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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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/ w5 |( x$ I% v9 X# c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 W/ m6 p! K0 ^' @4 q8 X行列式求不出,画图找不到根; k1 f2 ]& D, I0 R9 L* u" _
(*定义材料常数*)
6 R' `2 i9 C% Z% G9 s9 \Subscript[\[Nu], TL] = 0.25;% y' j5 \* A- s$ _& [/ w# I4 [( Q( ?
Subscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)
2 N* d! k+ M zSubscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)0 i' r9 F. i- I- C
Subscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)
. P- e* u& F( }% R( c$ QSubscript[\[Nu], LT] =
! }5 A5 q8 p: L" X Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];8 k- M! W/ e# F) }# S
\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];+ C% f! |+ Z3 Q' \
Subscript[C, L] = Subscript[EE, L]/\[Mu];
- L. w# W% R, m/ ^Subscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];
7 K8 t9 \4 b5 u2 Q% XSubscript[C, T] = Subscript[EE, T]/\[Mu];
/ y8 |6 p. [3 O& d& Y" L1 |Subscript[C, LT] = Subscript[G, LT];
@, R5 T* S( ^(*脱层几何参数*)
% j& }: J6 M% k/ w8 [' [! B\[Rho] = 1600;(*脱层密度*)4 q) A ]$ C8 Q$ q9 a& i
c = 0.06;(*阻尼*)
: a2 b0 G6 K- \/ r6 v& F: I. Et = 0.01;(*t每层厚度*)
! \9 [% f4 b1 O# F# l$ R6 i! Y Sh = 0.05;(*h为梁总厚度*)/ n. y! q0 q* T& d6 y
l = 1;(*为梁总的长度*)# R3 k8 r0 Q! K
Subscript[l, 1] = 0.3;(*为梁1区的长度*)
2 L/ _& Q* L. x* G+ I' i( NSubscript[l, 2] = 0.3;(*为梁2区的长度*)
" [' }7 L- Z, P) \6 tSubscript[l, 3] = 0.4;(*为梁3区的长度*)& v6 s% K0 A8 @, l
Subscript[l, 4] = 0.4;(*为梁4区的长度*)
4 ?" n2 M/ S' d. z+ f3 Znn1 = h/t;(*nn1为总铺层厚度*)
- e3 {9 V1 z g: cnn2 = 2.0;(*为上子铺层层数*)8 @5 K; y' B) g% E; b
nn3 = h/t - nn2;(*下子铺层层数*)/ D9 ]8 X; x/ ~% @2 Q: W
Subscript[h, 3] = t*nn2;(*梁的上部子厚度*)
0 x1 j& I5 x: a5 L- USubscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)
5 @5 X: r2 m, D c* MSubscript[h, 1] = h;(*梁1区的厚度*)* @+ o! d q' K
Subscript[h, 2] = h;(*梁2区的厚度*)4 q- q) n* O4 B. G9 {# M8 M
(*求各单层刚度*)
4 J4 @% y; o0 kagk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)4 D2 V4 X1 b; _, Y
& A: n9 H7 L9 `" H$ p' g4 A8 u
1 h1 y( {, F( C& p$ R+ O
ck = Cos[agk];(*列表求各铺层角度余弦*)
, L2 V. J- Y2 P' ^7 osk = Sin[agk];(*列表求各铺层角度正弦*)
5 R: P7 Q- z+ C; Bs11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +
# W( [- k7 q% h% q sk^4*Subscript[C, T] + 4 l) g! c- @, ]/ n
4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*). O0 F* N0 Q/ \/ x2 Y
A11 = \!\(
: n6 E1 Z, I+ m\*UnderoverscriptBox[\(\[Sum]\), \(k = - `4 D# E/ Y+ g [% x$ K* X
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*)
) Z7 a' q* ^' @4 q" vA21 = A11
( r$ V2 x6 C2 iA31 = (\!\( R7 j4 Y4 q# n2 A c5 ]" a
\*UnderoverscriptBox[\(\[Sum]\), \(k = 4 t" {* I( J: R7 Q0 F
1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*). d, b( B0 Q! I' r& P
A41 = (\!\(
1 {4 Z1 Z k' W% c\*UnderoverscriptBox[\(\[Sum]\), \(k = 0 S T- @4 P- O
nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)6 C& r5 J4 O2 W% d
' w/ _, F" B o8 D- u7 q
6 c4 P" T) p* c6 uPrint["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)- k" O( Y' ]# i7 P* b) J6 ?
