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本帖最后由 游龙游龙 于 2014-7-8 14:45 编辑
5 o0 a; ]4 J6 r- K1 y/ c7 r, v" s
8 i+ O$ Y' c$ g& P" v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5 Z3 b& K3 Y) W/ E0 j
行列式求不出,画图找不到根* t1 [6 B! z: N
(*定义材料常数*)
# V$ g' l9 S$ N( k7 N; I' MSubscript[\[Nu], TL] = 0.25;5 _% s6 ?$ @( v3 Q, v. O; F
Subscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)8 k, v9 F. s. q/ }) k5 B
Subscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)$ G3 H3 p" r# G$ h4 h: g. m* a
Subscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)
# W/ U; q0 U7 I) e3 C5 vSubscript[\[Nu], LT] =
d/ S3 @, @- D: W* v Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T]; Q. O m- |& Q: Q+ ?. T
\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];
+ E/ M! m9 k1 |/ X' \- _9 sSubscript[C, L] = Subscript[EE, L]/\[Mu];
9 n% o, _1 c9 K0 p$ i8 f, rSubscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];
+ N. ~% C3 {$ r5 JSubscript[C, T] = Subscript[EE, T]/\[Mu];
4 z. `3 X2 T: I& c$ G4 J3 \2 p. ySubscript[C, LT] = Subscript[G, LT]; j- D, M1 g% ~4 q" v9 {
(*脱层几何参数*)
! w9 L' g/ Z% O9 v5 n\[Rho] = 1600;(*脱层密度*)
9 w% o3 z9 t1 c9 y5 B! |9 ic = 0.06;(*阻尼*)+ `& ^; U4 w$ ?. M8 D0 A: H
t = 0.01;(*t每层厚度*)
) q1 j. G9 J/ `: J% ch = 0.05;(*h为梁总厚度*)& _. ~( X/ W1 }, X
l = 1;(*为梁总的长度*)
2 E: X4 P: ?: @ G* BSubscript[l, 1] = 0.3;(*为梁1区的长度*)
2 n6 G* H, D2 V/ r" D+ USubscript[l, 2] = 0.3;(*为梁2区的长度*)
3 P/ |9 D& [0 k$ z2 j$ M" ISubscript[l, 3] = 0.4;(*为梁3区的长度*)
* ~, @9 L4 T, w" Y7 J- SSubscript[l, 4] = 0.4;(*为梁4区的长度*)
; m$ @1 q) Q+ ^% Rnn1 = h/t;(*nn1为总铺层厚度*)* V N* A+ l; Y& o( N
nn2 = 2.0;(*为上子铺层层数*)
# P. x' `+ p+ A- x% v* y/ w9 vnn3 = h/t - nn2;(*下子铺层层数*)
# W5 a6 l% A2 M3 [3 W1 C% ^Subscript[h, 3] = t*nn2;(*梁的上部子厚度*)
, L, T# q9 w, F3 pSubscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)
6 d& ^, S) D4 [& L9 VSubscript[h, 1] = h;(*梁1区的厚度*), m: h5 ^1 F5 |
Subscript[h, 2] = h;(*梁2区的厚度*)* x% Y- X8 n, ]2 W
(*求各单层刚度*)
% O- J* L9 n; Kagk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)
( K; u# e; \: l* Y0 |+ G! V: W9 d8 Z4 x
8 H( O9 k8 x k: t5 i, w
ck = Cos[agk];(*列表求各铺层角度余弦*)4 H$ B! p* B4 C4 @# e0 x
sk = Sin[agk];(*列表求各铺层角度正弦*)
3 _- Y4 m" o" x7 p& W" ys11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +
/ g0 u# y0 |1 p& _/ k/ v sk^4*Subscript[C, T] +
+ v6 ^+ w/ u6 p: v7 ` 4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)" |2 x# [) J/ F# H7 x$ Z
A11 = \!\() Q; d! K6 U& J7 L7 d
\*UnderoverscriptBox[\(\[Sum]\), \(k =
4 x' K. n- W& ], \& W+ k } 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*)
: B8 L6 Q3 f" v2 R3 i7 {A21 = A118 _' }5 N1 R5 s" J q( U$ A
A31 = (\!\(( {9 o2 o, J. y& c' e
\*UnderoverscriptBox[\(\[Sum]\), \(k =
6 [; L1 a3 |4 @( _/ \, }: s 1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)
: D s$ _; k5 b, @ TA41 = (\!\(6 x7 g. h/ ~0 X4 u1 i. u
\*UnderoverscriptBox[\(\[Sum]\), \(k =
3 x6 w# N4 l9 y nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)0 i6 F9 ~9 Y4 h$ t+ A' y' z
. ^4 ]. b- G. M8 _2 h5 V3 F9 r5 _* O# I/ {
Print["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)4 d' x8 @ [% Z; n7 w, t
D11 = \!\(
; F; C4 W) _( v\*UnderoverscriptBox[\(\[Sum]\), \(k = ! M ]' [: t8 z) W8 l% ^
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*) g7 b6 ^6 J9 p! \5 r5 W' ~! e
\*FractionBox[\(t^3\), \(12\)])\)\)
) T" _2 s6 Z+ QD21 = D11
4 Y \ i0 e' L6 _4 H/ fD31 = \!\(: L7 T5 h! L, `
\*UnderoverscriptBox[\(\[Sum]\), \(k = 5 U4 n- i6 u. F" P0 ~
1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*
% T1 e1 d3 ~/ k: s\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)
% C; ^' U- u$ A1 I# a2 }9 B. ?% {D41 = \!\(; A) f) x+ `! j; Y
\*UnderoverscriptBox[\(\[Sum]\), \(k = 6 Q9 a, E5 g2 h! K$ `
nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*7 x& R+ j j- `, \6 Q
\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)2 z4 x& l V, b2 L7 y2 x
k1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \1 G, f3 w, S! A: ]" \, n( u2 k3 V
3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;
9 X7 |7 x3 V, i% s- Z' qa1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(
: ?' I0 {7 w2 b6 @ DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(# E! j& w: x) q- O1 p8 O
DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);+ b3 c% A' \' Y/ P8 {
\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \
2 s/ c1 O% b7 t+ F! o= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];6 s) r5 U# B. S1 e i. L
b1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \9 o( y2 w4 q# s( w. |* m* `3 c
