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本帖最后由 游龙游龙 于 2014-7-8 14:45 编辑 / e4 D$ X8 a' e5 S! I6 R: M- Y
2 z* @: B9 j" t5 u* Z- y1 ^) i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
1 `# g& U! |4 v4 F% r% x9 I行列式求不出,画图找不到根
4 n& c( u# Y) z% G7 Y8 d) O(*定义材料常数*)$ w& |! `1 f9 |9 P* L. }
Subscript[\[Nu], TL] = 0.25;/ Y% [: w; U! m# A4 s, G
Subscript[EE, L] = 53.8*10^9;(*L方向的弹性模量*)
8 Y$ [7 N* |1 T3 KSubscript[EE, T] = 17.93*10^9;(*T方向的弹性模量*)% r; T7 R2 l+ t: I4 j7 _
Subscript[G, LT] = 8.96*10^9;(*LT方向的剪切模量*)
0 n6 x0 ]! g' u: U5 j: E+ vSubscript[\[Nu], LT] =
$ j# `: g' h: y0 E7 n2 }# f Subscript[\[Nu], TL]*Subscript[EE, L]/Subscript[EE, T];* x! V2 u* @ P5 c* L
\[Mu] = 1 - Subscript[\[Nu], LT]*Subscript[\[Nu], TL];) W. J+ r {, w. D0 O
Subscript[C, L] = Subscript[EE, L]/\[Mu];' a' P/ Y# P9 N% x6 ~- g: B3 E r$ t
Subscript[C, S] = Subscript[\[Nu], LT]*Subscript[EE, T]/\[Mu];+ E5 h0 e l( P" E9 K8 U
Subscript[C, T] = Subscript[EE, T]/\[Mu];$ u5 g2 Q5 ?6 Z) n0 Y
Subscript[C, LT] = Subscript[G, LT];
: B) R4 a" C( {2 L6 K1 z(*脱层几何参数*)
% t( r5 [5 u0 S0 }! L# \\[Rho] = 1600;(*脱层密度*)- u* ^. J" B; L5 K( E( g; ?. \
c = 0.06;(*阻尼*)- w9 S: {; \ c" ^
t = 0.01;(*t每层厚度*)) L/ h3 F: U' I% r5 i: x) W% A5 ?
h = 0.05;(*h为梁总厚度*)
' N9 J, b4 [/ q1 A, K' ?3 rl = 1;(*为梁总的长度*)
3 s9 Y4 I* n. M* s- O! Z/ pSubscript[l, 1] = 0.3;(*为梁1区的长度*)" k: }8 t3 }4 O$ p
Subscript[l, 2] = 0.3;(*为梁2区的长度*)
) X' p$ n1 ?3 n- c! Y1 L: }Subscript[l, 3] = 0.4;(*为梁3区的长度*)
8 _: }) b) U; w! p8 RSubscript[l, 4] = 0.4;(*为梁4区的长度*)
+ T7 H% D& e7 }$ q" n, g: Onn1 = h/t;(*nn1为总铺层厚度*)& G% c% b) N5 q2 N9 ^4 p
nn2 = 2.0;(*为上子铺层层数*)4 P: G' j a& d. h
nn3 = h/t - nn2;(*下子铺层层数*)# L: o3 h. ^) ~# t) w
Subscript[h, 3] = t*nn2;(*梁的上部子厚度*)
) @/ n. V, x( k/ i+ s( ]/ oSubscript[h, 4] = h - Subscript[h, 3];(*梁的下部子厚度*)
: a( \2 ^+ ~- H% s7 q$ _1 TSubscript[h, 1] = h;(*梁1区的厚度*)1 t8 h& L4 k3 J6 ?! R+ j9 v, w' k0 k
Subscript[h, 2] = h;(*梁2区的厚度*)
/ Y0 p. [) e* ~; D5 P7 a0 @(*求各单层刚度*)7 c3 X$ G% n$ x. }9 |$ R
agk = {0 Pi/180, 90 Pi/180, 0 Pi/180, 90 Pi/180, 0 Pi/180};(*列表各铺层角度*)
+ W/ \4 B1 ?8 r# @- W# R# y$ L. @+ I9 F- D$ p8 b* K
1 S3 ^" R' Z l9 r* e1 I+ H; V3 P; q
ck = Cos[agk];(*列表求各铺层角度余弦*)( I" }' e& o# L8 c/ U