D11 = \!\(
& S' [. P; k( y* j8 N; q" |5 P\*UnderoverscriptBox[\(\[Sum]\), \(k = # V' I% B( I/ X$ g" x
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
- M# L9 p9 C3 A0 X5 \, S\*FractionBox[\(t^3\), \(12\)])\)\)0 }' [# C6 [5 B1 D$ z3 y- l
D21 = D11, |# q/ P ~/ w" n4 Y
D31 = \!\(
& z7 }1 q0 n# W' y( A+ p\*UnderoverscriptBox[\(\[Sum]\), \(k =
- ^: d1 h4 C& c1 ` _4 q- `8 o 1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*
3 P. K( i) g! y% d! W- v- W9 V) C\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)1 H+ A+ P1 _: W7 l! J
D41 = \!\(
2 i/ f" n: f+ Z3 b. l5 P: e\*UnderoverscriptBox[\(\[Sum]\), \(k = 1 z7 o- n. A5 K5 f+ p, T
nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*' Y7 A+ w9 Y* \5 `5 h
\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)
/ T# P8 [# w* F2 F2 { U" Ck1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \" g( s$ h; K1 Z, A; v
3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;" X b3 I' S0 ?# R( s
a1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/( W1 [, |8 U" d0 w# V
DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(* Z# Q$ ?3 Q, E/ x1 @% B
DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);
- B. t8 t+ ^ J/ s% Y {: A& O\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \
, r/ ]5 n( O, [, u' }) P' {& _= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];, Y2 V/ q+ l! E
b1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \
8 r4 C" [0 h. p5 k& k1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \
. I" q) [' g+ v2 c/ e# BSubscript[l, 2]/Subscript[l, 4];4 V" k: W$ b/ m# l7 d | V _# }
DD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);
. N% F5 T1 S! F3 iDD4 = D41/(A11*h^2);
, _+ c( A/ q/ gr11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[; ]( c; G; k6 [% `. W/ x
a2*\[Omega]^2, (4)^-1]; r13 = Power[
% ~& Y5 \' T R; Q! f. g- ~) M a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];
+ \. v# _& I5 t A0 _BB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},' y+ _. X# Z# e6 D
{0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},
5 w1 q5 k4 V" @) Y" V; f5 d {0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0, & `+ W B3 t4 z( z9 X) c" W
Sin[r12], 0, 0},+ M1 E9 L; @- J( D. v- }3 J. u
{0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0,
$ w2 `) |, j0 S" L+ ]. k Cos[r12], 0, 0},
8 x1 K$ p5 T% b2 ~ {-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11],
, S6 }# h( l& p2 F8 M 0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,4 \4 i/ D2 I1 W8 Q$ ~0 X
-(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0, # i, Y' W6 K& M0 I- B, x! ~) U! F
0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11], ' C0 d8 G) r+ p, P% @, q( Y0 ~
0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*0 V+ p) F0 Z; e7 A
DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},
, T. E' S3 K8 h7 v) R2 h {-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0,
6 t. ], x( w# c, }! N 0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11], 7 C/ n1 C0 S9 n. D2 B( y" K
0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*
! d0 F7 A9 D6 {( h' b0 j7 l DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,2 o2 v3 Y: {. Y7 V7 @* P
(r11)^3*DD1*(\[Beta]1)^3*Cos[r11],
H& e" t8 H+ g! s& | 0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3},6 I7 `6 R4 |" n* y
{0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*
1 V+ T: h9 c* C3 v( ^! [ Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],
9 t& w1 T* l0 Q9 s& p' {8 W0 x 0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*
8 k5 F0 d; `0 a' f& A- L0 w Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,' x' }. f! G: t6 q* Q
-(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*
$ U" N4 G( I& K5 W Cos[r14], 0, 0,
- t. X- b8 S, Q' v: m6 X -(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*
6 j3 n; r5 }9 S& F Sin[r14]}," o3 C0 L, K, s# B
{0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*% t9 K# d% g8 R- f, h
Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,' v# v% {7 `4 T2 F2 r* D
(r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*; E# U& L$ v& y: t$ Z/ T+ q4 K
Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],
* E# g! I8 X' S, |2 V2 P (r14)^3*DD4*(\[Beta]4)^3*Sin[r14], _5 n# h. N$ k' S: H7 @- b3 v
0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],
4 q2 n' G4 G: _6 t7 U* m3 M6 U -(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},, L" [8 {* D' B9 b8 Q' ?
{Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0,
# Y9 z% S; j4 \& l s% W Sin[r11], 0, 0, 0},
; s: S) j) F4 L9 B h {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1, . v# ~- p& e% L
0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],. h F$ C- c: F' d0 @& j
0, -r13*b1},- C3 ~ x- s0 A3 e( [' o/ J
{Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1,
! S1 t; ?; G: H2 c5 u/ m5 Z$ k Sin[r11], 0, 0, 0},
' @; k! z# l8 P; ?( p; G {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0,
6 G4 q" f* k& m. n9 W6 c6 U! w 0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],+ ]# P: W. H0 C. X
0, 0, -r14*b2},' @9 `$ O( B4 r8 z9 t ^* T
{0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,
0 t. o/ P% u$ S; Y9 A 0, -Sin[r13]},
* L$ l$ N; S8 H4 D/ x$ G1 k {0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0,
# J# {. z. K9 V9 W r13*b3*Sin[r13],
4 h0 }1 c4 Z& R* V a, i( i 0, 0, r12, -r13*b3*Cos[r13], 0},2 X4 \6 ~6 G4 a. s5 o
{0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,
6 J, j4 M: M* {& ~- O/ O6 k- k 0, -Sin[r14]},
( u7 W- d) ]5 [- e {0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0, 8 e A3 e) h, V8 i
r14*b4*Sin[r14],7 Q! i9 {. E9 x0 N/ a
0, r12, 0, -r14*b4*Cos[r14]}}
9 U0 ]7 s/ A2 R/ X0 _( |. waa1 = Det[BB]) i" {. I! d; P
Plot[aa1, {\[Omega], -10, 10}]
7 R/ a# a7 ~& ]5 S* xss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]
0 o4 G: [/ z' v/ p* Y( K& t8 b r# o4 c1 ^4 S! P: h" ?
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