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本帖最后由 游龙游龙 于 2014-7-8 14:45 编辑
7 Q1 L+ }# j9 e& K: a' x& k7 y, C
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% U/ U u5 i8 t. I( x6 [3 s
行列式求不出,画图找不到根
& {$ F1 \0 w; c(*定义材料常数*)
; L* g5 b5 M, k: |! I8 m; _8 qSubscript[\[Nu], TL] = 0.25;
5 p" ^ ]' A& u4 USubscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)
1 v& _+ K2 u4 q. L( aSubscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)
+ K+ p8 @. s' E, M" |& `Subscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)( b7 k' g) j# c+ }; P
Subscript[\[Nu], LT] =
2 J* t4 V4 b, i* U$ `* ? Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];
9 e; v. O5 m7 Y# |\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];8 O6 y' m- b/ x }
Subscript[C, L] = Subscript[EE, L]/\[Mu];4 W9 o3 o- u, i, z! L! E' z/ v( j
Subscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];: ~) F$ ]( b- t( X6 T% v
Subscript[C, T] = Subscript[EE, T]/\[Mu];
/ x1 J& a6 V2 JSubscript[C, LT] = Subscript[G, LT];/ i7 R- `: O* A* e0 a
(*脱层几何参数*)( e( p; j9 l+ [/ R+ y
\[Rho] = 1600;(*脱层密度*)1 v+ S5 H" ~' L2 f! G" e
c = 0.06;(*阻尼*): Q$ Q& Y) C1 O8 E6 C8 Z! c
t = 0.01;(*t每层厚度*)
1 C! h8 N" Z& [$ e( q0 Bh = 0.05;(*h为梁总厚度*)
" g3 h# o. z2 Q" q# k Fl = 1;(*为梁总的长度*)/ b) _: z* u/ o# z; Y6 R
Subscript[l, 1] = 0.3;(*为梁1区的长度*), Y' s3 ~' e3 y3 R
Subscript[l, 2] = 0.3;(*为梁2区的长度*)
. N3 W1 Q2 f; t% j& T/ PSubscript[l, 3] = 0.4;(*为梁3区的长度*)
: _8 d, M. p' D, A; W7 c. S; O% NSubscript[l, 4] = 0.4;(*为梁4区的长度*)2 a5 ]6 f( S* o2 g a0 v9 h
nn1 = h/t;(*nn1为总铺层厚度*)7 W: Z) s* a* T
nn2 = 2.0;(*为上子铺层层数*)
9 J& d1 Z0 d6 \nn3 = h/t - nn2;(*下子铺层层数*); a) V& K2 W* @6 q0 E, |! r; v2 f, v) f
Subscript[h, 3] = t*nn2;(*梁的上部子厚度*)0 W' c% f# o7 u4 C' {; `; s0 Z
Subscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)
$ p4 `7 @- `% Y0 m- l7 YSubscript[h, 1] = h;(*梁1区的厚度*)
' i; K+ I/ K2 k7 X) fSubscript[h, 2] = h;(*梁2区的厚度*)- P* ?* W% D: w/ Q+ j8 c! {, L
(*求各单层刚度*)' ^4 C& z: { z# a8 ^/ M
agk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)3 y; S _! p: C# F! c+ ` P8 ?
. _, q( a* W: e, c" [
. q9 D5 s- u; C5 `8 Bck = Cos[agk];(*列表求各铺层角度余弦*)
+ C4 b' v3 h3 ?6 L7 b, i$ Fsk = Sin[agk];(*列表求各铺层角度正弦*). t5 G. t' I) f7 q
s11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +
" B1 H# ^6 `% W5 B# ]5 } sk^4*Subscript[C, T] +
6 J; j/ u# Z0 |8 U% J0 u1 S/ w 4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)
4 }# \( L2 c. t2 R. U) \" s3 sA11 = \!\(% @8 U( h- q( t' u: e
\*UnderoverscriptBox[\(\[Sum]\), \(k =
) Y8 F/ W# H7 A2 `/ M: o 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*)( K' a. v# P, b* d% g0 ?