sk = Sin[agk];(*列表求各铺层角度正弦*)
5 S! T+ U* W% y8 B' d; D9 v7 ?8 Js11k = ck^4*Subscript[C, L] + 2 ck^2*sk^2*Subscript[C, S] +8 U: S z" x" q0 U; Z+ g) h
sk^4*Subscript[C, T] +
& n \5 W8 Z: v; q8 W* l P3 Y 4 ck^2*sk^2*Subscript[C, LT];(*求各区刚度*)6 T4 {7 K+ k3 G6 G
A11 = \!\(
$ q5 B3 x: K5 n\*UnderoverscriptBox[\(\[Sum]\), \(k = 0 J8 Z! ^/ M2 i K
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*t)\)\)(*一区拉伸刚度*): ^) \! E" L* X: H, V
A21 = A11
: K1 D6 h2 g: w0 SA31 = (\!\(4 @% c& u( |) X! E0 G
\*UnderoverscriptBox[\(\[Sum]\), \(k =
" X6 f. Z; h6 Y# z% I4 K) x% E 1\), \(nn2\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*三区拉伸刚度*)
/ z3 h. A' t+ w: R- n, qA41 = (\!\(
$ x& R/ S' C& N; @, _; W& T; Z. C\*UnderoverscriptBox[\(\[Sum]\), \(k = 9 d2 q: Y5 i+ i6 P0 R# D
nn2 + 1\), \(nn1\)]\(\((s11k[\([\)\(k\)\(]\)])\)*t\)\))(*四区拉伸刚度*)
G) ~4 {+ g3 f& r7 }" {
4 t- o: Q" N" y1 D* i" H
* ^/ A' q# p# I* ?. z; bPrint["A21=A11;D21=D11"];(*二区拉伸刚度、弯曲刚度*)
4 j* v) |- f. H8 vD11 = \!\(
# G6 {, E: n2 b\*UnderoverscriptBox[\(\[Sum]\), \(k = ! r+ W/ P: J7 p; k9 y8 D" I
1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*
, C2 K9 H1 Q. I\*FractionBox[\(t^3\), \(12\)])\)\)
; }0 Y. ]3 c8 {+ \D21 = D11
. E q2 R( r7 e+ D7 `; k z8 ZD31 = \!\(- c; {. P$ Y' V1 u( m5 V" j. I
\*UnderoverscriptBox[\(\[Sum]\), \(k =
, c4 x3 {3 n' n# B- X 1\), \(nn2\)]\((s11k[\([\)\(k\)\(]\)]*6 D% Y1 b* N/ N# Z
\*FractionBox[\(t^3\), \(12\)])\)\)(*三区弯曲刚度*)
8 u: F( G$ j4 zD41 = \!\(5 d$ C9 L$ b* L! E& }/ S0 z
\*UnderoverscriptBox[\(\[Sum]\), \(k =
! H. Y, c. b7 z: o0 ^ nn2 + 1\), \(nn1\)]\((s11k[\([\)\(k\)\(]\)]*1 x1 c7 X8 K5 r5 W' y. b B
\*FractionBox[\(t^3\), \(12\)])\)\)(*四区弯曲刚度*)
# u# b, w P: `. D; Ik1 = Subscript[l, 1]/l; k2 = Subscript[l, 2]/l; k3 = Subscript[l, \- f3 @' }6 ?3 z/ k
3]/l; k4 = Subscript[l, 4]/l; \[Alpha] = h/l;
3 o) Q0 o' A$ v8 |) ]4 a6 Z2 u) z# ba1 = (\[Alpha]*k1)/(DD1*(\[Beta]1)^3); a2 = (\[Alpha]*k2)/(
4 ~7 o" n2 N" a; U DD2*(\[Beta]2)^3); a3 = (\[Alpha]*k3)/(3 `( M8 S; p* A- t5 V1 ~# t
DD3*(\[Beta]3)^3); a4 = (\[Alpha]*k4)/(DD4*(\[Beta]4)^3);
" m5 x0 |- Z; W; U\[Beta]1 = h/Subscript[l, 1]; \[Beta]2 = h/Subscript[l, 2]; \[Beta]3 \9 p( _" r+ g: J* T" v% V
