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本帖最后由 游龙游龙 于 2014-7-8 14:45 编辑 7 V% o: Z) Z% b. h( T
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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
) L1 L9 ^7 ]8 M! C3 P3 _( p( \: z" G行列式求不出,画图找不到根- k1 [) B/ U! J- m) C8 {
(*定义材料常数*)& K e5 @6 { I/ W& \7 P) Y
Subscript[\[Nu], TL] = 0.25;9 Z* j- L$ f% [* w4 p% Z
Subscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)
M6 V$ D9 ?3 |' ^+ G7 X) Y$ xSubscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)! w/ h8 w; e& v3 X& ?& j$ l
Subscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)
3 M( u, j8 m; P/ x+ c1 rSubscript[\[Nu], LT] = / S6 n" H* m7 r7 L5 ]7 Q8 ?' N: L
Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T]; q: W! o1 O+ e8 u, |* E% \
\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];3 h% J) u7 \$ Y; u" H: W
Subscript[C, L] = Subscript[EE, L]/\[Mu];
& E$ k/ e5 a8 g# F) sSubscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];: n4 h9 B: P3 c8 u% T! R
Subscript[C, T] = Subscript[EE, T]/\[Mu];' X0 h" _# L! W7 ]
Subscript[C, LT] = Subscript[G, LT];9 W$ h7 o9 F' m D: _* b3 j) p
(*脱层几何参数*)4 e: F/ B& ^$ z7 |# C
\[Rho] = 1600;(*脱层密度*)
) \& X4 z! @ c0 S& oc = 0.06;(*阻尼*)
) Y2 ^4 D& q4 r, w% k. Z9 pt = 0.01;(*t每层厚度*), c+ b | G: Y3 S& N
h = 0.05;(*h为梁总厚度*)1 J, i$ ~ J- C/ P& m5 M& \
l = 1;(*为梁总的长度*)
9 a$ k9 r8 k! w3 i) F! z& ~/ PSubscript[l, 1] = 0.3;(*为梁1区的长度*)
! F( x/ |* ` r" cSubscript[l, 2] = 0.3;(*为梁2区的长度*)+ H1 E3 o# b8 g, A" Q
Subscript[l, 3] = 0.4;(*为梁3区的长度*)
! M/ X- `- j! ~" Z$ [6 ySubscript[l, 4] = 0.4;(*为梁4区的长度*)
1 o" A( a! }8 N) ]1 B' Y5 n3 lnn1 = h/t;(*nn1为总铺层厚度*)3 K' K1 m2 J* T( l7 G- @
nn2 = 2.0;(*为上子铺层层数*)
8 b R& U) D0 E- Qnn3 = h/t - nn2;(*下子铺层层数*)
% P: C5 ~ M& p; oSubscript[h, 3] = t*nn2;(*梁的上部子厚度*)
& t+ |* R& s/ RSubscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)8 G$ n+ S7 R/ g, O5 h4 V
Subscript[h, 1] = h;(*梁1区的厚度*)
/ U7 b: s: Y+ M4 q/ N7 Y. q9 K0 nSubscript[h, 2] = h;(*梁2区的厚度*)5 t- G# \: \% E& U
(*求各单层刚度*), \8 C. G( T+ q0 z& W' r( |9 d
agk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)
' g) d) @# O5 S6 M' W
8 S- W) u9 v* l% d! S7 |! j6 o8 q! g# A$ k
ck = Cos[agk];(*列表求各铺层角度余弦*)3 I8 O- D" y9 J: Y5 ?
sk = Sin[agk];(*列表求各铺层角度正弦*) z' B2 t3 ~0 F% v
s11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +
' T/ l" h B: [# {5 M7 \ sk^4*Subscript[C, T] + . d+ [ t U8 |
4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)
! E# ]' H2 J( j/ s- _% [A11 = \!\(# _' t5 D5 ]4 i. F+ y; `
\*UnderoverscriptBox[\(\[Sum]\), \(k =
k1 a9 X. H. N 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*)% b4 z; ]: C. B
A21 = A11' `4 V4 [. i2 V# C
A31 = (\!\(
( L: ~2 \: Y1 Y/ S1 P( L4 B\*UnderoverscriptBox[\(\[Sum]\), \(k = 0 h; y( v& N/ P3 v3 C
1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)
" }6 w5 J0 A7 i- OA41 = (\!\($ \* T! Q' @* n, g1 l
\*UnderoverscriptBox[\(\[Sum]\), \(k =
% e, {( g5 [6 ?/ D, K, f% h nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)
) t5 X" _, _& G; s, ^8 L" s* \* v4 E0 p* V& t
* k( C& U* {4 j8 ^. e: C' n e/ Y
Print["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)+ R/ |1 s9 X9 S: f7 O
D11 = \!\(( m7 t, u6 X$ t* @" ^
\*UnderoverscriptBox[\(\[Sum]\), \(k =
1 z" @; {6 Z6 ]0 u% t3 d 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
9 C7 O4 C: i. |0 q\*FractionBox[\(t^3\), \(12\)])\)\)
5 m/ R, [! H* v0 m7 S, w, qD21 = D11
8 r0 F n% B* Z' {2 {4 ID31 = \!\(/ {% w8 k5 |- }2 o# V5 _( ]- ?
