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本帖最后由 游龙游龙 于 2014-7-8 14:45 编辑 6 c) T: s6 [. W2 s& T4 D" }
* B# y: r. d- ]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, G4 q# f# d" d
行列式求不出,画图找不到根
* d2 P& Z0 y- O5 a(*定义材料常数*) _- m# ?" Z `1 K) i: D
Subscript[\[Nu], TL] = 0.25;8 J5 n% q/ @/ y8 x
Subscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)
" v- R( I! j- B1 ASubscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)" T; [ L- D6 m1 F# D
Subscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)
7 g9 G- Z/ W* @6 x6 Z, i# O8 LSubscript[\[Nu], LT] = 4 e L# `$ W3 q/ |- }; j* g! J" P. w
Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];
4 t l, K5 J1 j1 s8 d5 [\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];; V: S' @5 `1 V) u6 W* E
Subscript[C, L] = Subscript[EE, L]/\[Mu];' s' I ~( I2 @. z, Q
Subscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];: n: `, D3 m& N, [; O: e) U
Subscript[C, T] = Subscript[EE, T]/\[Mu];
L. o' _# N+ L: NSubscript[C, LT] = Subscript[G, LT];: z2 |. }) ]8 v0 p2 X: e' @ o
(*脱层几何参数*)' O. x& e$ S8 V/ B
\[Rho] = 1600;(*脱层密度*)
! a; k7 m- Q: w. E b% Ec = 0.06;(*阻尼*)# o+ L! R! Q( q+ o
t = 0.01;(*t每层厚度*)
% Y; C8 W) |( f8 @$ {% rh = 0.05;(*h为梁总厚度*)
* Y9 Z/ {7 \) cl = 1;(*为梁总的长度*)
: y% _1 B5 ?8 ~" @- YSubscript[l, 1] = 0.3;(*为梁1区的长度*)
1 J* W9 ^4 k) S9 ~ n/ LSubscript[l, 2] = 0.3;(*为梁2区的长度*)4 B K3 S' ?( \3 F7 }$ W+ j
Subscript[l, 3] = 0.4;(*为梁3区的长度*)
5 y) [0 u$ s/ m; L- B& D" }Subscript[l, 4] = 0.4;(*为梁4区的长度*)
+ s+ q! Z5 `7 |( [* b0 l# unn1 = h/t;(*nn1为总铺层厚度*)
# J) w: f0 j/ q* c6 xnn2 = 2.0;(*为上子铺层层数*)) _7 K: K, }9 W# ] J) {
nn3 = h/t - nn2;(*下子铺层层数*)
1 _( J' ` m1 N; M' {" l& GSubscript[h, 3] = t*nn2;(*梁的上部子厚度*)
/ M6 y+ ?; ~/ ~. |( f' P5 U% ~Subscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)8 Q& c8 K8 l* r( `& }: S0 f' e) g
Subscript[h, 1] = h;(*梁1区的厚度*)
; j" s( ]* E$ Y+ O% Q4 uSubscript[h, 2] = h;(*梁2区的厚度*)$ R3 D' L4 n) U, Z7 h# k7 h' ^6 ~
(*求各单层刚度*)
0 R3 s2 P& d: K" @ ]6 lagk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)7 |& J; ?4 D' r
$ y: p, w% l; q4 I3 f. q0 V
' ?) k9 h1 ^+ [/ z2 j) _
ck = Cos[agk];(*列表求各铺层角度余弦*)$ e+ |& e( C/ z7 r3 P) K" c! r
sk = Sin[agk];(*列表求各铺层角度正弦*)
& b4 r9 J4 B; l' Ls11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +
+ h+ S9 H$ P. r9 J sk^4*Subscript[C, T] + 5 B8 [$ B$ G* ^& Z
4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)
9 ?; A) Y' v, k' kA11 = \!\(' x" ^" ~8 k; n. `
\*UnderoverscriptBox[\(\[Sum]\), \(k = 5 V7 k J+ d1 _
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*). t0 W1 l1 ?& R. [$ w0 B. g
A21 = A11
# r0 o0 X7 m" T; _' Q7 G- {7 DA31 = (\!\(
9 Z( T& A0 }2 f- L\*UnderoverscriptBox[\(\[Sum]\), \(k =
0 K1 Q" i1 h- D: ~8 `3 @1 F1 x: `8 w6 M 1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)
4 }- b% P2 N) B- LA41 = (\!\(
5 M7 P4 Z/ H7 L3 C4 [( k9 @\*UnderoverscriptBox[\(\[Sum]\), \(k =
) Q8 C. o4 E# t2 [! J, w8 \8 w nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)
! C1 {7 X5 c% [' T" _5 v& H9 e @$ R/ T( t" x3 H: y
$ ?# L/ ]) G1 M7 D
Print["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*), ]" V2 y6 m6 ]7 F2 {
D11 = \!\(# [ o, t8 x8 ~3 t+ T" ^/ b* l @
\*UnderoverscriptBox[\(\[Sum]\), \(k =
3 s" K% r! C" i3 s& X 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*% J+ K& D5 x. T9 g% Y
\*FractionBox[\(t^3\), \(12\)])\)\)/ C7 J4 }- e: X7 t4 A7 i
D21 = D11
* F: \% Y2 N# U) M! [# R5 wD31 = \!\(
' d# v9 D2 A- X2 o# `\*UnderoverscriptBox[\(\[Sum]\), \(k =
) p' j6 e6 u6 o4 {/ M 1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*
2 @4 M, D q% S% t- c) \* j% H\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)
, f9 }' m- {; S' vD41 = \!\(! l: |) |$ o) h
\*UnderoverscriptBox[\(\[Sum]\), \(k = . E* k. M# e) ]) A; \
nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
" }7 ]; j# u# F) L- w9 g\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)
7 S3 X" q- j* j3 m" U* Y5 ok1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \
8 J4 m" }- I0 \0 |0 F5 y5 m3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;- l, Y8 ^1 `& Q: E
a1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(
# R8 t: L/ Q0 H# s/ J, v DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(
" O5 p z9 U8 E% a- d DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);
4 {( _; z! `8 U; N H" H\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \( J) V- {; T# L+ x! I5 @9 J
= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];