= h/Subscript[l, 3]; \[Beta]4 = h/Subscript[l, 4];
, Z9 b$ b: \& E- S" |b1 = Subscript[l, 1]/Subscript[l, 3]; b2 = Subscript[l, \
* Y: I5 ?7 n( \' E$ n& K \6 k4 O% F4 C1]/Subscript[l, 4]; b3 = Subscript[l, 2]/Subscript[l, 3]; b4 = \
4 t; k$ w8 z4 ~' g WSubscript[l, 2]/Subscript[l, 4];3 w7 p2 {# z' m X: Y% m0 V
DD1 = D11/(A11*h^2); DD2 = D21/(A11*h^2); DD3 = D31/(A11*h^2);- W1 ?$ Z( ~+ t' p4 c: w
DD4 = D41/(A11*h^2);
. p$ F% O. _3 B7 L9 O- |r11 = Power[a1*\[Omega]^2, (4)^-1]; r12 = Power[" V* U/ A' r/ b5 [
a2*\[Omega]^2, (4)^-1]; r13 = Power[
$ d. }6 Y. e' t6 [ a3*\[Omega]^2, (4)^-1]; r14 = Power[a4*\[Omega]^2, (4)^-1];" d: \4 o- h; }$ _% k, }( ?' u) g1 Z4 r! N
BB = {{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},' ^1 m/ s; K* T5 o& s9 s) M$ Z' O
{0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},
I/ y- x4 j- }& S {0, Cosh[r12], 0, 0, 0, Sinh[r12], 0, 0, 0, Cos[r12], 0, 0, 0, 9 n" k% ^. c7 R$ c9 t
Sin[r12], 0, 0},
' p3 J) a, u4 @# _ {0, Sinh[r12], 0, 0, 0, Cosh[r12], 0, 0, 0, -Sin[r12], 0, 0, 0, % o4 [: \$ K: k9 K* q
Cos[r12], 0, 0},7 w$ y8 d& L$ c( q# j( G+ D
{-(r11)^2*DD1*(\[Beta]1)^2*Cosh[r11],
+ i8 R6 M! {" Z8 n& v( a 0, (r13)^2*DD3*(\[Beta]3)^2, (r14)^2*DD4*(\[Beta]4)^2,) K' i5 r" o/ K3 c
-(r11)^2*DD1*(\[Beta]1)^2*Sinh[r11], 0, 0,
% C) W8 P5 t, K& }# v# t 0, (r11)^2*DD1*(\[Beta]1)^2*Cos[r11], 3 i d/ s% J4 v% n6 I
0, -(r13)^2*DD3*(\[Beta]3)^2, -(r14)^2*DD4*(\[Beta]4)^2, (r11)^2*. W$ m$ s: n8 d- } `
DD1*(\[Beta]1)^2*Sin[r11], 0, 0, 0},
. K9 ^/ e) G; z7 Q* w {-(r11)^3*DD1*(\[Beta]1)^3*Sinh[r11], 0, 0,
0 x5 P2 A4 w6 I- y# H! C 0, -(r11)^3*DD1*(\[Beta]1)^3*Cosh[r11],
1 V/ \+ y' {0 B- u9 {2 C, w& L3 D 0, (r13)^3*DD3*(\[Beta]3)^3, (r14)^3*DD4*(\[Beta]4)^3, -(r11)^3*
# N l2 c) I& k1 | DD1*(\[Beta]1)^3*Sin[r11], 0, 0, 0,
' ]3 s0 I9 r. A$ H (r11)^3*DD1*(\[Beta]1)^3*Cos[r11],
- z8 e4 Z+ c6 s) k, I5 L1 o* w/ h7 N 0, -(r13)^3*DD3*(\[Beta]3)^3, -(r14)^3*DD4*(\[Beta]4)^3},( i" `( N0 d8 U4 f
{0, -(r12)^2*DD2*(\[Beta]2)^2, (r13)^2*DD3*(\[Beta]3)^2*
- s2 [' u; ?, }, ~9 A7 a Cosh[r13], (r14)^2*DD4*(\[Beta]4)^2*Cosh[r14],
1 m: u8 m5 S3 ^9 u! [( n 0, 0, (r13)^2*DD3*(\[Beta]3)^2*Sinh[r13], (r14)^2*DD4*(\[Beta]4)^2* s( W8 b6 T! }% @" `" B+ G/ X% e
