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本帖最后由 游龙游龙 于 2014-7-8 14:45 编辑 8 Z4 w1 b# {. G8 t" e: ?* [' A
7 z& Z6 m, N% V2 c; m' S' ~& n ^* s) E
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
9 q1 V! `2 W A# a, c0 ?行列式求不出,画图找不到根/ ], i- {. I* y) h: E/ P
(*定义材料常数*)
8 S, g0 y) I" \0 L" GSubscript[\[Nu], TL] = 0.25;
L! \$ H9 y5 V) A2 @Subscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)
8 _) ?" ?/ ^! g/ |/ w+ H- I1 \Subscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)
* L2 w# {' [+ y/ ?% ^ a5 GSubscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)- L. _2 Y) |# X2 @) l
Subscript[\[Nu], LT] =
' b, n. j4 s. R1 x g Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];- p" a0 G7 V" t, c; ~* n# M
\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];
$ o1 ], |% ~, ]; m4 {, fSubscript[C, L] = Subscript[EE, L]/\[Mu];' J( Y; p$ a, |& s
Subscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];
3 ~/ W; V/ ?' iSubscript[C, T] = Subscript[EE, T]/\[Mu];
' v. ~* }/ x' f3 k# d8 ?, ^Subscript[C, LT] = Subscript[G, LT];" o. |0 o+ r' s# r+ Y) D
(*脱层几何参数*)
) _8 N: ]3 Y9 T! |\[Rho] = 1600;(*脱层密度*)
# R0 G, E9 Q) { [- n5 Hc = 0.06;(*阻尼*)" B4 @8 W0 s9 d& t3 x
t = 0.01;(*t每层厚度*)% b# p2 |6 F1 |8 {% b9 _" H
h = 0.05;(*h为梁总厚度*)
2 G& ^& B& B1 c+ U" L9 bl = 1;(*为梁总的长度*)) s, v% V6 Z: I; G9 V6 a( x
Subscript[l, 1] = 0.3;(*为梁1区的长度*)
, U: W' x0 x+ e7 W2 P F9 x& v5 L2 FSubscript[l, 2] = 0.3;(*为梁2区的长度*)( [7 G J) q# {# L- m
Subscript[l, 3] = 0.4;(*为梁3区的长度*)9 E: f' Q, D3 A7 j h8 C4 f4 G2 P, K
Subscript[l, 4] = 0.4;(*为梁4区的长度*)* M* @' g( o/ z: q; n Q
nn1 = h/t;(*nn1为总铺层厚度*)
: x) j0 W- h2 T4 c; |/ Qnn2 = 2.0;(*为上子铺层层数*)8 F8 y8 d+ ~$ ]0 S. [7 k# K1 J
nn3 = h/t - nn2;(*下子铺层层数*)9 v* }# k9 c6 b/ F
Subscript[h, 3] = t*nn2;(*梁的上部子厚度*)6 ]: g. L- V/ a; j: J# S8 g. K
Subscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)6 K3 {8 N, \- W( t
Subscript[h, 1] = h;(*梁1区的厚度*); U" p* W$ h2 ?8 u2 Q
Subscript[h, 2] = h;(*梁2区的厚度*)! _" o8 p4 D' I, k8 L' e5 Z0 @3 n
(*求各单层刚度*)
x& s7 v& a* U+ uagk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)
- ^+ U+ F" i" i, d0 S- I
7 Y6 a$ `) K8 q: @7 I8 J
0 e6 r% I" [ s1 T7 F0 ick = Cos[agk];(*列表求各铺层角度余弦*)) T+ u1 B/ @* a; t' c% R
sk = Sin[agk];(*列表求各铺层角度正弦*)7 @! q4 e4 { W
s11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +0 @ U% ]% b# Z* c
sk^4*Subscript[C, T] + / D5 E9 g( H' r5 m
4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)
|: V/ A- B- eA11 = \!\(( |" h3 ]. I; g3 k7 X! `3 ?* C! i+ m
\*UnderoverscriptBox[\(\[Sum]\), \(k =
4 w( u2 ^6 {1 I+ ?0 ?: E9 Z 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*)/ A# Z9 e2 E* q$ j* o! K
A21 = A11; ?1 M6 i; y' k( n8 [
A31 = (\!\(
* D8 a5 N- i6 Y1 |7 I\*UnderoverscriptBox[\(\[Sum]\), \(k = 6 G( |7 V# m/ K' ` S; T
1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)
, S: W% q/ d7 M& n: _* YA41 = (\!\(
0 u- p6 M" e) s7 a5 `5 ?\*UnderoverscriptBox[\(\[Sum]\), \(k =
" [2 K3 v' L! ], T8 k$ ~ nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)
. _2 b0 p0 a; A& A- I3 L; v) r( J( d0 t8 U$ ?
