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本帖最后由 游龙游龙 于 2014-7-8 14:45 编辑 / N7 H: R6 O' y: R, k0 p+ w4 @8 q- ~
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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4 k) D, R" [$ D. K! A6 A
行列式求不出,画图找不到根! K. X0 t- Z% f5 m" ?9 U3 ^& x
(*定义材料常数*)+ f# `2 E* v1 t# |$ K% i8 x' [
Subscript[\[Nu], TL] = 0.25;
7 M! E, \: H; B+ u! s/ ~+ WSubscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)2 H6 q* r7 {3 h7 I, I; G
Subscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)
& D. Z6 J, O( c7 uSubscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)7 m/ f j7 n) t0 I
Subscript[\[Nu], LT] = 4 r* v( q! z( R
Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];
8 B- F6 ]' E% s5 B/ o7 ~4 f\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];% S3 l$ h9 |* ]
Subscript[C, L] = Subscript[EE, L]/\[Mu];
. r T6 x2 x- q& OSubscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];
" f: {) ?9 M0 N- s4 }: |Subscript[C, T] = Subscript[EE, T]/\[Mu];
6 f0 `( _$ M L! \4 m, QSubscript[C, LT] = Subscript[G, LT];! L3 W+ o- r# s
(*脱层几何参数*)+ @2 Y1 c, `, w; }: |
\[Rho] = 1600;(*脱层密度*)
( x, X' o2 D7 n& `" R) }5 r" d8 sc = 0.06;(*阻尼*)5 U* E |: ~; v
t = 0.01;(*t每层厚度*)# _" y& _* p% b1 Q
h = 0.05;(*h为梁总厚度*)4 R: U2 j4 v1 f- u
l = 1;(*为梁总的长度*), p$ u0 S+ U( C# I
Subscript[l, 1] = 0.3;(*为梁1区的长度*) f! }5 l$ q, d. e% [8 ~
Subscript[l, 2] = 0.3;(*为梁2区的长度*)9 Y/ f, L* V5 x& g
Subscript[l, 3] = 0.4;(*为梁3区的长度*)* u: [1 {* V1 e, T* w& \) }
Subscript[l, 4] = 0.4;(*为梁4区的长度*)
0 x* D# U& F `nn1 = h/t;(*nn1为总铺层厚度*)& j0 a. J8 ]) b0 e8 w
nn2 = 2.0;(*为上子铺层层数*)
5 t4 l& M4 y- S% unn3 = h/t - nn2;(*下子铺层层数*), {% H! D* v& ]5 z F( K
Subscript[h, 3] = t*nn2;(*梁的上部子厚度*)$ N j: c1 a' \( j8 E2 G) S, U
Subscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)0 @$ W, {8 c* ^/ Y' l% B
Subscript[h, 1] = h;(*梁1区的厚度*)8 z1 }7 e1 N; j& N
Subscript[h, 2] = h;(*梁2区的厚度*)0 Q: F0 A% j+ ]* A; \
(*求各单层刚度*)
' U/ W* O+ k# N2 @0 T' ?agk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)
/ F$ ~$ Z/ ?& ]6 v( T* \7 k9 D3 E/ b0 d9 v. g* T5 ?% E
6 x; |9 ]+ y6 {7 B3 L. l& ?ck = Cos[agk];(*列表求各铺层角度余弦*)
0 u7 D$ f0 E8 ^) {2 isk = Sin[agk];(*列表求各铺层角度正弦*)) J- _. y5 a' V* y* _
s11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +) Z9 e5 `/ c, \, Y5 @9 Z! O
sk^4*Subscript[C, T] +
8 b, @( E; g {0 ^0 S) i# @: m! K 4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)" Y% @# \( u1 [! h- Q
A11 = \!\(
" E5 ]* B; I! K1 E& \- W7 h\*UnderoverscriptBox[\(\[Sum]\), \(k =
9 Z. g, j5 S% T5 `. o8 W4 r 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*)# L4 r% d0 y$ ~8 S; I5 U0 i
A21 = A11
) \- f# s4 ]7 iA31 = (\!\(
9 X; x ]5 h3 I( A! \ d\*UnderoverscriptBox[\(\[Sum]\), \(k = * y+ y' B* H: h
1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)
8 G% ^+ \0 ^! [2 kA41 = (\!\(: a; R# c [2 Y) m: A
\*UnderoverscriptBox[\(\[Sum]\), \(k =
% F7 @0 h# I' C- O4 a nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)5 ~! h5 @) R- n1 S
) c$ o+ o$ K. A# P9 h9 E
% P/ H; L8 C' a) l% z5 K; ~Print["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)
4 @6 A% s) {; h# K' ~$ ~, G: ^D11 = \!\(! b0 G0 f. \8 A) X
\*UnderoverscriptBox[\(\[Sum]\), \(k = # i+ s! h( Y6 \- w. d# @4 c% v
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
6 r, @1 [" o6 ~; F& F. C" i\*FractionBox[\(t^3\), \(12\)])\)\)
# ?9 v( `6 Z3 F. a7 z, c0 G- {% }D21 = D11
& [& @9 b4 x! x) YD31 = \!\(, j# r ], R: r' y
\*UnderoverscriptBox[\(\[Sum]\), \(k =
( q1 q; _5 V3 S3 C% [) I. v 1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*2 r* @& b& a: g* G5 C- [
\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)( F* ^( M6 _# e
D41 = \!\(& {/ J) m9 h: R$ ^" a' f% Z# a( Z+ ?
