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本帖最后由 游龙游龙 于 2014-7-8 14:45 编辑 2 B1 Q# L4 {( z6 B
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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
' `- G1 f c5 s' z行列式求不出,画图找不到根
' c9 q4 w0 r% a. U7 B' g& r, ](*定义材料常数*)
4 ~* T+ z7 @ Z2 {& y6 G7 TSubscript[\[Nu], TL] = 0.25;! _5 j, f0 W2 ~( O
Subscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)
$ _% ~7 i; |& p7 [, X5 hSubscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)
4 @2 z; c! n3 s- @; O: T4 [5 c4 nSubscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)1 M8 P, E/ V! S R7 K" o# O
Subscript[\[Nu], LT] =
1 r L; x1 p8 _$ U8 G. v Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];! g c' s0 g1 `/ W$ U
\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];
9 ?# g. G. i3 SSubscript[C, L] = Subscript[EE, L]/\[Mu];
& V' E4 W$ G- W1 f' OSubscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];3 x% O4 Y, {8 H' w) I
Subscript[C, T] = Subscript[EE, T]/\[Mu];
0 y! X9 O. I7 w& E1 ySubscript[C, LT] = Subscript[G, LT];
3 x3 ~1 [+ o$ v$ p6 ?" R$ O4 ^1 s(*脱层几何参数*)8 N" W0 f/ Q/ x
\[Rho] = 1600;(*脱层密度*)/ b$ n' l0 ~# P0 @
c = 0.06;(*阻尼*)0 B8 s& j! s/ ?+ D
t = 0.01;(*t每层厚度*)' n5 S" t$ O1 i3 p! @- A' Z
h = 0.05;(*h为梁总厚度*)
( Q1 A: q+ \. j: b% nl = 1;(*为梁总的长度*), d) l+ K# \, `! {' \
Subscript[l, 1] = 0.3;(*为梁1区的长度*)
0 y7 t: ]# ~" U# e }' W& b4 ZSubscript[l, 2] = 0.3;(*为梁2区的长度*)
4 _; h# H/ z8 c1 {& H+ YSubscript[l, 3] = 0.4;(*为梁3区的长度*)( k' ]2 W r, p$ e- L! u
Subscript[l, 4] = 0.4;(*为梁4区的长度*): i8 _& H9 ~( d9 S7 H8 W
nn1 = h/t;(*nn1为总铺层厚度*)
( Y/ t. A" r+ j/ Znn2 = 2.0;(*为上子铺层层数*)
& k& u. p# T+ r1 U; D( m0 q0 |nn3 = h/t - nn2;(*下子铺层层数*)
* b% D3 z4 b! C8 }: U1 {; w; ~1 eSubscript[h, 3] = t*nn2;(*梁的上部子厚度*)
4 l$ K+ w# V/ D; K8 V$ a USubscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)$ E% C6 Y h, E- s* ]; k
Subscript[h, 1] = h;(*梁1区的厚度*)# ]" k9 \6 ], }! J- m0 p- ]7 K1 o
Subscript[h, 2] = h;(*梁2区的厚度*)
2 c: z2 a- Y. y( I0 L0 R3 T(*求各单层刚度*). B1 p. R$ U7 J' c1 t; l. r# e
agk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)
d0 b# i- f& M2 _9 e' o
! |8 M$ J d) a$ {6 a* {/ I$ y3 a& n9 r
ck = Cos[agk];(*列表求各铺层角度余弦*)
% z/ X/ d2 H) G8 jsk = Sin[agk];(*列表求各铺层角度正弦*)9 [* v8 e( H; H7 F+ p
s11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +3 ~$ I0 ]8 q: J
sk^4*Subscript[C, T] +
/ |- P7 Y# c1 u- O3 u" z 4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)3 Y J0 Q* a' L! P2 ^8 d
A11 = \!\(
; \( T6 ^5 T' q& Z2 w\*UnderoverscriptBox[\(\[Sum]\), \(k = ; P; Y# D" z' _, T) s( y
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*)
+ O% `3 {2 R, D5 fA21 = A11
0 Y% z! h, F# Q' WA31 = (\!\(
c9 c. e; t- C' d3 N\*UnderoverscriptBox[\(\[Sum]\), \(k = & b% ?+ J2 R, c6 s8 f
1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)8 a7 X1 _- I# [5 h; _% }
A41 = (\!\(+ }* j( x, o$ W) x( T) |+ h g
\*UnderoverscriptBox[\(\[Sum]\), \(k = m2 c* m# Y P" L, g
nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)
8 V! X$ s* P' @. a N& Y; e+ q
( m7 i1 v5 r3 O/ ~
5 R7 m8 a2 U2 Z: g$ mPrint["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)
8 J! H, D! u$ j; _4 |& Z. XD11 = \!\(
( |$ T; v% V' [2 j0 A+ \\*UnderoverscriptBox[\(\[Sum]\), \(k =
9 V2 s! u" y! |0 I& Q 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*( p2 }) ]& N- M0 w1 s
\*FractionBox[\(t^3\), \(12\)])\)\)
" X/ S) R* K: x2 V" X+ kD21 = D11
2 m1 u" C2 u* ]' k" G9 L2 LD31 = \!\(
N- M I4 ^6 x; b\*UnderoverscriptBox[\(\[Sum]\), \(k = ( e- [% |! G5 I) E# k
1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*
; k. x( Z( T0 m" I\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)% F6 \9 @$ P- S* {/ W; k
D41 = \!\(5 [& @2 Z# f! b* w$ B/ k
\*UnderoverscriptBox[\(\[Sum]\), \(k = 1 n8 J$ d S/ V' g! `3 E
nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
8 K" F: l' h& p; K3 w$ x\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)
: C9 D @* ~) \0 E4 Y3 a! l7 `k1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \8 ] J: d$ v/ e2 j6 |
3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l; H# h* C. D" }+ d! p1 c
a1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(5 _9 R: w6 g5 ~2 P7 [& I; T6 c
DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(
8 X$ M) P4 h) }2 j- j2 Y DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);" I L9 w; a0 ?- j* S
\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \
* i1 n9 }2 A2 O5 ~$ A= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];
l$ m0 W. s1 B0 c" Mb1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \
( Q5 [$ W4 n& r5 ` k& I/ \6 h1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \5 s2 X% o0 B1 A: V
Subscript[l, 2]/Subscript[l, 4];! i% p. Q: J4 C
DD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);
% B" ~2 }% K) g+ H5 L) Y4 |DD4 = D41/(A11*h^2);1 V4 P4 _+ K# _2 a
r11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[
5 ~" M: p4 e2 @$ I a2*\[Omega]^2, (4)^-1]; r13 = Power[
4 U' }& ^, Y7 s. a1 _1 s* `- h( t; ] a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];, [9 w9 m" f: s6 }" n, {5 p7 ?
