- 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
' w, Z8 {+ C. t5 @' j' G3 t# I* x( ^0 B7 e2 x
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; N7 n' L( S( l
行列式求不出,画图找不到根
) }& s9 C3 G9 j7 u+ ]9 A(*定义材料常数*)+ W$ n, y; H% M2 u, f. q
Subscript[\[Nu], TL] = 0.25;4 R3 ^- U# y9 W& H9 q7 r
Subscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)' T: M/ V2 o' v- u) V6 ^) V7 M
Subscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)
: w% r% T4 r+ ASubscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)/ o4 x% }! D& t4 z- O8 i- A4 v
Subscript[\[Nu], LT] =
; P4 E# V" O/ v7 C Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];# W/ R- w9 |4 o8 D( \) {$ q9 c- P
\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];* S6 j: @2 ^, K- Z/ w
Subscript[C, L] = Subscript[EE, L]/\[Mu];% t) `; F; ^+ R; [+ u0 e
Subscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];0 B6 ^. p* q0 ?
Subscript[C, T] = Subscript[EE, T]/\[Mu];
, t( h% l! W' U |' KSubscript[C, LT] = Subscript[G, LT];7 D+ Z$ _3 u& ~4 ~% f8 F
(*脱层几何参数*)
9 U ~/ `" o0 g X0 o+ d\[Rho] = 1600;(*脱层密度*)
. i; d5 Y0 B5 t- Lc = 0.06;(*阻尼*)
9 Q' p, w3 V `- D$ Z! u5 s1 Nt = 0.01;(*t每层厚度*)
" H+ Z# Y2 w! f. [: ph = 0.05;(*h为梁总厚度*)6 x' m( [& a+ Z8 H+ v# Y
l = 1;(*为梁总的长度*)/ d; [5 i( K5 f( o; @( x K
Subscript[l, 1] = 0.3;(*为梁1区的长度*)
* \& {$ x) R0 G( o8 R) U* GSubscript[l, 2] = 0.3;(*为梁2区的长度*)8 Q, h& R* Z: _5 y
Subscript[l, 3] = 0.4;(*为梁3区的长度*)% d( l; M( b: s) b
Subscript[l, 4] = 0.4;(*为梁4区的长度*)" y- E; u1 l: W9 @1 ~
nn1 = h/t;(*nn1为总铺层厚度*)- N# n5 h& Y1 a. C2 R7 N, z
nn2 = 2.0;(*为上子铺层层数*)
0 ]8 _; V7 r4 ]! u0 Q$ s5 m6 Nnn3 = h/t - nn2;(*下子铺层层数*)' A6 K; ?# m5 ^
Subscript[h, 3] = t*nn2;(*梁的上部子厚度*)0 d: r( `. N" P2 `/ S
Subscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)
+ g1 l* Q \" ?0 ^Subscript[h, 1] = h;(*梁1区的厚度*)+ o- @) r6 p: s$ q
Subscript[h, 2] = h;(*梁2区的厚度*)
f; P B/ j& k* b! \% p: w4 H9 S(*求各单层刚度*)% U& ?: B5 n2 j1 t8 ^6 i9 Z
agk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)
8 q% C: f+ q# M* J; s- I" [. k* v6 D. a9 q6 O' R+ `
7 f) T# X" t0 I
ck = Cos[agk];(*列表求各铺层角度余弦*); R- J1 N8 m/ i7 T
sk = Sin[agk];(*列表求各铺层角度正弦*)- u/ X) z5 W) Q( F- W
s11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +. V) u: v# T' v6 r% C
sk^4*Subscript[C, T] +
9 ?1 F) k# T* T$ J 4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)$ H& y; B4 H4 N% d! J$ S- e
A11 = \!\(
% ~7 A6 u0 p! `' R\*UnderoverscriptBox[\(\[Sum]\), \(k =
6 v7 U: j: j. r E 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*)
1 t8 g5 u4 R' B% t0 u" SA21 = A11* j, U4 L( Z* |4 O. q1 r
A31 = (\!\(8 P( \0 s/ }* ^0 Q4 w5 a, [
\*UnderoverscriptBox[\(\[Sum]\), \(k = , c2 R! o- P$ b: g! z
1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)
+ ?$ Y* f$ W+ q3 p) ?3 kA41 = (\!\(
/ v: [* P2 j1 p4 T1 ^3 E& R\*UnderoverscriptBox[\(\[Sum]\), \(k =
+ A. f" N( V8 c) F nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)
, ]3 P9 _" f3 _6 ^4 G& h$ K7 B( O1 k: y
( k! A J6 m/ Q) y
( x+ p- Y# D, o0 GPrint["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)
7 {0 T2 ?( Z' [6 CD11 = \!\(
4 g2 k9 l# l) h( Q/ U$ H+ R, k5 |) v\*UnderoverscriptBox[\(\[Sum]\), \(k =
$ @6 Z7 O/ O$ Q, A( N: A8 j 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*2 ^* `1 _3 Z2 \) n2 X3 E
\*FractionBox[\(t^3\), \(12\)])\)\)
7 {+ e9 n, A0 B9 L2 }D21 = D11! q7 P( P. W- v4 Z! [& s
D31 = \!\(
l* {! X$ o; b( g+ U3 @\*UnderoverscriptBox[\(\[Sum]\), \(k =
9 i k6 S; D h$ y- ^0 J 1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*9 R7 G1 l( H+ ]/ W W0 T" e
\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)
$ y) \. ]8 w# W: v$ ZD41 = \!\(" X( D3 }3 @0 R D: y0 J( \
\*UnderoverscriptBox[\(\[Sum]\), \(k = 0 C/ w" D8 u9 X
nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
. I+ |+ g3 I: e# q k\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)
# K# I; l" N" }$ \* Q7 `: v# e1 Tk1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \
$ T( ?* V% I2 ^7 x; X3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;4 e$ w3 Y' r* q$ |- z
a1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(+ P7 m* O2 o7 ~: E8 T) ]9 \
DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(
$ b7 A4 ^+ T) y6 d6 E DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);
$ t r3 T9 u' |\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \
9 y6 X: o8 E& ]* K$ {6 n7 }7 ~= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];