\*UnderoverscriptBox[\(\[Sum]\), \(k = 8 L1 D( @' p6 W; u. S: {4 n6 v- d
nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*% l. o D! D/ V4 u6 v# u. ]
\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)$ E# ~7 c" y/ [: f$ p
k1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \
1 v; a, O& C; G( r7 I( t `3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;
* L# E+ V% R9 P- K# u" x8 ua1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(& P+ C# [& s7 D R" m
DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(
) K) \. V& s5 c& ?, `+ r+ B DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);
' m5 g8 o% V7 f2 ]& T1 z9 b\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \
1 D; M: _/ |8 k# {5 K= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];
$ M+ i. p6 }$ g# b9 cb1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \- B X! Q) W, A- k% N: l
1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \% Y4 L* r9 m* w+ M- ^
Subscript[l, 2]/Subscript[l, 4];
# U% J4 ?- Z" t N" m3 P9 `DD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);- B3 z) w/ m+ @. ` F
DD4 = D41/(A11*h^2);
1 ^$ @! M; r3 B2 i0 O7 n, ]r11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[( s+ }& N' C3 t5 N
a2*\[Omega]^2, (4)^-1]; r13 = Power[
# |4 T5 A; Z- B# ]7 s- w a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];
' S0 @2 c" B* qBB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},
+ Z4 c! b) e6 W3 Z1 H' K& n {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},
' s2 }- G, q2 p) K+ G {0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0,
( C2 ~- R: V- P1 { Sin[r12], 0, 0}," i e. w0 W0 T: U4 t
{0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0,
" l, |0 c& K$ ~3 `3 I* ~ Cos[r12], 0, 0},# v/ h7 n4 _" L0 I
{-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11], - Q0 M0 i- ]6 g& F
0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,, T) Q- b' X0 A
-(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0, ; q& b' M7 t, [$ ]3 K, S
0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11], + z, W/ o7 v' {: g1 |
0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*- T5 T$ F& h$ E5 l5 t9 k1 O& L
DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},
" l) `% h# V1 @/ m: J1 F {-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0, 6 {3 d/ g; g8 v5 C5 G
0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11],
/ p5 w# U# l0 h2 [5 _2 ^ 0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*
+ y' g0 k. C( M4 t$ E DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,
: x$ F& \. q5 n) Q (r11)^3*DD1*(\[Beta]1)^3*Cos[r11], ; l( M5 C5 U0 o6 c% E4 p6 g: n9 x6 O
0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3},
6 m/ U! {! z( k \$ i1 \2 [* M- U {0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2** _0 q K! B+ L0 I2 `
Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],7 Q9 J; e' b; n5 l' T; P
0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*
4 ~* y: l+ O# {8 K7 ]8 Z Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,* ^# L# [) l5 m8 q) g
-(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*
3 b# g Y4 }* ~7 f+ W2 b Cos[r14], 0, 0,) _& {7 J/ p! }' U- i4 \ E
-(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*
* l! V+ ]0 Y: d- ^: V6 l Sin[r14]},8 g5 W: d& S; [8 g( R
{0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*6 F# p q7 U3 U, T) u
Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,; T" Z P: D' n' p
(r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*
1 Q: n8 `7 W' u7 `: \, ] Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],
) n7 ~9 u4 {* @6 `( @ (r14)^3*DD4*(\[Beta]4)^3*Sin[r14], / Y& w9 y/ N) _( Y: W
0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],, {5 i' M0 n! y+ j; P& O" n
-(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},
, b0 A4 Y) Y, r+ @8 M {Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0, 2 G; M" c7 k; ~0 ^' g" p% Z0 b
Sin[r11], 0, 0, 0},9 T$ z4 Y9 U! U! M
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1, $ \' ?, b8 C( v1 d
0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],3 S% g/ l6 m( h- R
0, -r13*b1},: ^7 l. n+ Q- C, j, t# ~
{Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1, 9 \4 B: M/ _- ~& z$ w4 i- ?3 q
Sin[r11], 0, 0, 0},4 C |, C7 ?9 s" B# x# ^
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0,
% W; m& @6 B1 b. ~% ^# v 0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],2 w- p2 w" u3 E3 u
0, 0, -r14*b2},/ ]$ |( e7 Z+ M0 r
{0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,
' y0 `7 ~- G- a9 j! C) e/ T 0, -Sin[r13]},
( t) P, q: c: j; m {0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0, ; j2 M/ }* h8 H
r13*b3*Sin[r13],
* o6 g4 X& F. B 0, 0, r12, -r13*b3*Cos[r13], 0},
' z+ i6 s0 d( Y: @! q# v" S! u8 C {0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,7 g$ x/ Q' U& x' h
0, -Sin[r14]},* z/ i9 {* Q2 k+ B' l4 |
{0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0, ! m& Q5 c- r7 } e; g9 d
r14*b4*Sin[r14],) p* C( \, p: ?2 k5 N# m- }
0, r12, 0, -r14*b4*Cos[r14]}}: X" @ r k \/ c' X+ \
aa1 = Det[BB]
3 t( w' {5 x/ w2 iPlot[aa1, {\[Omega], -10, 10}]0 A0 O6 a/ S# w7 J# P
ss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]4 ]' R; H0 y# ~3 O2 b
1 J! A1 R7 l5 `- M0 Q( D' C2 Z
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