- 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
/ M! |% h( C: A: }/ y1 ?4 P0 m
" L9 Z" x* x0 L# T" P5 m( P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2 I! H: P/ W: w }
行列式求不出,画图找不到根
. r7 G9 H K( c( H! f }' ^2 {(*定义材料常数*)2 k) A/ f. _3 T4 t4 S
Subscript[\[Nu], TL] = 0.25;$ t+ C+ \' r/ Z& D( A; O
Subscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)
! m! r# C" P( u+ j2 H4 uSubscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)
/ R& x E* E; m! e; ?Subscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)
* O# }# R( u+ ]$ r, r+ i! p- j GSubscript[\[Nu], LT] =
. z1 X- G( R ~ Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];
1 E A# n0 d. w$ h& j; @3 }\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];
( [' D/ W! _; s5 U& `Subscript[C, L] = Subscript[EE, L]/\[Mu];
+ z! Q6 Q9 H' Y3 {( ^Subscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];9 ?. i# t1 L6 {+ `, o5 ?3 {
Subscript[C, T] = Subscript[EE, T]/\[Mu];
: \7 E; ]- Q5 ~ n; P/ sSubscript[C, LT] = Subscript[G, LT];
. |! b7 _% J/ q. ]$ H& @. R5 [/ v& `( p(*脱层几何参数*)
" R1 w3 D0 t( k, g, g, C7 p/ }" F\[Rho] = 1600;(*脱层密度*); F( E8 @$ ?8 A5 `% s
c = 0.06;(*阻尼*)
7 M/ W9 W5 I* H: |- B& U& ?t = 0.01;(*t每层厚度*)
- @: P% Q0 {5 {8 b2 Hh = 0.05;(*h为梁总厚度*)( R2 f6 G# ^" q" _1 S6 {
l = 1;(*为梁总的长度*)
6 ]/ B% S9 ] ~+ A- jSubscript[l, 1] = 0.3;(*为梁1区的长度*)
3 z% ~5 B" P0 r Y2 a5 \" Y" {Subscript[l, 2] = 0.3;(*为梁2区的长度*)
- C5 J& _# ?, K+ C- }- ^# A* VSubscript[l, 3] = 0.4;(*为梁3区的长度*)* Z @4 ~0 _( t: i8 Z3 U' Y
Subscript[l, 4] = 0.4;(*为梁4区的长度*)
* F: f8 V, K0 w% \3 vnn1 = h/t;(*nn1为总铺层厚度*)
0 U% I1 Y% N( v) Onn2 = 2.0;(*为上子铺层层数*). j% [9 y" ?% T6 c3 M0 Z
nn3 = h/t - nn2;(*下子铺层层数*)
6 T, z8 {" W" G R! F$ ySubscript[h, 3] = t*nn2;(*梁的上部子厚度*)4 K. c A* y: S1 F0 D6 E$ V) e
Subscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)' A8 C& B e' |5 g' H; j% T
Subscript[h, 1] = h;(*梁1区的厚度*)8 Q1 X+ Q( ~: V1 i8 P
Subscript[h, 2] = h;(*梁2区的厚度*)
( B* O$ ]+ u7 S(*求各单层刚度*)
& _6 Y+ s+ C1 v! jagk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)& ?4 @0 o$ q2 y0 `
' _. ~ o/ z3 S8 G1 W
4 K7 j; X( g& q1 M1 [9 V, P! uck = Cos[agk];(*列表求各铺层角度余弦*)
' u. n/ A+ u& k: T2 j+ X( tsk = Sin[agk];(*列表求各铺层角度正弦*)
! ?6 V/ |/ T, G2 J- f0 X, I' qs11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +
, C$ a U+ l9 y7 k sk^4*Subscript[C, T] +
- c' a N$ ?9 Y, P6 _! y, o# W# i9 O 4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)
. C2 [7 E- F0 X, X0 i+ Z/ N4 [9 `A11 = \!\(. @. i: z" h. ]' a# s7 f1 I
\*UnderoverscriptBox[\(\[Sum]\), \(k =
: q' }) r y$ `0 [7 O, d' I 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*)
, s7 h4 Z9 m3 x* ~; GA21 = A119 F. ]* L5 O5 w' p( u0 O
A31 = (\!\(
2 M1 ]' _5 ^2 n" W) p& S; V* f\*UnderoverscriptBox[\(\[Sum]\), \(k =
2 O! _- \) {; y' _ 1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)
: |9 x1 R J+ W, ^$ a9 ~( |: ~A41 = (\!\(
! M% M: I. c$ a f# e\*UnderoverscriptBox[\(\[Sum]\), \(k = " \* S' S5 K. z8 P2 m
nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)
9 b0 \. d: Q- B: r7 H) m; D& s, x& k' }6 [& V& Z1 _
9 i: R" ^, l8 N6 U7 {. O6 V* l
Print["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)
, O2 }, _- w8 ]8 S6 b7 c/ FD11 = \!\(
# T8 l0 L+ [7 h+ b\*UnderoverscriptBox[\(\[Sum]\), \(k =
7 K H8 j) N) { 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*7 q1 j9 o$ q9 ]3 l8 `8 H3 e" N9 g X& u
\*FractionBox[\(t^3\), \(12\)])\)\)9 L3 _3 w ~5 z# f
D21 = D11& s+ ] K' J& J8 v, R
D31 = \!\(
5 P# q$ Q5 J& S; p\*UnderoverscriptBox[\(\[Sum]\), \(k = ( T4 U4 R: F8 ^7 N% t+ @
1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*4 O: c3 C% O, {* ?! {$ f* E& W
\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)
& { G5 h& I% L) ?D41 = \!\(
0 Y7 U2 _7 g; w\*UnderoverscriptBox[\(\[Sum]\), \(k = / N ~2 ~4 l$ y: T9 O) M3 f% L
nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*8 X3 K0 q6 ]" E+ C( J- B8 F
\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)+ R+ F+ \" ?5 T& C7 t
k1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \, m1 K9 p- T; F2 L% F
3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;
1 x) J+ s2 j7 p7 \ ~( Aa1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(
) ]) o z' A( v- V( X. }' I; U8 W DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(2 b: G0 N/ Q/ g5 X) b- i
DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);
. \+ x3 I: V) e\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \
/ X5 W# b/ h3 q= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];8 S6 {& e: E' r U, ~1 z$ u