" P0 h' @* v6 a; k) l/ mPrint["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)' W' z" b, |" [ B3 O( B( T5 ^* r
D11 = \!\(: }; ]' P' S4 k5 l% [$ H( \% E
\*UnderoverscriptBox[\(\[Sum]\), \(k = & M; A7 |6 R4 z* H, o) h' L( O
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*, d+ f7 O! ^9 r+ ]2 D" {
\*FractionBox[\(t^3\), \(12\)])\)\)* \2 w" s; O1 C' @( A* F$ ~4 Q/ K
D21 = D11
/ T, C! O/ x4 i e+ Q: {5 V% SD31 = \!\( q( Z9 }, ~+ [6 E
\*UnderoverscriptBox[\(\[Sum]\), \(k = 1 o, ]% i1 F$ q7 I4 F
1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*; d, s9 z7 b, s! V
\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)
1 A* V- j5 ~; aD41 = \!\(- M8 J6 ? w- N5 ~4 V h' P( h
\*UnderoverscriptBox[\(\[Sum]\), \(k = 5 ^. K( R+ Y' P( a
nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
6 B1 _5 Y9 C( d/ h8 D$ ?. G. X\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*); M: |& X. ]$ e/ t
k1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \1 o4 d3 j# P; k6 D
3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;
; |1 m5 P7 A9 U' F$ P0 Y8 Ja1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(
6 L. q0 W* t' Q% Z DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(
; [+ r4 v- x) m. e- { y; a$ U DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);
' ?5 t% `9 Y" J\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \- w1 I0 v/ n1 e; p
= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];$ J; Z9 F; y5 r8 M2 a2 H, M1 M
b1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \" R1 W; M1 s' J# r1 ^8 L+ J
1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \
: g4 E- f# G) o; z8 v& D1 FSubscript[l, 2]/Subscript[l, 4];5 b6 C X# a$ x6 o" X
DD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);+ C- j/ b8 x0 u+ F/ q; u
DD4 = D41/(A11*h^2);4 S4 `* K3 U: j5 O G/ [
r11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[; Q( W' K4 Q6 W7 u
a2*\[Omega]^2, (4)^-1]; r13 = Power[ \: W5 v& }1 X8 `- k+ N
a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];9 m4 X$ J' M3 ~1 y% x; e, s, K# z
BB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},
) ^2 b& {9 {, d! h {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},
5 n9 w* K, _) j/ D {0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0,
- U) h& g% k" y: ?$ B ` Sin[r12], 0, 0},
! w7 w% W' A/ ^6 E/ o4 d {0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0, % B% ]/ P* i# Q" u: e- u- X
Cos[r12], 0, 0},
1 x. T5 H9 j4 ^ {-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11], . b8 s' C" A' b: b
0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,- N- J2 d( C. ]8 L9 B$ s* j/ C
-(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0,
{: v; f+ k3 O1 f; J% s 0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11], 6 P9 [ M) R9 r% R1 S x
0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*% x* n+ m# j$ {3 B5 C5 W- P
DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},
* y4 h7 x% z# ^, z! X2 Q {-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0, 3 d1 q$ F6 D# d' w/ ~
0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11], ' b3 i5 t/ g; k0 H& z8 z- h+ ?/ U) l
0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*7 a/ U3 j$ v0 G7 S% f5 a
DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,
2 O/ F0 U1 b) R+ F* r$ C3 I* l( }; ` (r11)^3*DD1*(\[Beta]1)^3*Cos[r11],
5 C! R; l% g2 T9 Q c; y1 i 0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3},
7 ^1 _2 s) I# ?2 H5 ^ {0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*
4 {6 q4 d) c7 `5 V! ^. @ f Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],
, ]! G/ B! U# v: t3 k& J I! [ 0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*9 X6 A. s& ?' [5 d' g0 \
Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,5 N# L; B6 V& ^- {' g, s, k
-(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*2 h* I! R9 r( z# c" E# T
Cos[r14], 0, 0,4 j3 t8 k( c0 ~8 [& \8 P/ ~
-(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*
! Y' ]8 q- ]9 O9 F% G# n Sin[r14]},8 ?# s) X0 b. M \
{0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3* ?7 U2 s3 `, J: N9 c. n
Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,; s( K% e5 b! Y2 I3 }( R3 _
(r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*
; k$ _& H' P x; e$ q; M3 F' X Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],: i6 b7 J/ d6 y1 y0 M, @( e
(r14)^3*DD4*(\[Beta]4)^3*Sin[r14],
9 ~! |! x0 k4 V" s% S 0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],4 H ]0 M" U! p% K5 U# v
-(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},
& e) @- @3 e& u1 O {Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0,
2 ]8 B* ~+ C; x' i ^, V% L Sin[r11], 0, 0, 0},
+ t: ^# ~. o5 R% s/ C l) x {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1, ; [- b5 o, r6 Y. N. O
0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
: O7 K7 y+ g: ?# W* V C Z0 _) T) }/ g 0, -r13*b1},
. v, l) g( s2 J: m& n {Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1, 2 d7 {$ A6 B2 @% V$ H1 {
Sin[r11], 0, 0, 0},& b' ]( G5 y- F# R" U
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0,
* J/ I* Y/ x2 `# T, { 0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
8 Z: s7 V% _; @! b+ r 0, 0, -r14*b2},7 W* K, e4 f1 S' S1 Z# i D
{0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,
% ~9 J, l# w' l: l 0, -Sin[r13]},: L @& ^6 T/ Q+ O( \! n9 d
{0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0, + p- o5 S' o# n" N6 H! c+ x4 e
r13*b3*Sin[r13],
/ V4 u4 V* x+ V% o 0, 0, r12, -r13*b3*Cos[r13], 0},
. w) p8 Y- q2 c" Z' j$ q& h2 T2 B {0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,; W; y) d- @: ~# a8 s# P
0, -Sin[r14]},
8 S8 i8 `, g1 k {0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0,
+ x J' D9 o' Y' @( ~5 W r14*b4*Sin[r14],1 i1 O5 z; n2 {: a5 |
0, r12, 0, -r14*b4*Cos[r14]}}9 ]* k7 n3 v3 u
aa1 = Det[BB], f! w. l6 D# R: s$ t4 E9 `
Plot[aa1, {\[Omega], -10, 10}]7 E( J% u Z) N+ c" F+ }7 X) r+ V
ss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]& Z$ a, \+ E+ D7 X2 C
5 B! N' q( s8 M8 M* R; Z3 k |
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