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本帖最后由 游龙游龙 于 2014-7-8 14:45 编辑 # P" D5 v/ j- I5 A5 _0 [6 n2 e
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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" l0 y& k* G% C- }$ @1 W
行列式求不出,画图找不到根$ ]2 o$ X' p7 B9 e, D6 T6 F
(*定义材料常数*)
0 e3 t6 q* h; w2 k3 S: ~Subscript[\[Nu], TL] = 0.25;
1 G. d" X6 q I$ c- K0 oSubscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)9 D7 F2 x8 g& H2 Z' g
Subscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)
5 t1 v) L/ m% VSubscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)
; T) ]9 D) L1 h# @( M# O8 B- N. s" ^Subscript[\[Nu], LT] = ( ^6 d" C) j- X- [" B& B
Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];
. Z M- f/ C1 T' H& J/ ?* n\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];
2 G p: H* ~$ FSubscript[C, L] = Subscript[EE, L]/\[Mu];
, z* ~# B5 O2 U+ m+ \8 @" {# L2 uSubscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];1 K& l: v4 m$ K7 {& S# ?
Subscript[C, T] = Subscript[EE, T]/\[Mu];/ n! b2 l. Y2 a+ }0 t
Subscript[C, LT] = Subscript[G, LT];
6 @2 O u. e( q8 x/ A(*脱层几何参数*)3 B. {- c$ I" ~+ x; m" {
\[Rho] = 1600;(*脱层密度*): O+ E% y- g% f/ n
c = 0.06;(*阻尼*)
% U' X. c4 k: |0 f9 ut = 0.01;(*t每层厚度*)
. {, Z# Q3 h' f: U8 Fh = 0.05;(*h为梁总厚度*)
$ i( l/ [0 d- q1 k3 |" Tl = 1;(*为梁总的长度*)
- _& u5 J* T7 l6 Y1 E4 x0 OSubscript[l, 1] = 0.3;(*为梁1区的长度*), c! d; k. O0 f, v8 D
Subscript[l, 2] = 0.3;(*为梁2区的长度*)8 h9 A* y" W" e- P# B! i! K
Subscript[l, 3] = 0.4;(*为梁3区的长度*)4 Q2 e5 F, h v$ q: y9 \2 u) N
Subscript[l, 4] = 0.4;(*为梁4区的长度*)$ C" @5 v9 {3 N2 f+ f. C! L
nn1 = h/t;(*nn1为总铺层厚度*)$ g2 D' C9 ]% t. m. U$ i
nn2 = 2.0;(*为上子铺层层数*)
6 M% Z$ D7 u: V' \6 _nn3 = h/t - nn2;(*下子铺层层数*)
8 s p U! a8 q0 aSubscript[h, 3] = t*nn2;(*梁的上部子厚度*)2 V4 t9 ? C. b* F6 y' ~
Subscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)+ ]) k: o% o1 d$ P
Subscript[h, 1] = h;(*梁1区的厚度*)
& b+ \2 c& S) _' ySubscript[h, 2] = h;(*梁2区的厚度*)
" G. v3 f+ V- r! m2 F, i W+ T(*求各单层刚度*)
- i2 v% k7 {% P+ J% |agk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*); Q1 a- t, d* P) Q
{) y6 j8 a' f# ~9 P8 ^+ Z( J
; e9 P, n# l8 ? e9 @/ D7 rck = Cos[agk];(*列表求各铺层角度余弦*)7 V( q0 ^& Y. j! {9 f8 g
sk = Sin[agk];(*列表求各铺层角度正弦*)! d3 `- r, C& y6 b1 ?
s11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +
( `. }# b8 t6 T% c sk^4*Subscript[C, T] + - ?! w' {( L: a1 H" D$ K7 @
4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*), @: l# F* t! O* b+ r) b4 w
A11 = \!\(
5 [) [3 Y, j( |4 a+ q\*UnderoverscriptBox[\(\[Sum]\), \(k =
! I2 U" x, J$ G0 w& M- z$ m 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*) k5 m1 A4 w- Y; D1 _! b
A21 = A11& o N1 ^/ f: b5 J& _" H
A31 = (\!\(7 B7 Z/ h+ n3 u4 @& R' F
\*UnderoverscriptBox[\(\[Sum]\), \(k = ; b, T6 {8 {- i6 O! ?+ P- i5 Y
1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)/ _- x3 K3 }" {$ N& ?* _( v0 x: B
A41 = (\!\(! Z1 K2 @* |* N8 d5 w
\*UnderoverscriptBox[\(\[Sum]\), \(k = ( w! D+ ]- M: `
nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)
- f) v9 J, U/ A' c# o6 l' D& \
, S3 `0 r% q2 u6 @" P( b) V
" q# ?: m5 {( c# f) q3 g3 l% N. o8 `$ mPrint["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)
0 s+ Y. Y3 p3 Q6 g: j# M. JD11 = \!\(. o! S- E# u$ d1 s$ s H, }
\*UnderoverscriptBox[\(\[Sum]\), \(k =
' A+ M( V3 b9 E+ T4 l: b" b4 a 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
0 o: ]6 q. N. _( H! M2 ]\*FractionBox[\(t^3\), \(12\)])\)\)
1 s8 ~+ ]* C' Z: bD21 = D11! i7 W, |7 z8 ~
D31 = \!\(
& _+ Z* u! }8 V$ ` Q8 @\*UnderoverscriptBox[\(\[Sum]\), \(k =
7 C- p& A/ m! ^9 `- e7 H 1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*$ x3 K) p! s1 Z. z" X* z! Q! w2 ?3 Q
\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)
) G, c6 t: M/ A2 h/ H! qD41 = \!\(
( ?0 p4 y2 ?3 _. E6 J\*UnderoverscriptBox[\(\[Sum]\), \(k = 6 s* W- m8 m) a8 K, s( ?4 l% a
nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*$ G _6 B3 z" z
\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*), x- V- a4 `4 @( O3 ~
k1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \
- x8 `. ~& j5 _( Y1 ^* ^" q5 Q! u3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;$ a9 V: O8 O% t9 m7 G# f) Q
a1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(# z. y" k1 j2 U. B l+ ^' n
DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(
3 [: i/ ]9 f, \9 V/ g$ v# s DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);7 k/ H) }: P7 s4 f! W
\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \2 [+ e$ |7 F7 D. c8 m* }
= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];
