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本帖最后由 游龙游龙 于 2014-7-8 14:45 编辑 9 s% ]. Q( ?* S. B7 n r% U
3 X6 l$ A" t. x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; @* }; n( M J. V. Q1 E
行列式求不出,画图找不到根
, I! a' U2 {3 \1 S$ d7 [(*定义材料常数*)& S; l8 f4 K" K& w: b1 X
Subscript[\[Nu], TL] = 0.25;
3 t Q. t6 Q2 E0 }- n E8 F" G& DSubscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)! H" ~' f3 s& o# l2 Z3 ]* @/ R
Subscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)
/ B* ^4 G" |" D% i# G- Q8 p4 V* \7 }( FSubscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)
8 a- w% A4 `/ a6 pSubscript[\[Nu], LT] =
+ D4 P4 Y! N. q$ | Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];- B6 ]; h) [/ b/ |$ Y( g9 T
\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];; a/ M* w. o$ l$ p) `* s
Subscript[C, L] = Subscript[EE, L]/\[Mu];
# T" s. s7 x0 ISubscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];: `9 A; H" e) g) j& z- T; w5 b
Subscript[C, T] = Subscript[EE, T]/\[Mu];
E! g) D. Q% M4 s+ j! N- sSubscript[C, LT] = Subscript[G, LT];
1 d; X; A8 v" L& k/ z(*脱层几何参数*)
* H( r. q4 d+ Z\[Rho] = 1600;(*脱层密度*)
2 Z; m6 c) J# s, G& [ O4 kc = 0.06;(*阻尼*)
4 x1 p) Z2 @* ], i u5 G, Pt = 0.01;(*t每层厚度*)
2 f+ }0 q+ ]2 E S, p5 W3 ^) N" Ch = 0.05;(*h为梁总厚度*)% i+ t9 }1 W' _" @
l = 1;(*为梁总的长度*), A3 o K2 D. G5 d
Subscript[l, 1] = 0.3;(*为梁1区的长度*)0 u9 k; t g8 K: W: J
Subscript[l, 2] = 0.3;(*为梁2区的长度*)8 x3 T' _9 u! H, z4 Q0 W/ D
Subscript[l, 3] = 0.4;(*为梁3区的长度*)
5 i" z% b& U7 HSubscript[l, 4] = 0.4;(*为梁4区的长度*)
$ N4 F5 _: X# Znn1 = h/t;(*nn1为总铺层厚度*)
, w `& q- }2 H9 A0 f% h3 N0 }nn2 = 2.0;(*为上子铺层层数*)
) g$ M6 m2 }8 ^8 N8 P8 l+ snn3 = h/t - nn2;(*下子铺层层数*)5 D+ X9 ]& \% W1 A
Subscript[h, 3] = t*nn2;(*梁的上部子厚度*)1 _" r2 w% B1 K
Subscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)3 w8 D! j$ X+ {
Subscript[h, 1] = h;(*梁1区的厚度*)
) S3 O% `" {! p' }' e( [5 KSubscript[h, 2] = h;(*梁2区的厚度*)
0 D' C2 X* p+ p/ [, ](*求各单层刚度*)9 ^; O o' k* N# }& M
agk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)
( d2 p6 d* n* h( @' Q9 v6 l8 c& G" J4 h
5 @& U5 A$ {- b8 w; d) l0 Q0 m* ~% Yck = Cos[agk];(*列表求各铺层角度余弦*)3 W( n1 l( R% e, z N1 d- n
sk = Sin[agk];(*列表求各铺层角度正弦*)
& v3 J8 w1 B5 b5 us11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +
1 p0 I, j' n' ^; s) E8 u8 K sk^4*Subscript[C, T] +
/ T( s4 Q" B0 q) X# Z8 ^6 j: J 4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)
+ N s$ x' I. Q+ v, tA11 = \!\(( E6 m& p; Y$ m( ]
\*UnderoverscriptBox[\(\[Sum]\), \(k =
$ a, b- P) K# u+ Y 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*)4 D+ ~' w9 D% m! `% f+ Q1 e
A21 = A11
% o' F( N1 s8 SA31 = (\!\(* Q1 P* T# \/ }6 X- H# U& l
\*UnderoverscriptBox[\(\[Sum]\), \(k =
9 z) c: V$ o: X, x. _4 E 1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)
( _; `1 h$ u# X. ^3 |6 @, [A41 = (\!\(
+ ]7 W* }/ n6 t4 F' _$ X\*UnderoverscriptBox[\(\[Sum]\), \(k =
8 t. w) | W2 @; c+ ~( T4 K nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)
' Q- B) c6 C5 q9 F3 x! z* F9 I" @2 ?6 T+ y7 j
7 s4 q2 n! t+ C" a2 U' PPrint["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)- f X: M4 c' \% d6 L/ k8 L2 p2 H
D11 = \!\(
2 K+ S* @ X/ f\*UnderoverscriptBox[\(\[Sum]\), \(k = ' s; |' f2 Y" O0 {. N
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
6 \6 ~& m0 m- y9 S$ ]! t\*FractionBox[\(t^3\), \(12\)])\)\)
; s9 P% E) _$ P1 r5 Y7 U8 Z/ ND21 = D11: b6 X P* N# p5 _8 w: H: Q! ]
D31 = \!\(
1 l/ I: ?/ H5 w/ m1 z\*UnderoverscriptBox[\(\[Sum]\), \(k = + A/ p$ S0 H/ E- _$ H
1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*+ `! x4 e z! e/ b8 Q0 t
\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)
/ P! ]; H+ i( Q- T6 r2 PD41 = \!\(
9 Q5 n( y' j, `" b, T\*UnderoverscriptBox[\(\[Sum]\), \(k = - N* ^+ I1 I* [$ V8 H- |) A4 y
nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
& A: w( X- `$ w9 n$ \\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)
5 r$ L) c7 K. Tk1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \
& s# c% N* _8 H% G3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;
0 g: X; N" m& N o7 f$ m aa1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(
, U/ }! H7 g' w DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(
. Y; q6 _! U. j DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);) x/ ?$ l/ q& Z# _% }2 k
\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \
' z% T6 W! E( z( M6 Z. p& T= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];8 R: x0 Z3 j9 \, {; w
b1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \
' X+ H2 i/ `7 v9 m9 m' Y1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \
$ w5 b6 ~; k% Q r4 x2 ?1 a: LSubscript[l, 2]/Subscript[l, 4];
, O+ G) v9 Y& u, }' b- UDD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);
5 [5 Q! d/ N$ q& m, pDD4 = D41/(A11*h^2);: o' J1 a( ^+ Z3 f4 Q7 Y
r11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[
m1 k! m* ^) ]0 e a2*\[Omega]^2, (4)^-1]; r13 = Power[, s& D! y3 H% X1 h3 P6 r8 [
a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];8 l9 ~* q" \5 d7 y% q
BB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},
0 b# p, Z5 ]# ?( W, O! L) @ {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},
# K% p! P7 W) U$ d9 n {0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0, 1 m" W! Y. V$ n- ~/ P# U- Z4 m
Sin[r12], 0, 0},
7 ?0 V) z5 O. K {0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0,
' }, O. W1 h- o, F Cos[r12], 0, 0},
7 r1 F. o+ \/ e6 r4 z/ l. k {-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11], 4 {6 U) a/ g! E% B- h
0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,
6 X2 I4 l$ {( @3 f$ S0 m% t. h -(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0,
- k) m+ ~. ]2 B 0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11],
7 r( I0 j2 ]; X% r# c! t) |3 } 0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*
5 a% m# \( u4 V, V& m DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},: b. R* ?" S; F, Z& |
{-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0,
- G4 V8 ?, O" x, k 0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11],
" z7 x5 W3 Y# k" c }1 F 0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*
1 w) U: |3 s8 [% b+ A DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,- S/ v# K8 w' Y) s% ]: B0 _
(r11)^3*DD1*(\[Beta]1)^3*Cos[r11], + {% E# e! N3 \3 V) O7 Y+ w
0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3},
; y& R) w' i7 S5 R" x7 p {0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*0 A) H1 B) ~- s$ f; y& D8 c
Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],+ ^% W7 W+ c0 L1 e* L
0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*
0 y2 f4 H( N S' \! z% W Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,
+ ~) o' D5 Q5 }0 K, e$ f9 |: K -(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*
2 ] N: \2 P! V3 [# g7 `4 _! ~. X Cos[r14], 0, 0,
B& V+ _3 z. ?. c: q& ^/ H& P -(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*
0 B) b( j$ _( u& I8 s8 K Sin[r14]},! ~5 [- k% ^* _4 _8 \% Z# k& D
{0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*
! m! m4 }: y2 L/ S; B4 Q# b& J6 G9 W Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,; E0 z# y2 y; V% P) L5 }: a$ n$ |
(r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*
C3 H$ Q8 \/ C: b% v! [1 N Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],$ e. ]" L, K T( R) Y
(r14)^3*DD4*(\[Beta]4)^3*Sin[r14], / A; c2 T1 F: e7 X$ z$ U% e9 x
0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],
! x; Z! W6 P8 Q2 l ^7 S -(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},
% @. x5 l/ x: o8 H) y5 Z8 i6 a {Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0,
( b) F8 W2 w8 T/ s8 \& w0 ~4 f, C+ o Sin[r11], 0, 0, 0},
+ z* ]- d) O( X1 @: X1 r2 ] {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1,
% S9 h/ h5 [8 M% C 0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],; Y% I/ s& f8 F2 t5 \
0, -r13*b1},
; _" L1 u6 v" B8 R9 b2 c5 f {Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1,
( H. Q: ~9 i4 ?' ^% Y) D' L5 a Sin[r11], 0, 0, 0},# J" {- ^$ Z9 Z- O- Q9 Y5 J
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, - P" X/ \6 r7 {6 v6 ~
0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],' q+ O Q0 [; d; b8 t$ n4 u2 R
0, 0, -r14*b2},6 c/ p" x# |+ i; S2 i
{0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,
/ q$ K8 g' c- j2 d9 m( _+ e 0, -Sin[r13]},
7 {* t _- W# o& {4 h! F$ V {0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0,
2 ~& _9 z% {- i/ B, x2 O B! T) w r13*b3*Sin[r13],
( c/ h% q. T* ]8 b a, h 0, 0, r12, -r13*b3*Cos[r13], 0},( R e0 `3 @+ D) t* l7 _
{0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,
& d2 f: y9 _3 D( c/ W 0, -Sin[r14]},
6 u. n+ P) O5 a3 _/ y; N) v2 x5 R {0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0, 1 ]. b+ h0 @" Z% \* }+ H: W
r14*b4*Sin[r14],) s; O2 ^; @ I* ]/ I4 s6 v" n4 [
0, r12, 0, -r14*b4*Cos[r14]}}
) {$ a6 W' p Yaa1 = Det[BB]; b7 X/ e5 d( M" u( J! v
Plot[aa1, {\[Omega], -10, 10}]4 ~* n8 ^. j2 i# q
ss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]/ p5 i2 R: l8 E7 {. \' m6 z
0 D0 f) N! C3 U B0 h0 v) \2 `
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