1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \
) V( e5 _1 H: Y5 z- `Subscript[l, 2]/Subscript[l, 4];
& x- r7 b, ]8 g# C: vDD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);
' S/ T9 Q" V( v$ `' T! s; DDD4 = D41/(A11*h^2); l7 G, |$ Y J
r11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[
" n2 B7 J( y" l' W a2*\[Omega]^2, (4)^-1]; r13 = Power[( a: I, z1 ~# ?& O& R( k
a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];
, v" m: P5 Z }1 n+ }3 ]( yBB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},
) @7 T3 J8 Y3 x$ Q/ q- ~) Z {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},6 D1 y& P5 L! d! h
{0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0, 6 |% c/ x+ h, T% g
Sin[r12], 0, 0},% A$ s* {. P4 S8 q5 E! m
{0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0,
+ y4 U7 D P* z! V. I/ v9 H Cos[r12], 0, 0},) l+ m( v2 A8 k# f6 U" ]# r
{-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11], 5 ]" Z( G7 u- v/ j1 |+ |
0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,5 \3 n* N8 x. u/ |8 s$ w& u
-(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0, 7 b7 {+ V1 c$ p, ~' j# V4 j5 a8 V
0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11], 7 [2 l+ B) V% ?! C k5 A
0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*
& M! l0 m# ?* q. J DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},$ R% p$ D0 m. f% z5 h% L
{-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0,
0 p8 _- i& U6 ^# r O9 S, |* T 0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11], 3 s( A9 g/ T0 y( [
0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*/ v: s+ a7 l' J) {: ?- o
DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,
0 P, A D. |2 ^ (r11)^3*DD1*(\[Beta]1)^3*Cos[r11],
' U, V( O/ K% G4 Z 0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3},3 v" v( r1 s1 e8 L4 b
{0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*
: I" ]2 a8 H2 V z6 r' g/ _8 L Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],0 z+ [7 e |& c, F0 d
0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*
/ N- Z# o- F& E* J* n Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,
2 C: K+ |: T# Y. @6 F# f. I* s -(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*( V) k' l; y1 G2 u1 }0 F2 N' }
Cos[r14], 0, 0,* ]7 [: r( {8 g- N7 G/ r! w
-(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*
6 q) V$ q4 u+ a7 N' y* C& q+ n Sin[r14]},7 |+ ]# W1 d, [* M" K1 F0 K+ z) z: s
{0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*
. U) x5 r4 H+ m Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,
$ [- V2 f! ]4 s0 x* x# X# {4 |& R' Y (r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*5 o& [- F1 q8 g2 A* a( x) n; O
Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],& l/ C1 H2 F0 Q& o; h% D: @. A# N0 M
(r14)^3*DD4*(\[Beta]4)^3*Sin[r14],
( V' q8 m' N" F5 x1 V: v7 C 0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],
, ?3 t$ ?! ^; {/ s7 T u -(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},6 I. w6 Z# n7 _9 `7 M
{Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0,
1 [ Z& Q0 [) ]+ M Sin[r11], 0, 0, 0},
9 G+ R, \, r0 O6 M1 I2 y6 q {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1, ( t) ?0 t# j& e& X1 Y/ C. t+ G+ ?& E
0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
0 I; P. e; l8 i2 {$ \ 0, -r13*b1},
) Q+ _- A) P, D$ D {Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1, & k/ K6 H3 x: C7 @& T" d
Sin[r11], 0, 0, 0},
$ w3 `# m9 j6 H) b# g! V {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, 0 L* Y+ j3 A* D& @. ]
0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],+ a; W9 O- h m. _4 r! x
0, 0, -r14*b2},5 v0 C& t- _0 G7 T$ {. ~
{0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,9 ~9 u$ i8 ?7 j7 D
0, -Sin[r13]},
+ h& |- A7 K/ v/ W, u/ N {0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0,
$ c! Z8 ^ W* a" Z! t y9 E r13*b3*Sin[r13],
9 V3 G- M& V4 e6 W i% Y# B2 G 0, 0, r12, -r13*b3*Cos[r13], 0},
! S6 J9 e$ b9 p# y+ O {0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,
! y: f2 v. n; m: F 0, -Sin[r14]},
5 f+ ], h- O) a- @( Z: ^. h2 {3 k% P {0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0, ; q; p' E- z& W" q+ n& X
r14*b4*Sin[r14],0 ?7 D o3 D/ I4 E; w; c5 d6 i
0, r12, 0, -r14*b4*Cos[r14]}}
% j8 [! K& W' O; C/ T2 jaa1 = Det[BB]
. l: u/ _0 t9 `) O" U( }Plot[aa1, {\[Omega], -10, 10}]
+ K; o/ c4 Y4 r3 }ss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]
d8 @: @- [6 b! _: s' F& X4 t$ C2 h6 Y4 ]* T3 @0 q
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