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本帖最后由 游龙游龙 于 2014-7-8 14:45 编辑 " j3 K, }" p3 O1 v' { \
( i& O+ |1 O" Z% P* ~# O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 {. U! V% u5 b
行列式求不出,画图找不到根2 W, O) A% B7 S$ [
(*定义材料常数*)
2 {0 t: ?- P% c' Z) H1 cSubscript[\[Nu], TL] = 0.25;
" g) [! t: v r" C+ O' x: |5 }Subscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)) {3 r: e1 A s* m: ~1 K6 U' n
Subscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)
6 }+ i. U \6 p6 DSubscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)
7 V& r+ M% x1 I* f+ GSubscript[\[Nu], LT] = 8 E+ G1 ?5 m% l) u1 p# \% z
Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];
* `0 @8 U! q2 b/ o\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];& t, j, P7 \0 Z: K) Q8 z1 ~3 A
Subscript[C, L] = Subscript[EE, L]/\[Mu];+ G( A8 C) i+ @) W# I
Subscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];
) n _, v0 v9 m0 h) \) fSubscript[C, T] = Subscript[EE, T]/\[Mu];0 R: J# N' [* b" O/ d
Subscript[C, LT] = Subscript[G, LT];
' X2 [0 W6 @: ]" ](*脱层几何参数*)
5 e0 W, N: A7 Q8 O\[Rho] = 1600;(*脱层密度*)7 G" }9 |( h& c4 Z* O
c = 0.06;(*阻尼*)& ~5 d$ O( Z/ A3 g. r
t = 0.01;(*t每层厚度*)! u) [$ Y0 W3 T- y
h = 0.05;(*h为梁总厚度*)
" L( e* |; c) a( }* \l = 1;(*为梁总的长度*)4 C1 u+ Z6 ~$ k' V0 D& C/ E2 T4 B
Subscript[l, 1] = 0.3;(*为梁1区的长度*)& y$ X, G. V7 V( O) n- ?5 C0 w
Subscript[l, 2] = 0.3;(*为梁2区的长度*)
) u' S, c; ]3 a% q6 eSubscript[l, 3] = 0.4;(*为梁3区的长度*)
) p& n3 r, n7 e5 _; {- O6 e" s+ ~Subscript[l, 4] = 0.4;(*为梁4区的长度*)
9 L7 C% M4 e1 p$ a9 fnn1 = h/t;(*nn1为总铺层厚度*)
" i4 K z2 O( j8 s H) \# f# a5 unn2 = 2.0;(*为上子铺层层数*)
5 X F$ t4 j5 t0 _! i6 E Cnn3 = h/t - nn2;(*下子铺层层数*)( M) l$ o5 w6 w: J+ Y
Subscript[h, 3] = t*nn2;(*梁的上部子厚度*)
( K" e% X l5 z- A% f' TSubscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)
9 n; K. K# L% A# a4 w& p PSubscript[h, 1] = h;(*梁1区的厚度*)8 P: w% N" [" e" H/ B$ g5 L8 f
Subscript[h, 2] = h;(*梁2区的厚度*)
& S( F* m+ u4 e/ `/ [/ _9 t(*求各单层刚度*)
7 s6 x3 d U9 U4 w- l2 ragk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*), y8 S6 C& i" [- Z
b# a- k$ j4 ^$ P" E
; w* B% @ a, t7 I0 {# F' ~' i( sck = Cos[agk];(*列表求各铺层角度余弦*)
4 O) j1 U: y! Q9 o. wsk = Sin[agk];(*列表求各铺层角度正弦*)- v% T/ s% d7 R9 e& L. K- W+ m2 D5 _, b
s11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +: E. P/ |7 o3 c, w& F
sk^4*Subscript[C, T] + $ ^( D& D2 l+ V) c I7 {
4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)' ]5 l9 L; \/ u0 o
A11 = \!\(
I; \- i4 D% \* |2 B\*UnderoverscriptBox[\(\[Sum]\), \(k = & m4 J D( u0 h8 I1 h& R
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*)
: O" J# X* B: IA21 = A11 s$ a, ]$ n& y. T
A31 = (\!\(" ?( |7 J/ J( b: v% j6 _
\*UnderoverscriptBox[\(\[Sum]\), \(k =
1 P( p" p% b6 c; B+ l# \+ w6 h% g 1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*) q4 J. u4 R+ N
A41 = (\!\(+ [, M0 `+ {& u4 y" ^ R% l( N
\*UnderoverscriptBox[\(\[Sum]\), \(k = 4 p4 B3 ~9 U) Y0 [3 e) y7 @& W9 M
nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)
. J! f& b0 Z5 A& r2 c3 o3 `' s" ~
/ }6 e# [3 d- O
1 l" \2 U6 j# \% ePrint["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)% T2 K% p2 h8 [
D11 = \!\(: ?$ Z* K6 q3 R1 _1 z: N
\*UnderoverscriptBox[\(\[Sum]\), \(k = , M0 ?5 B \. X1 h+ A
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*2 c7 `4 B5 ~) {9 a5 I
\*FractionBox[\(t^3\), \(12\)])\)\)
0 Y+ r) x0 m/ u DD21 = D114 |3 Z- H5 f5 ?' G* \6 {% n
D31 = \!\(! E/ b& r( f, i8 j4 S
\*UnderoverscriptBox[\(\[Sum]\), \(k =
- P8 M+ Y3 B0 s8 J 1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*9 K' E G h) n+ b! N' M/ g$ w0 u9 Q
\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)* N; D; h; l9 r5 ~5 S
D41 = \!\(
3 n' O( j! t4 R& f- S% M) G" [; z\*UnderoverscriptBox[\(\[Sum]\), \(k =
* c, D9 h+ N. M1 f% c nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
- w) A* ]2 Q2 b% W& E0 \# Y# h, W\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)
! \/ o2 p |& @0 u" G7 K9 Rk1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \/ T( c' a# f3 T: K- ]' C; ^; t& J
3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;
+ v9 `$ i3 m6 v9 Z+ N# ea1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(8 l& c* M4 Z5 L1 ~, U
DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/($ @4 q- w/ f x; O1 r9 r2 f0 d
DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);% @ U8 `; }% I7 n* \; D+ R) h
\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \
9 g. T J# t) P; ^% {$ _= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];- {2 T8 _$ j2 C7 Q! @+ a1 n