b1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \
' H* ?% J$ b% M. I; J. v0 h1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \1 B; ]+ c9 \" \8 P) D4 a* a! H) U/ ?2 O9 G- [
Subscript[l, 2]/Subscript[l, 4];
% {! ?( w, [$ \2 v, M! lDD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);
2 B- r; N6 Y8 Y J2 C6 IDD4 = D41/(A11*h^2);8 t7 ~2 q# b: d1 m# i' r" Z5 W3 a
r11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[
) k4 T& C) m, ^7 `: @) I a2*\[Omega]^2, (4)^-1]; r13 = Power[4 Y4 T% F% b I1 ^- Q- x! y
a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];
( S3 A* y3 b4 v( jBB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0}," x: _$ x2 j* l6 u; R' d( s$ B' j
{0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},8 p* O' W/ E- ?, B
{0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0, 8 M- C/ K. {/ Y* d8 }( ?3 p
Sin[r12], 0, 0},/ B2 y! ?/ w, U6 K3 X$ [
{0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0,
0 @4 R' c# i9 R" H, }) L Cos[r12], 0, 0},0 e- I+ u+ c8 @. t0 ^
{-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11],
4 S$ f9 D$ F$ ~# N" h 0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,
" \' P3 r- ~: l. t9 | -(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0, 5 o1 T: T0 B( K% z6 t
0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11],
" Z/ E* s) G' n. N 0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*
* M; T6 M P! u7 w: E9 i+ t! A, p DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},! J$ I' F3 y- k2 }+ h$ A0 o
{-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0, ( @6 Y. Q9 G$ M+ V6 X
0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11],
6 F6 b" s6 w9 t/ V 0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*7 a4 j8 u5 ]* j4 p' p
DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,
" P/ C* a9 H. K. v B5 [0 E (r11)^3*DD1*(\[Beta]1)^3*Cos[r11],
5 `$ w G, Q% P. H; s) ^- R- h 0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3},* U( c# H/ z, d" o0 @& l2 a
{0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*
# W5 E5 w) L! }5 G# O+ K Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],
( |% A, x3 @$ A' c 0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*
9 q7 l- B' F* a$ F Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,
; J' v/ o% W& w' {' z; E5 Z0 g1 P -(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*1 w+ [: f8 o- ~: B; _6 B
Cos[r14], 0, 0,
- D3 p5 v! e& ^, U6 q* y& Q# |$ o3 E# S -(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*
7 e3 C7 v5 |8 ^- Z( V) l Sin[r14]},
! _5 x0 p% s/ w0 W% r5 S. K8 T {0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*
- b" ]0 v! Z% o N. ~ Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,7 Q; f% x5 K% ~
(r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*
, U9 b+ }" Y. r- A5 W Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],
8 ^" o- k" E" \ (r14)^3*DD4*(\[Beta]4)^3*Sin[r14],
. M9 e3 F& c# W+ B$ ]9 v& P 0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],
& s, h" Z4 r8 Q -(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},
% R6 R# z0 v) K7 O) R- s3 Q {Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0, ; k+ \- [: T8 P4 p- i8 u+ Q4 W8 V
Sin[r11], 0, 0, 0},
# F- x$ l4 @" T( m {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1,
- y. ^6 |) S% a( O; S1 B& } f' L 0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
/ x0 X7 a1 T9 v 0, -r13*b1},
4 X% f% i' h3 ?. Y, d1 L) y* J5 C0 N {Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1, ! z$ f- i9 n: L* b
Sin[r11], 0, 0, 0},! H( _. \! d: I, Q- s/ o
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0,
- J! B1 D* G; I/ c 0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
4 e( U' X6 m* A4 J7 x2 F 0, 0, -r14*b2},. o/ i! E z2 o: Q4 ?& ` k$ p
{0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,# x; k8 ]: Q+ e+ ~1 I
0, -Sin[r13]},
* V5 w1 K8 O6 D7 P2 w {0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0, * u1 | B, |# G \- q
r13*b3*Sin[r13],1 V4 X5 P- Y$ @1 I. M6 S
0, 0, r12, -r13*b3*Cos[r13], 0},! w4 V- s0 |, r. t& [% }6 q' a
{0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,
/ A3 Q9 q; C6 p9 I 0, -Sin[r14]},
8 K; ]8 T- u m/ ^- W x2 o {0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0,
3 ^3 Z4 R W$ N1 R2 q r14*b4*Sin[r14],3 ]9 o6 s3 z. ]7 b
0, r12, 0, -r14*b4*Cos[r14]}}
$ N2 a% K& y, X5 Y7 jaa1 = Det[BB]
8 P) b# G! ?( B4 ?$ ?: @1 SPlot[aa1, {\[Omega], -10, 10}] ^) _2 w: N$ L; b, w7 `
ss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]
7 j/ h: j5 ^! g+ Y# F6 i
( C8 x$ w4 G' B" M; i |
zan
|