1 D) \! T. f; j' @b1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \. A0 S4 \5 l% |$ ^! M
1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \. e# p" O7 x5 @$ P# u
Subscript[l, 2]/Subscript[l, 4];
' s5 C8 p/ b/ S, a8 b' B! ODD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);0 y; i3 X% ~! E& y( o
DD4 = D41/(A11*h^2);/ z9 k) I& q0 q$ R) A
r11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[9 k" T1 \+ ]& p/ v4 X' W6 V1 c
a2*\[Omega]^2, (4)^-1]; r13 = Power[. Y& ] E7 A/ U3 k& d
a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];! H9 g! p9 x4 G3 `6 l' e9 T
BB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},' `6 J4 c# H/ E+ [0 E
{0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},
$ Y3 q5 A! W) ~/ |; M {0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0,
5 a$ S9 ~/ y8 K1 U& U- b$ v) J/ t Sin[r12], 0, 0},7 x! N4 }8 d6 ~" i$ w6 S, j
{0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0, + \2 Q) N: L: J5 T/ E
Cos[r12], 0, 0},
# z' `* w. x' `8 `2 m6 x3 b {-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11], ; w( M7 |% Y1 o, H
0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,
& z: q* |- o3 f! m+ C -(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0,
c5 O( c% L) q. u 0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11], 7 P2 K7 D& D5 v& |- v' p9 b$ J
0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*# w; A! x+ l! d- z) D+ M# c# u
DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},! n. J8 a: C: T! f" q, B0 N2 P. h
{-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0, 2 H) a% ^$ u& p7 |
0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11], 3 c/ J& S! Y$ Z3 ~$ Z
0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*
4 C$ J+ g2 @5 n1 S# N9 H DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,
* }- Y" p6 P x. ?% k (r11)^3*DD1*(\[Beta]1)^3*Cos[r11],
& }( F7 V, ] }) ?9 Y 0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3}, y) g$ l2 R4 J J2 w2 a7 O
{0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*( I: u8 B" D- }# p# n$ b( a3 U7 X5 f) @
Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],8 s. @8 ]0 {+ _4 r
0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*7 z5 ^) E- c# M c& r9 y" g
Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,
( L( H, j2 J9 ~: a- K( T -(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*
: l, V% }- w9 k/ b9 S Cos[r14], 0, 0,% E% i* K9 h" h& w/ M, ~/ ]! B! G
-(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*6 y4 N5 L+ f; h. M: x d/ W- @2 f" q
Sin[r14]},
) `3 T5 w" j( m* ? {0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*4 s% j( a7 p, Y' h$ s8 e
Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,3 V! p: B$ }& a# q0 X
(r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*
" p1 i x# E$ i4 ?& x Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],- C: U2 H: L; k
(r14)^3*DD4*(\[Beta]4)^3*Sin[r14],
0 L; t- |7 a; Z 0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],% ? v a7 \: Q3 d
-(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},
/ {1 J# m# A1 v; n& z {Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0,
/ }0 P* E: p6 D9 x Sin[r11], 0, 0, 0},4 }; s% l5 S- y ?
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1,
% p* K# F* a; e& T7 c 0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
' B5 P& A f5 k4 h/ i9 ? 0, -r13*b1},
: h5 X9 G0 Y" ?8 s {Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1, 4 Y/ t4 |$ k6 C, a& G
Sin[r11], 0, 0, 0},1 B# A+ y1 w: Q# U8 \9 m8 H# C
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0,
3 V, K2 n6 {& q2 Z9 d# v' `$ i 0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
* A# ~ S/ \+ { 0, 0, -r14*b2},
5 P, w' Q1 W3 F" Z, P5 H2 l {0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,. b$ }. j7 l5 X7 D
0, -Sin[r13]},
, q9 z/ s# E: ^1 M6 V e% O {0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0,
# I* k9 g, F9 O( v3 }* q r13*b3*Sin[r13],! b# a. R5 R; P ]
0, 0, r12, -r13*b3*Cos[r13], 0}, ~$ m$ u, S0 V
{0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,4 r: b) c# d4 \
0, -Sin[r14]},: u& U. n6 q Y$ F2 u
{0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0,
8 L! m, f5 ^; Q0 c, j r14*b4*Sin[r14],1 y8 W! [2 g# s, r6 u
0, r12, 0, -r14*b4*Cos[r14]}}! }) e$ b/ J; m) T; p% Q5 f
aa1 = Det[BB]/ }- a: T t6 Z
Plot[aa1, {\[Omega], -10, 10}]5 z9 \& M0 s7 z5 M- T
ss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]
% `- L9 Z( _" x( e$ z" k. Y- J$ X7 {) z7 q+ \, f
|
zan
|