* E4 U' K! b$ l7 `6 t% gb1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \5 x, k% ? e7 Y
1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \
5 Q1 p) P( T; V) J7 ^Subscript[l, 2]/Subscript[l, 4];
& [& W/ n/ @0 ?. _2 @' tDD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);
% _( E/ `4 r5 {1 ^# y( l* {DD4 = D41/(A11*h^2);
4 D7 L! {( a M6 ]6 zr11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[
' }8 |! B! u8 e" t, j: V a2*\[Omega]^2, (4)^-1]; r13 = Power[5 `0 c m& P: N: z7 _( R0 _. R7 ]4 S
a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];
0 l5 a1 G; t/ ~! K( l# IBB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},$ g6 y, g( K) H" c, {: h
{0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},1 F9 H1 o! w, y' A
{0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0, ! }; l9 d; v* g
Sin[r12], 0, 0},
$ n2 a" m: \" w {0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0, 5 r1 w- e5 g2 \& \( k
Cos[r12], 0, 0},
) O4 g9 R s: p% g k( w4 t {-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11], : a# F; D# |9 b8 |, F
0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,! C6 X: z4 x( H3 o
-(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0,
* D6 ?* c& n6 }: B. | 0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11], : z& [9 W8 S U+ N' k
0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*' k0 j( g8 L& W6 m9 P' e4 B' I
DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},6 o$ Y; P1 H) r% z8 I6 _3 e: t/ F
{-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0,
) R! F$ p: u- c 0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11], 5 C: R6 f" e& W8 J- p: J
0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*
! d; p6 a$ C* ]6 e DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,
: d3 Y* M, Y) _8 G (r11)^3*DD1*(\[Beta]1)^3*Cos[r11],
7 K( {5 X( a7 `' L8 y% f/ u4 _3 L9 E 0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3},
# R% S# [& \7 z {0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*' u* {: h2 O$ `4 a; n
Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],
, n, u8 I" y# I 0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2*
$ [- a7 ~7 t2 I* a! N3 j Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,
" A" O/ b- b6 C -(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*4 Q8 o/ R$ S6 \9 A0 k. z" _
Cos[r14], 0, 0,; K$ z- A1 e& Z# l8 j7 T
-(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*7 _7 {) i! T& [: d8 P$ Q
Sin[r14]},1 n' D5 {0 k; |- z# |0 M
{0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*7 |. J, z2 L+ I
Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,
* j5 O" s. _4 v `* c6 y (r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*8 _3 }) B" B' u
Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],7 J$ V6 O/ H0 ?" v/ X
(r14)^3*DD4*(\[Beta]4)^3*Sin[r14], ! E. k$ i! f' y4 w
0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13],
8 j1 V3 e) e; j' y" f* ~0 `. ~5 j -(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},9 S+ j6 Y( u1 Q* a) M5 _( @' K
{Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0, % y; u$ V: N ^0 s* z6 z! S1 j
Sin[r11], 0, 0, 0},) H4 R. R' Y; w, l6 C) ^; e* C
{r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1, ^) s/ o0 L. k2 D& }5 c
0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],3 z9 ?4 }' W" ?/ q+ F s
0, -r13*b1},0 e1 ?2 g/ }6 z- c
{Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1, 9 z) J) L: E1 o" z& L$ N
Sin[r11], 0, 0, 0},
( M R$ q4 j J% Q$ G% m4 c, _( N {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0,
( L3 D [) \/ U4 u$ f 0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
: [# F# Y9 k, J, T! ]& P' i, a: q 0, 0, -r14*b2},( x- s- n! h! L! B8 l! p6 `; r
{0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,& D" c, ]/ m: k( x& f# y
0, -Sin[r13]},
G& C. m( X0 Z. V" Q$ I1 ^7 { {0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0,
- i& ^& O: R g( O2 c1 }9 M9 Q r13*b3*Sin[r13],
% g. p8 @* i2 n 0, 0, r12, -r13*b3*Cos[r13], 0},4 |/ `" h# C/ G/ a
{0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,
5 b" z" g& [- k/ T4 a3 V n0 _2 q. T 0, -Sin[r14]},
( Z0 R. I0 m. Y6 {/ X {0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0,
0 a4 M1 T9 |) f% S- r; i r14*b4*Sin[r14],; c+ Z' V" c- }
0, r12, 0, -r14*b4*Cos[r14]}}: J& M- d9 Z$ }0 X& \, K
aa1 = Det[BB]
4 A5 d* l& Y: J" pPlot[aa1, {\[Omega], -10, 10}]
' L- H9 l+ m0 {) wss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]
4 g* V. v8 n+ g+ j+ l9 e1 {/ f8 q2 q/ }, A
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