BB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},0 c) i( a4 y+ i" |* U
{0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},
2 e; a. }5 `6 g' t5 a7 M" z$ s& A+ q {0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0,
& t# c0 M, W8 e9 | Sin[r12], 0, 0},
- ~* L" W4 Y3 I* i( v$ {, y" u( m3 K3 @ {0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0, ; }# O: _: g& B! I! s" K
Cos[r12], 0, 0},2 ?4 P% n9 i- M2 O+ u! f
{-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11], 4 F/ k0 O- t% M! Q! t3 L
0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,1 t/ Z' C7 G7 z- X
-(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0,
$ f- w6 u3 M2 l) T5 x/ i# S& n 0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11], K" z* L' ~# N- _ t
0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*
- |7 U6 P4 C) \% q/ T; y3 j9 @0 ` DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},+ F: C+ b( P$ V* ]: Y
{-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0, ) j5 m2 M) m; d2 X
0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11], 4 h: A. M, S2 u0 u* Q, \6 |& z* [1 G, \
0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*2 ^* ^/ B# R& A6 G
DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,- W$ U2 F# Y+ |: ?' U4 [
(r11)^3*DD1*(\[Beta]1)^3*Cos[r11], ' I, Z8 w+ f) h0 F( Q+ @( G
0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3},* v& d/ K% ]" j) C/ q
{0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*% W# U2 z& c/ g* |0 W4 p# }
Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],& S! g; q1 m0 @
0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*% ~0 N' y1 f& {4 ?0 h
Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,
; E5 m/ n) I O3 i0 L9 X$ o -(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*: {: q! c! D! H) r
Cos[r14], 0, 0,
! l8 ?2 A, i, ^/ G6 p X% L -(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*5 }+ q9 j" R% c2 ]4 N9 I
Sin[r14]},0 Q2 w! K5 [' G0 U
{0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*
$ n, W( Y2 h3 S3 g' U Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,5 X" N L" |- |4 A4 {- w G
(r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*
: _! c2 u) t7 t J: K' _ Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],
/ f x S. t* H3 g0 ~1 a# c, G (r14)^3*DD4*(\[Beta]4)^3*Sin[r14],
$ ?9 u L2 O+ c/ f; i. t 0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],
: ~7 @3 B6 s$ v. r' e; p5 [1 t b" { -(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},
: z4 K; [1 e# P2 ?& f; l {Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0, 2 l& f+ G2 C9 ?4 @* E2 P+ t
Sin[r11], 0, 0, 0},5 s9 L( ^/ w$ B$ G% m, L
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1,
' o- M7 U% F) `$ s; ^& O 0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],: S3 t9 J" k7 a# k# @/ D" x: N, M$ k
0, -r13*b1},8 S8 i7 @* o# r: N4 f! t: z! d
{Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1, 9 q- p5 U F- W) S& a4 l0 R: ^
Sin[r11], 0, 0, 0},
9 R P; j, t" W0 a+ b% g {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, p) b0 s7 V( b) p: @9 I. a; f1 r0 R
0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
0 k1 L; m/ ], ?' f 0, 0, -r14*b2},$ ^5 A) M# ^' s7 q' W8 U
{0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,0 R2 ^# u- C9 \$ n
0, -Sin[r13]},
* P3 Q. F& y6 ?1 q) J {0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0,
$ w: Q9 b% p4 `" T r13*b3*Sin[r13],
" f( b0 k7 ?. x 0, 0, r12, -r13*b3*Cos[r13], 0},
! r5 j. t) g3 k1 v) L1 L! ~. K {0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,
+ a! @% c8 _0 F 0, -Sin[r14]},1 \ l! X" Z. z! m; u' `
{0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0, / p3 c' k: j1 f% p# F% ~" v
r14*b4*Sin[r14],$ ]- G% f5 a# O; S/ r% G
0, r12, 0, -r14*b4*Cos[r14]}}
3 J# j: |6 A) ~$ Aaa1 = Det[BB]
1 ^" t* z8 F4 g2 W, ePlot[aa1, {\[Omega], -10, 10}]
4 j9 U4 u9 m2 w% |9 d* |5 }, @" ~ss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]8 R* |* P& H- }+ _
5 B ?: i( E. ]! v [
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