A21 = A11
$ [0 D$ @. X$ hA31 = (\!\(
% `+ U2 l/ `' l4 i" @% W1 W\*UnderoverscriptBox[\(\[Sum]\), \(k = 7 i6 Z0 Z& q; a& F& ^% _" d6 \
1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)( i; {' w/ k) g- H T( ?( Z
A41 = (\!\(% y% W7 r5 x% j; _' o% }
\*UnderoverscriptBox[\(\[Sum]\), \(k =
3 w. F; t4 ]) O+ o! P0 C- S nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)
3 h6 | o! m8 G! _: U
4 R& o" l* K$ t6 k, q8 t) ^
2 |" ?/ j8 ^- _# e% n3 WPrint["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)5 o/ H- r* M1 g! {1 j$ S
D11 = \!\(( U0 p9 v- I1 w( J2 |: v! E: }. f3 A
\*UnderoverscriptBox[\(\[Sum]\), \(k = 7 G7 x R, T- i7 X r; u
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
2 W9 Q& g N i\*FractionBox[\(t^3\), \(12\)])\)\)% J$ F, h) T% Z3 P) Y
D21 = D114 h9 l5 M% K9 g1 h
D31 = \!\(
L2 g8 p& O7 H* q9 Y$ K6 u\*UnderoverscriptBox[\(\[Sum]\), \(k = ; d$ n" k- W6 b* T, J Y
1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*6 k, g) a9 \) h( s
\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)$ [1 z6 N. w& u0 K- Q8 \. N( V, P) p" c
D41 = \!\(
5 |" w3 x$ I1 {\*UnderoverscriptBox[\(\[Sum]\), \(k =
8 F& H9 b0 G& ~* X2 i' f nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
( Z4 w) l$ r; U& S! Q\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)
% ^" H; d5 X( g2 ]k1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \
5 W. e, a5 R6 D- M2 V3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;% C" s! @, Q" S" j$ ]6 {
a1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(
5 W1 X8 }& x; t' m8 n DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(0 J. D5 _" z- [1 }, v
DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);
. E+ Y7 s0 T4 y) I& V$ e" X+ o\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \" p- I* f/ J; S; l6 b: T9 H3 r0 f
= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];; u" c, v+ o" b# F. |! P* S$ E
b1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \# L3 d( F" R+ P9 Y4 L
1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \- U% J/ t4 j$ u: Q' M9 u
Subscript[l, 2]/Subscript[l, 4];
! P" e# }; ]$ nDD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);
- g7 i2 @( U: q6 j+ S# zDD4 = D41/(A11*h^2);
$ {4 r* Q, w" C$ ^1 d" or11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[
$ ]% q/ E% R6 ^( I2 z$ D a2*\[Omega]^2, (4)^-1]; r13 = Power[9 {( n9 J/ x0 B" w) d" C9 [% b
a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];* n D+ N3 G# V3 z! X1 |7 k0 h
BB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},9 X4 v/ F8 C# z0 a
{0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},5 v; Z: I( y9 C5 h
{0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0,
% E; U6 F/ [- P# }0 X/ W" r Sin[r12], 0, 0},' X: E) C' J# G9 _( G9 G- E8 m! z& G
{0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0, 9 S0 B5 e) O& ~) S
Cos[r12], 0, 0},/ r! C4 i! C9 d0 g
{-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11], 6 ~. i2 ~# Q+ B2 y
0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,8 }0 A6 d, f* [3 A
-(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0, ; D) G+ K3 |" a7 f. z. A8 ~; y
0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11], + V8 s1 s2 ?8 v4 ^! C6 x) p
0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*; C0 I/ C# z- Z8 ^
DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},
2 x( \7 y, q, s. N: a {-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0, 6 z7 f$ @7 M9 E; K% _
0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11], ; o) l4 \0 ^2 f, g1 ~$ t' I# s, e7 {
0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*
8 e8 l/ ^1 W* i& H' l1 ?! w- x DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,
t ?7 ]3 f1 E, R8 h* }' j (r11)^3*DD1*(\[Beta]1)^3*Cos[r11], 9 O; [' j( A2 v. p p; a
0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3},
, ^; C& J) Q; p# Z2 D" u8 H3 `$ k, H {0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*1 A0 ~6 B1 y& P8 }
Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],
8 H2 H# p- n+ W) q) e/ n 0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*4 [- F- a+ N5 v+ h5 A, @& a; c6 y
Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,8 T0 [( z, h, v! a' q7 h: I
-(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*2 s$ k9 U9 n) D3 M! I: b" L3 ]
Cos[r14], 0, 0,
Y: R& {$ {' c0 o. a6 D4 `0 } -(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*" o' X M3 k: i# k0 C2 Z5 C% j8 w4 x
Sin[r14]},
7 I' w6 |; V2 {. { {0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*
; R3 u( C' F6 B/ |# H$ t Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,5 H0 D: R6 Y7 x3 o5 i" {1 G
(r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*4 r: B& c8 K8 N3 Q
Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],) | S U( G$ C. ^7 g
(r14)^3*DD4*(\[Beta]4)^3*Sin[r14],
& c Y% x0 \4 F1 J. L 0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],/ _7 I8 v0 Y( F
-(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},! i6 X5 z* Z8 T* ?
{Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0,
' Z6 g5 g% b7 r6 |) L: f Sin[r11], 0, 0, 0},
, L; \3 E/ ?$ F4 b {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1,
0 c* ~. O; U) Y; x: ] 0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],& K* N7 F" v& i4 l
0, -r13*b1},
/ |. ?- k g8 s |! v7 T C {Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1, ( n$ K% q! I& L4 o4 c
Sin[r11], 0, 0, 0}," \ f% e8 t, ?* L- A/ I
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, " t$ R& {6 d5 F: M
0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],* f- n. D/ T5 t% C
0, 0, -r14*b2},
) ?. W9 o+ E, _# E {0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,
2 w7 F, t5 ~0 {# Q 0, -Sin[r13]},* w: p' t* Q% f. j
{0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0, p1 G- y8 \' p+ h7 [3 j, D
r13*b3*Sin[r13],
9 y4 e* D. L8 O" m' g$ e6 H n 0, 0, r12, -r13*b3*Cos[r13], 0},- ~) g( g* P- F; v; U
{0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,- B$ Y& S/ z0 h4 n: T
0, -Sin[r14]},
' a) J' W* k& X4 V5 K' s {0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0, % ?' k6 _* p& ]% P! G
r14*b4*Sin[r14],
$ _; G. p1 x& i, o: h0 j8 b 0, r12, 0, -r14*b4*Cos[r14]}}8 c' Z. j6 W' W
aa1 = Det[BB]
) w% P( L0 |2 @+ A2 }/ E2 NPlot[aa1, {\[Omega], -10, 10}]0 I) ]+ Q4 Z; O4 @# m% ^" W1 `! P
ss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]7 }3 n2 q, q& @6 V6 {
' p! \) q6 k7 r8 I4 b: j |
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