度*)/ J* J# H' b Y1 |" r+ O% ~( w
Subscript[h, 2] = h;(*梁2区的厚度*)
' i! q5 j; l3 d$ v' X3 w(*求各单层刚度*)# ^9 @3 @8 G$ J
agk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)) r$ m( E6 O6 e w. s9 U7 R- _6 z
O! g7 @" n( N( ?" h3 ]( W4 Y& O/ Y& z0 J3 G7 \
ck = Cos[agk];(*列表求各铺层角度余弦*)3 W3 O5 J- Z; w* e a5 y y
sk = Sin[agk];(*列表求各铺层角度正弦*)4 a- S2 P7 f5 a' z7 d
s11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +
1 }/ {- K) ^, T P+ u/ r9 p* y sk^4*Subscript[C, T] +
. ]4 g7 p7 M: |% [6 ]* i. F1 x 4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)
/ U& E8 X5 W. y0 tA11 = \!\(
2 ?7 V/ \9 G6 j* y3 U( _3 e, J\*UnderoverscriptBox[\(\[Sum]\), \(k =
9 U& c* A! F. d- o* {3 o# H 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*). l5 o" b& a7 c" T
A21 = A113 Q5 e0 N1 V1 G2 }8 ~7 T& K% w7 B( W
A31 = (\!\(
0 z* a& C5 }4 u" M4 J' F\*UnderoverscriptBox[\(\[Sum]\), \(k = 4 y+ e5 w( `: b3 _$ T
1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)
" h* V1 Y& U8 @5 Y. t" J# OA41 = (\!\(
: S |6 ?* Z. m/ e& v\*UnderoverscriptBox[\(\[Sum]\), \(k =
. j# e) P) R, G; D. q3 p# r nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)4 [8 x5 ^% h3 J, H/ ]! x
& I. p, w* M# j! M9 L9 p2 b! i* y
) \" \& H2 r. p. v4 E5 qPrint["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)7 R- t% f3 {% y6 m+ [$ @
D11 = \!\( H- H+ z3 K; Q' u& A
\*UnderoverscriptBox[\(\[Sum]\), \(k =
) L6 V t, ^; ?) Q1 y' l+ ^ 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*% v# ~ { R* w& s
\*FractionBox[\(t^3\), \(12\)])\)\)
: N1 t9 O6 L9 |. B6 MD21 = D114 ]+ o1 g. i$ O) c. P; @, m# p$ k
D31 = \!\(
, I3 N* Y0 J/ F& ^* F: E\*UnderoverscriptBox[\(\[Sum]\), \(k =
7 {; T8 W2 e1 H: L: D' b( d, ^ 1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*2 U5 i& _; L( B
\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)
4 d5 d( P! u. lD41 = \!\(
! Y) ^- r8 J) S# M: v\*UnderoverscriptBox[\(\[Sum]\), \(k =
9 H( E( a& j# U1 z- ^ nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*, Z( o; ]1 ^! t' a! f$ K& D
\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)
& V) b4 W0 |9 h& l0 hk1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \
0 j( b( G3 K$ M2 d: `6 @3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;
. J" {7 i8 n6 x; H8 \; n# ca1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(
* Y1 b# ]9 ?( H$ Q DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(
% b" c$ ]' Y& t; }& g. w. a, x DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);
" M0 q, w4 \, z/ j2 r2 N\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \
- O) m5 y% N+ k1 F= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];
* E7 i! Q1 ]8 \b1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \/ d6 ~3 G0 D6 A ?9 w
1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \
: l" d' \0 X% }& [* t% B5 Y1 T9 jSubscript[l, 2]/Subscript[l, 4]; ~3 Q' Z6 s* u( x* O- ^. v
DD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);
" e" H: ^% L. S$ d8 o! b' n1 @DD4 = D41/(A11*h^2);
# {2 F, Q( a; k7 I5 f$ W% G9 wr11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[2 `$ m" G" `7 Y, l. u6 K- C' d7 U
a2*\[Omega]^2, (4)^-1]; r13 = Power[
. l) B# C. L) a+ o8 Y a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];6 M- }3 z: `( Z: o. U
BB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},
{7 Y5 j- b3 }! @. y* \ {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},7 N7 h" L5 F+ P w6 Q8 J
{0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0,
6 V% K$ S; A, | Sin[r12], 0, 0},
" ^: L% r- M9 X1 s$ t) d& m {0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0, ( L6 h0 J; p, m4 B6 V0 p- X
