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本帖最后由 游龙游龙 于 2014-7-8 14:45 编辑
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5 b8 N7 Q j7 Z) s: ^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) |. o, V2 f+ E* A6 F# }& Z2 C
行列式求不出,画图找不到根- ]* A/ X9 o0 d& N' A! Q
(*定义材料常数*)
# V( {% S i+ e3 ~! s0 |Subscript[\[Nu], TL] = 0.25;4 c# v1 G5 n' m0 [$ I5 c
Subscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)1 J6 t* P) v5 K
Subscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)
$ F, q& F% c! p: s; WSubscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*), y1 `% j+ q' W8 w1 ^' V. B" b; w7 Q
Subscript[\[Nu], LT] = 7 f* s8 _; b1 s: {; f" ?
Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];
) I: c3 v9 H% ]: {. }# q0 t\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];
* V5 K; [) j) l8 M1 v/ {( C9 ]5 W3 pSubscript[C, L] = Subscript[EE, L]/\[Mu];0 ~) e8 r H [# F- e* h4 o
Subscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];! |" l* B5 M- I0 N2 G& e
Subscript[C, T] = Subscript[EE, T]/\[Mu];
. A2 Q7 m/ [4 v( `1 D m0 VSubscript[C, LT] = Subscript[G, LT];% h4 w5 v: p5 @1 d& R* g5 E+ x
(*脱层几何参数*)
1 m0 L9 T- Y1 d" f# t# v5 ]\[Rho] = 1600;(*脱层密度*)
5 ]' n" ?3 f$ ac = 0.06;(*阻尼*)* n+ a% {. |9 v0 X5 _( ]! w% N1 y
t = 0.01;(*t每层厚度*)4 C$ D- i4 E" Y% ]( o# [
h = 0.05;(*h为梁总厚度*)
! K* [8 Z# z! ]) u0 H, H( vl = 1;(*为梁总的长度*)
. y f$ M9 B9 _4 ^- D) ]Subscript[l, 1] = 0.3;(*为梁1区的长度*)1 Y' f0 b+ k1 v0 B4 y- _( A! k' [* S; ]
Subscript[l, 2] = 0.3;(*为梁2区的长度*)
2 a: c6 K5 w4 O- M5 zSubscript[l, 3] = 0.4;(*为梁3区的长度*)7 T2 i/ b+ M8 @# F8 g) Q/ ?5 V( ^0 u
Subscript[l, 4] = 0.4;(*为梁4区的长度*)
' g2 b* e/ z, H6 z( h3 Bnn1 = h/t;(*nn1为总铺层厚度*)
8 ^& q0 f" ?1 p9 b G5 k& ynn2 = 2.0;(*为上子铺层层数*)
" M3 V7 N# u' o9 V1 v7 cnn3 = h/t - nn2;(*下子铺层层数*). |! t! ~& ]; s6 |- F' S
Subscript[h, 3] = t*nn2;(*梁的上部子厚度*)& f2 _7 r! R7 G
Subscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)
! i, j& [4 Y. u+ T, R! }8 XSubscript[h, 1] = h;(*梁1区的厚度*)
1 S' L0 V! ~* L R5 a8 }" {* R1 ^Subscript[h, 2] = h;(*梁2区的厚度*)$ Y& z0 P: V) Y- t( h
(*求各单层刚度*)
: _' a2 ~& w7 l0 }, Z$ jagk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)
7 F4 H# w, l& w9 M; a( B- [$ i u* j$ c' r" }" E
) L8 H; O$ H7 m3 X( F
ck = Cos[agk];(*列表求各铺层角度余弦*)' Y C; L, a, E0 G' X
sk = Sin[agk];(*列表求各铺层角度正弦*)
( X Y: Q- P8 S7 {' N+ _' `$ Js11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +
! ]" D8 _4 j) V# R: H# [5 @& h1 ^ sk^4*Subscript[C, T] +
- q, ?: o" n- _+ y1 Y. p$ j 4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)7 ^% O' O1 m I* {, l6 u9 K: t
A11 = \!\(1 C/ d) m$ \+ Y! A0 l% H) G
\*UnderoverscriptBox[\(\[Sum]\), \(k =
7 r ?, _4 H: K$ U- g5 R 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*)6 J! H2 O$ U% c8 ~& Z& t0 C
A21 = A111 `9 f2 b% l. @! W, }2 |
A31 = (\!\(* g9 s7 p. W( _5 H* J
\*UnderoverscriptBox[\(\[Sum]\), \(k = 9 w: ]6 _4 [ a5 D' G, T* k
1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)+ G E p- t, C4 W2 M& J/ m$ d, E1 l
A41 = (\!\(& C7 X+ K" Q. N* B: d, |: ~$ n
\*UnderoverscriptBox[\(\[Sum]\), \(k =
4 m5 H- i* |5 }; a! i nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)0 s% O z# L8 }7 G
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6 Z+ y3 T" @$ c+ ?3 w8 m+ O
Print["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)
/ p" Z" ^$ q7 I* j* dD11 = \!\(0 o0 C6 R4 ^2 }- e! \% k
\*UnderoverscriptBox[\(\[Sum]\), \(k = ! D$ ~" G: C+ C V; S7 r) d, [
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*; C5 S+ Q" v. a$ }8 F1 X i8 {
\*FractionBox[\(t^3\), \(12\)])\)\)
, M3 r w; X+ _$ _D21 = D11: p" e7 H9 u, P1 b( M
D31 = \!\(& \2 K* E8 T9 r1 e
\*UnderoverscriptBox[\(\[Sum]\), \(k = ( R' Z. X$ J* u7 S3 Z- X
1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*9 }+ l3 ~8 k# M# ~, m9 e5 r) J
\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)
$ v& F- L& f" k1 J6 k; b6 q8 f! bD41 = \!\(
; h c7 A+ z) L/ \2 `! c+ L% l\*UnderoverscriptBox[\(\[Sum]\), \(k =
( u: c9 S+ n \- `; C nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
! @- A: D! I! w0 u, j9 } M\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)
5 _3 x( l2 X9 L; n, w2 Z: ^k1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \
" ~1 y( v7 ^ \. V1 i* m3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;
0 G1 x" V+ X6 d, T! {9 Oa1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(* O, Z9 F" V2 P6 e, F( P0 t
DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(
+ H9 N2 ^, V, e0 [ DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);
0 p6 d" x& ^; o) M4 }6 O\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \3 f2 U6 U, h. r X
= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];$ x, \8 A& K! j$ ~* ~
b1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \
# e8 `# @ t& V$ T& I1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \4 B4 P4 `; K" }% h$ C
Subscript[l, 2]/Subscript[l, 4];
4 F! o. k! T/ j$ b. h& C2 Q5 a- T2 B, YDD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);6 p" D$ U: |7 ~( u& S8 c' J5 D
DD4 = D41/(A11*h^2);5 r" |( _; l. l- N t H
r11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[( H8 t& D1 G7 l! L- d
a2*\[Omega]^2, (4)^-1]; r13 = Power[$ G9 {0 Z) F6 M6 l" g, ^
a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];- \7 Y5 U& o4 o& e
BB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},% C; \6 ^( U6 e7 R; H2 F
{0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},
& O5 _8 h5 b" Q7 R {0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0, ) B* l J- {! A$ s
Sin[r12], 0, 0},
2 A+ o1 g0 y) b4 j! T3 q {0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0,
5 d+ e+ v/ ~' i, r3 w" ] Cos[r12], 0, 0},9 k! h5 t5 w4 c9 v0 p" W' c" x
{-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11],
! g8 X* `! D3 I6 A6 H2 }2 @ 0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,
5 ?# O5 D& t' P) y, z -(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0,
& h) j* e: o4 l4 V: Y/ @: y+ o 0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11],
# o; i7 `* v& Q$ N6 e* r+ a+ Q 0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*" K' N# F9 |' J! U$ W C
DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},. \$ Q$ A3 I* L5 u1 U( ?
{-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0,
1 G1 c( d! i u' Y, i+ ~& d% c 0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11],
+ c( J1 L7 X$ {, |6 V5 ]: o 0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*
6 s6 ?6 A2 O: l0 J DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,
, f- x* x( y! @4 f/ ] (r11)^3*DD1*(\[Beta]1)^3*Cos[r11], * o9 N* g5 m# x+ G" b
0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3}," q% f; h) _9 R" x
{0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*
: Q+ Q; ]- G* g+ n3 l Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],
. T9 s5 D$ f: B6 k2 e 0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*
5 c# e5 N+ Q [3 |) V Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,
9 _# k' N3 z$ H0 Z -(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*: N# G6 ^* s: k! i: b
Cos[r14], 0, 0,2 Z. [& ]' m8 E) M+ V* ^. |4 M, q
-(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*
0 P- S7 Y9 Z* ?6 R1 b4 K9 } Sin[r14]},
$ {5 U3 \% x, u# a; j2 X {0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*
3 f9 f, b. R8 j! P8 X+ G; n2 b( p Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,! q! N4 v. A" m. W2 Q* `
(r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*
# n2 }, c: i- j$ T( ~ Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],
# }) v o) j2 P% k9 A: ]4 E& P, G; V! D) x (r14)^3*DD4*(\[Beta]4)^3*Sin[r14], " Q0 V3 _( S& T* y g
0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],+ a* _0 r+ ?( C7 B( ]1 b& B n! m
-(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]}, w" w2 P8 }0 L0 L. L3 }4 y
{Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0, ' r/ \% v9 X' L2 r7 l
Sin[r11], 0, 0, 0},- D: c) c4 e% o8 r5 @* C
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1,
" Z, w p/ O! j9 x% [9 ~3 A 0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],: B( s8 z$ x$ K. u
0, -r13*b1},$ X1 v A0 [" s. n: C+ B
{Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1, + v z9 ^" Q, g$ W* I" O! r
Sin[r11], 0, 0, 0},' U; c' v2 R4 ^5 I
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0,
& J9 X) k3 `3 @* ]- D" a 0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],2 E5 g% V6 u V a6 o7 z
0, 0, -r14*b2},: |) h3 @/ g" n: Q/ K8 _
{0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,
" `1 m( R, Z1 `. C6 d8 A 0, -Sin[r13]},
) C3 D! d3 U$ G {0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0, 7 w, f- g! K# V. O) e, a+ B, ?: x
r13*b3*Sin[r13],
& l" L* i z# {! ~6 i 0, 0, r12, -r13*b3*Cos[r13], 0},+ z+ J7 H" O) @, N
{0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,
* F g6 P7 F) R# H; i# w 0, -Sin[r14]},( {& {% ~8 G; R6 X Z- j
{0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0, 7 F0 K$ Y# {* d) k) e/ j% V, m
r14*b4*Sin[r14],
# Z" [! ~) C$ M7 b/ O4 G8 c: D, M 0, r12, 0, -r14*b4*Cos[r14]}}
$ Z' w4 |1 `5 Q5 g9 F" y" @% H3 |aa1 = Det[BB]
h- ?& z5 x% a& a% WPlot[aa1, {\[Omega], -10, 10}]3 N1 e# |: n, z- h$ R0 M, a! y( @6 P3 L
ss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]1 @# M2 W, |0 Q8 |6 U
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