$ Z9 X j9 r) S, d+ t. pb1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \
# D+ O/ e. k: ~4 L' d1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \3 K: D7 c. F- w2 Z" G5 L! n
Subscript[l, 2]/Subscript[l, 4];- o# X6 H7 ^' d) t+ L
DD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);+ r2 V; N+ s: h7 ?$ C8 s+ {1 \& v
DD4 = D41/(A11*h^2);( P6 h: }6 [2 O' U1 }% g
r11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[
( F' l* ?+ r& z( m& {% E, f a2*\[Omega]^2, (4)^-1]; r13 = Power[! W' L8 q% k& _5 K. P/ N2 n
a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];( }. j6 D: Y4 A& A- F: k8 `% b& d
BB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},; j( w2 T3 @) ~: [
{0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},
# V5 n8 H4 a" @, N6 f/ M {0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0, 9 ?6 O G4 z* t) @1 d/ i
Sin[r12], 0, 0},, Q+ L* l$ W/ F
{0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0, 5 ~9 K4 }! a1 C1 c9 s
Cos[r12], 0, 0},
s1 v/ F% E& E1 L' [( v( H {-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11],
2 H4 v3 a/ ^" r( ~4 c- _3 K5 T 0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,6 {( _- `/ W* F! [
-(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0, % c. j; t" f! R* N q! n; v
0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11], 1 C% H4 {$ V1 w" V0 s2 F
0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*
" u$ V, u: M% d DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},
# b, O6 l" [, W7 D! Z6 O {-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0,
7 J$ V$ ]$ U$ ^: w j8 g R 0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11], $ V7 ?3 P7 o5 H, W6 J) i6 F
0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*
1 X2 m: t. d# H$ L# e DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,
8 N6 S- }' Y: Y" @' o! M5 B6 C C (r11)^3*DD1*(\[Beta]1)^3*Cos[r11],
8 `0 G1 @: Z: D9 f @ 0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3},
9 F* V, f- ~; x, \0 _- ` {0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2* [8 C9 b" F- }# \ Q4 K M( r9 X/ _
Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14], \1 I4 {7 j5 h: m3 E
0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*3 s% d/ T0 c @8 o7 d
Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,
" D! l6 ^: w9 r2 l8 n# C( E; } -(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*, ^" O I- p3 a5 H6 n/ S3 r
Cos[r14], 0, 0,/ j+ ]1 t, l0 Q3 J
-(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*
, N. r) y3 L3 m! U; X, b6 C Sin[r14]},
: u/ ] _$ T" J2 w+ h7 I1 [1 X9 _ {0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*
2 B6 L( J0 B; V6 Q6 L2 X; m, \ Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,
0 ~ \# R5 w. r L (r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*2 U' S) u3 U3 ^8 @
Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],, t3 j) z& y: |; U
(r14)^3*DD4*(\[Beta]4)^3*Sin[r14],
+ ]; P- x6 g; W- x% K/ k 0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],
+ l, O9 B7 P/ Y/ _& v# L+ I& d2 N -(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},
' p5 l8 _" e% j! l5 |, a. s/ K {Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0, ( n2 Z N' ] Y+ q( @
Sin[r11], 0, 0, 0},6 m: Q. B. q( [
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1,
: n/ J; }/ n4 T4 r 0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],# Y) Y- W& \0 R3 ?4 R( l& s# q
0, -r13*b1},
! @; Q$ I+ D# _" @, j5 q1 Z {Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1, J. ^/ Y. ~5 y7 d9 [) p' w
Sin[r11], 0, 0, 0},
! i/ p8 C8 i8 {5 T) q {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0,
3 M' k9 b- M& G+ {5 k* c 0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
4 B( z. s/ b& V! g" _ v 0, 0, -r14*b2},
& g" f4 b+ I. V$ N; m {0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,- h; u* K e) e5 O$ q6 |3 r
0, -Sin[r13]},
2 I+ |; R1 s G% p) Z; U2 Y3 ~ {0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0, ' q6 R* F/ F/ {, f+ E. n
r13*b3*Sin[r13],6 \; Q( q& y/ l3 w5 g: Z
0, 0, r12, -r13*b3*Cos[r13], 0},) ?* i$ R2 u0 K. J$ I6 `
{0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,
7 a2 ?3 j+ [- \6 `+ }' u 0, -Sin[r14]},
5 R2 D. u' H1 I1 `( o) y V0 d {0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0,
: f/ m. R, u. z& z5 B* g) i& e, n r14*b4*Sin[r14],4 u3 l9 O& g9 `1 Y( Z
0, r12, 0, -r14*b4*Cos[r14]}}* q* n, ]" \2 t1 K& N/ }3 a3 T
aa1 = Det[BB]- `1 J8 P1 |- P0 q* `1 y/ S1 b5 g
Plot[aa1, {\[Omega], -10, 10}]& H( Q$ r. D# U f7 n& A: P
ss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]
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