\*UnderoverscriptBox[\(\[Sum]\), \(k = , }8 d& Z: @% `! u' N
1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*, B0 @5 a7 p" i: q) M
\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)+ A. B4 ?2 Y2 N3 Z( W
D41 = \!\(8 ]2 o! s7 e5 e
\*UnderoverscriptBox[\(\[Sum]\), \(k =
0 r' R+ a% z' ]" ] nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
" _; r1 s/ y& s. e: N; G4 ]\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)
1 [5 q' z5 L" @: d9 i! Wk1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \7 O& z- i$ {; q
3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;: t/ G4 [( i5 X5 G+ q1 U
a1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(
% V; `% Q; ~5 q$ S c DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(
( B8 d4 V: b$ `, j9 \7 S DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);: p% v* T9 P* [6 S- e! h
\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \4 \% Y% r( u5 }% H
= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];
& R* U0 b) _( d- F7 B' ^b1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \
2 V9 b& J6 P) v3 I9 F8 |$ g1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \
1 w) m u2 i1 A6 L; z5 Z' ]) USubscript[l, 2]/Subscript[l, 4];/ S1 E) t9 n5 N ^- T3 i
DD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);
& j m0 l5 q3 ?% e% g6 D3 d; h3 L) |& cDD4 = D41/(A11*h^2);
S/ j' l% i Rr11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[
4 Z3 @$ m8 u+ W# I7 h a2*\[Omega]^2, (4)^-1]; r13 = Power[
& b. `! J* r; f9 |% l' G a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];9 s/ B; k/ h: ^5 b* m8 `
BB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},6 e$ ~+ P& K5 Q! i+ f+ @7 `; I+ v
{0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},9 ?! }" Q$ H! [: U
{0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0, 2 x3 G( m& L* ?/ I, {
Sin[r12], 0, 0},6 m8 d/ p7 R# W
{0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0, , C$ W$ [7 C; g1 S1 p$ f! i
Cos[r12], 0, 0},
3 R) P n( A( ], z! V) x {-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11],
9 b$ T5 W) F2 w4 Y* a1 v7 x) H+ l( s 0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,
+ X8 j9 N# u2 U4 N- L! J -(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0,
( Y j2 G S9 K 0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11], / z% W3 s2 w; ~" S& ~6 o& m: J/ m% t
0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*
9 W( E2 h5 w( p& Z0 g3 f DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},
8 \- M' w( v( z, V" @. R- Y+ } {-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0, ( x2 p6 \% o# F$ K, \4 j" V
0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11],
6 E2 g4 {; ?8 I6 g 0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*6 \# ^$ q6 \; K3 ~( m
DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,
! P, m$ E0 ~2 @, H4 B (r11)^3*DD1*(\[Beta]1)^3*Cos[r11], - U4 X2 V! o' V# B; ~
0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3},
2 g K( M* T ^9 s1 Q {0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*
7 Q: O3 c D- V/ \0 v* H4 y Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],
H3 F9 ^0 Y3 w# @2 j 0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*
F' N0 Q7 l8 A. ^$ F6 o# m! j# E/ W* a Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,2 n( p# Z) Z4 ~" _
-(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*, u! j( r, S' a$ e5 Q8 F3 J
Cos[r14], 0, 0,7 S$ N; k9 B" V9 t, ]
-(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*
' L& v( i/ D9 ~/ A4 V N1 E Sin[r14]},
" |* S8 N3 ]" @& F9 u {0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*
0 Q' u! n0 b$ k, G u+ V, Q" r5 e& }& q Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,
- D4 p) ~/ Z# P: H) o/ \ (r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*) l# l- a* ?9 L: i1 j
Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],& y. |* h! N( {+ |$ I9 R
(r14)^3*DD4*(\[Beta]4)^3*Sin[r14], 5 r( n: I; D8 Y: D; T' p
0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],' {& ?* P1 ^6 U8 `# M
-(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},- @3 E% v$ x5 n" J, C3 t
{Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0,
+ X) o- ?/ J$ D) Q J! R1 O- w Sin[r11], 0, 0, 0},
! t# r$ h- S6 S- c5 s1 A" Q {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1,
: Q( W6 @. J/ z, W/ W1 G; K 0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
9 Q" A H2 p- a9 l 0, -r13*b1},, k. g6 c& b2 A8 k# v, F
{Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1, / V/ [- L! W) |4 M8 o
Sin[r11], 0, 0, 0},) j) M6 A" n2 e% M8 K
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, 4 W! L4 @* ?2 m2 k* V" H: Z
0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
5 z9 p. ^$ E5 {& {( d 0, 0, -r14*b2},: o* {3 E1 h% C4 U# O
{0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,5 n3 U4 w$ `: j
0, -Sin[r13]},. F" s0 x! O0 v
{0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0, Y/ m' `; K( N9 Y* x
r13*b3*Sin[r13],1 @; S# z5 c3 {$ F- |1 a1 b
0, 0, r12, -r13*b3*Cos[r13], 0},
& m+ \* O+ p2 V3 Y; j. p1 T) V {0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,% X3 G4 ^6 n5 X# J. l
0, -Sin[r14]},$ Z4 h5 n9 J" j8 C& U/ b2 o# V
{0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0,
; t# m4 U& i% A' k: J) H' r% ] r14*b4*Sin[r14],+ _5 W9 }1 R# H* o; j
0, r12, 0, -r14*b4*Cos[r14]}}
7 E6 U: ]5 X7 H7 n6 ~* y6 C+ uaa1 = Det[BB]$ b9 ]% ?- K) N. [
Plot[aa1, {\[Omega], -10, 10}]# W8 c5 Q3 q' i: x( T
ss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]# g& D1 m; ]$ T- E
: w# _0 z& ]5 H9 u' d- t/ u' z$ @0 B |
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