Cos[r12], 0, 0}, B' g& [) r% F9 J
{-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11],
/ M4 q3 l& ?4 d& r T 0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,
. e* n; S3 ^' O: }! V* T -(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0, " i) Y0 }0 e( _4 V3 Q1 a% w7 a1 K
0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11], " U1 S, J$ j# r" a! z T* @
0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*
& @% s2 L# W8 u. Z/ y7 T4 B5 V DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},+ k& I9 q0 J% p+ }4 q; m
{-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0, 1 o' N4 G Z! r4 Z
0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11], 8 T+ }1 Y1 g8 L7 z/ M2 U# @
0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*- I5 e% [) ~4 X/ E
DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,( J* v0 ~' K/ W, s! m
(r11)^3*DD1*(\[Beta]1)^3*Cos[r11],
- B3 p0 B: u a w0 z% [ 0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3}," q6 r# H. L/ f
{0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*
% O& Z3 s/ z( w& |; d1 S Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],
, j2 A: Q" m, R7 O3 l 0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*
- S+ `+ r" {' Z9 g' N Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,
& t7 B" j; S" d2 g: p5 y( W7 w! z' h -(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*) h) w4 T6 ~' u2 Y6 \
Cos[r14], 0, 0,
8 P1 N7 @# X" V; y8 t -(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*: G2 k& Z; g; s2 Q
Sin[r14]},- f. f j, k$ G" r! E2 ]: Q" H, v9 ^& I
{0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*: A. v7 t) Z2 P1 M, h5 C
Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,
/ ^$ o6 j6 j0 z! Q1 j (r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3** K# v$ N& e; Z. K4 D& n
Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],
/ _7 G& ]( S* L: _ (r14)^3*DD4*(\[Beta]4)^3*Sin[r14], / ^4 A$ t# l( z- r8 X7 U, I/ b( K
0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],
; M! K* ]2 M5 h6 B; M+ d -(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},
$ g5 E. y6 X4 N6 U {Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0,
2 u1 Y5 P2 x: B- ^/ y Sin[r11], 0, 0, 0},! N; K N& Y. s$ D- k1 k
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1,
i2 R& N/ o( P; i6 w0 B 0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
" v# @5 `! v0 C1 M+ i9 A; f 0, -r13*b1},, U: q1 e5 y' b, w5 X+ F2 X
{Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1,
$ `* g5 r4 ~/ E) ?+ e, b. e4 D Sin[r11], 0, 0, 0},/ N& ~0 V6 I% T7 @, e% k
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, 8 `% @9 b% o& _/ \/ I) x
0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],: P7 F# e9 S* d1 I" `
0, 0, -r14*b2},
e, O0 c' u' M9 X( f {0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,! n. V3 O# u7 y! a1 k2 x
0, -Sin[r13]},8 F; I1 u4 y& j* @1 l
{0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0, 2 u; Z( m. x8 S6 t; p2 A7 X
r13*b3*Sin[r13],
1 c9 O4 }+ @6 j! a6 ^ 0, 0, r12, -r13*b3*Cos[r13], 0},
7 v: G7 H( F: t0 q {0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,
$ a1 R! F9 W( x7 L 0, -Sin[r14]},+ @. V# M2 w( \, |4 ?
{0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0,
7 _, c" |1 e7 _. ?, {' u& [ r14*b4*Sin[r14],8 y3 q1 Y; d' U" r& p5 Q( E9 K
0, r12, 0, -r14*b4*Cos[r14]}}
- Q- Z3 T, i8 Q& Baa1 = Det[BB]% }, H! G8 ~5 ~8 G6 v
Plot[aa1, {\[Omega], -10, 10}]4 ]+ |+ d, v& _; p# e
ss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]
" t+ X9 L" L, `- J, B0 ~: q. u6 T" O+ m) i7 l1 ?) |. W
|
zan
|