b1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \# Y1 o9 y1 j- t
1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \
4 L' C) f* q6 d5 O- |0 ASubscript[l, 2]/Subscript[l, 4];4 d) Z& W# K6 k
DD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);7 K. t8 d v( |) w$ G
DD4 = D41/(A11*h^2);
" I" Z) U$ \' ^* M% S( o, M( S% hr11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[% t; M$ P: F& s1 ~6 L
a2*\[Omega]^2, (4)^-1]; r13 = Power[
$ P* b3 X0 _# V/ o% {: {% n) k% L; ^: t a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];8 w3 M# J* a0 R1 J0 p
BB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},/ k; L# b7 M0 s
{0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},
8 M/ j6 M W1 {: A; o {0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0,
0 _" l" R: {' K% Q Sin[r12], 0, 0},
9 `/ B/ a8 P7 O& j6 r {0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0, " L: p* W& h6 j
Cos[r12], 0, 0},
- l4 e; ]* J5 u- w$ l {-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11], 8 H8 i4 X& R# i1 G# }' r$ c: ]
0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,) D) D0 f; |+ U! N
-(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0,
8 f4 S+ Y" w! ^ 0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11],
/ V" B5 E3 l l+ P 0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*
X' P% Y+ W, ^* ~" J9 m DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},
" f3 ]7 d! g8 l4 s- k/ r {-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0, " ~& y/ C% c! B9 b( }
0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11],
) D. x" _& E+ e 0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*& G: L$ \4 L R7 k6 C
DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,
8 }) _* f2 i1 o8 w (r11)^3*DD1*(\[Beta]1)^3*Cos[r11], 8 ]2 f6 \/ E! ?0 J" N. ]0 w
0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3}, n3 ?6 r8 |9 A: u9 p3 Z& D4 P
{0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*1 a- b5 `2 b# b
Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],+ q7 I) z8 s& a. X% m k
0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*
: H3 w. ?+ D2 ^( \! h Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,
6 A! z5 J3 D! R -(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*2 Z; m4 J. Z( s
Cos[r14], 0, 0,5 O" i7 o% S+ n/ @; ]
-(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*
- l2 Q: E. _# e5 L: X$ O Sin[r14]},/ }$ f' l% L1 O6 Z) A
{0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*4 L6 A& u- U# K2 F! D! t+ T
Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,1 `4 Y3 o6 X4 O: ^6 t9 W. B: `- `
(r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*! g" P5 z: o8 O9 \5 ^8 L$ P$ b
Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],
" J S2 e* B: F, t9 H+ o4 J6 S (r14)^3*DD4*(\[Beta]4)^3*Sin[r14],
+ h8 n' t; H, a) Z 0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],
/ L$ `# S) j z -(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},: S3 Z% h' E3 U
{Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0,
) F2 ?: z3 I3 ` Sin[r11], 0, 0, 0},) Y9 ?; u' e; p# f4 Q0 V. c
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1,
! {4 F& Q8 x! T, r 0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
! J- |* `4 a$ M6 L3 H/ @6 H( c z 0, -r13*b1},
- g! l; Y) U0 m2 z- I" f% C {Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1, 7 W2 b. a" \1 |) A$ M. l) e
Sin[r11], 0, 0, 0},8 b1 a; i- r* y* z6 t- Z P2 U
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0,
: J* G: `" K+ O+ x$ `$ Z5 { 0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],' y& N; w6 U3 t: e
0, 0, -r14*b2},! V& c! o3 c7 b; e, R( _! T* l
{0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,; e6 u" q0 |2 X: @# Q# Q( H
0, -Sin[r13]},
6 J3 }7 T. x) i0 J3 T0 N3 c+ Z {0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0,
+ G% y8 a9 c8 r8 k r13*b3*Sin[r13],6 @6 L7 n4 J/ X# f% a
0, 0, r12, -r13*b3*Cos[r13], 0},
1 X' k% x. k( c# u {0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,
9 K0 A' U- C* `3 w ` 0, -Sin[r14]},
! e' n% P; X" m3 Q" g {0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0, + f4 [, O4 \9 V# y
r14*b4*Sin[r14],
# k& {( J* q, _* _. U 0, r12, 0, -r14*b4*Cos[r14]}}2 E" p, U2 l+ I/ R* K6 D# e2 n5 q4 V
aa1 = Det[BB]1 `4 P9 V L) B
Plot[aa1, {\[Omega], -10, 10}]' P; I# F& B& }1 K3 q2 I
ss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]
. `% y1 H5 G/ n8 f+ j- w
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