Sinh[r14], 0, (r12)^2*DD2*(\[Beta]2)^2,
* `1 \, o$ ]$ g5 O -(r13)^2*DD3*(\[Beta]3)^2*Cos[r13], -(r14)^2*DD4*(\[Beta]4)^2*
$ @7 k4 i9 M& }' J9 y Cos[r14], 0, 0,
# \' U) g5 i4 K, [/ m -(r13)^2*DD3*(\[Beta]3)^2*Sin[r13], -(r14)^2*DD4*(\[Beta]4)^2*
8 M2 z. b+ o1 a! {$ e: _ Sin[r14]},! l, O2 L, f7 l! K# s- b+ m4 v
{0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sinh[r13], (r14)^3*DD4*(\[Beta]4)^3*
9 P5 E6 w" k3 v Sinh[r14], 0, -(r12)^3*DD2*(\[Beta]2)^3,
% c" ]5 O+ n9 y* z (r13)^3*DD3*(\[Beta]3)^3*Cosh[r13], (r14)^3*DD4*(\[Beta]4)^3*) f7 J Y: c4 j' g% P" U" L
Cosh[r14], 0, 0, (r13)^3*DD3*(\[Beta]3)^3*Sin[r13],1 e* X' V# S' _0 w0 Q
(r14)^3*DD4*(\[Beta]4)^3*Sin[r14],
+ a% o" ?& w3 E" T 0, (r12)^3*DD2*(\[Beta]2)^3, -(r13)^3*DD3*(\[Beta]3)^3*Cos[r13]," m' J' j! v: W8 L+ n- @
-(r14)^3*DD4*(\[Beta]4)^3*Cos[r14]},
4 |! r6 i7 x! u" u! q9 h {Cosh[r11], 0, -1, 0, Sinh[r11], 0, 0, 0, Cos[r11], 0, -1, 0, & S( O0 J5 C4 n: J( x6 S9 n) m
Sin[r11], 0, 0, 0},
3 Q# V' p! z$ W1 e" K {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, -r13*b1,
3 h: c. q* E. M+ t: ~! c* m" u X" l 0, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],
" J8 u: W; W; ^+ I. Z& ?0 D# O4 a: ~ 0, -r13*b1},; Z. c- {% X8 T9 Q
{Cosh[r11], 0, 0, -1, Sinh[r11], 0, 0, 0, Cos[r11], 0, 0, -1, / [3 ~0 W9 F3 v0 h" \" b/ m
Sin[r11], 0, 0, 0},
! c. s% u7 q9 ?$ F {r11*Sinh[r11], 0, 0, 0, r11*Cosh[r11], 0, 1 Z! `; a$ y. a% V( X: q7 Y( `" b
0, -r14*b2, -r11*Sin[r11], 0, 0, 0, r11*Cos[r11],5 z0 u; M: J! b n
0, 0, -r14*b2},, h! @- W/ h2 L, {" T
{0, 1, -Cosh[r13], 0, 0, 0, -Sinh[r13], 0, 0, 1, -Cos[r13], 0, 0, 0,
* @ ]% j3 v: B) d- w! Z2 v 0, -Sin[r13]},
; U1 j u: P3 J0 w {0, 0, -r13*b3*Sinh[r13], 0, 0, r12, -r13*b3*Cosh[r13], 0, 0, 0,
, u3 [8 f- z8 F" |3 s% d% n4 f r13*b3*Sin[r13],
4 z7 U7 a. C$ }/ q. @ 0, 0, r12, -r13*b3*Cos[r13], 0},
- ]" X# X; Z& A, @4 D0 F0 Y {0, 1, 0, -Cosh[r14], 0, 0, 0, -Sinh[r14], 0, 1, 0, -Cos[r14], 0, 0,& G1 e9 j7 ?5 g
0, -Sin[r14]},
z. _2 @+ \8 N% [ {0, 0, 0, -r14*b4*Sinh[r14], 0, r12, 0, -r14*b4*Cosh[r14], 0, 0, 0, # ~& Z2 G9 w" g' H( U; Q0 x k
r14*b4*Sin[r14]," a( u" f u1 p* Y+ D
0, r12, 0, -r14*b4*Cos[r14]}}" r# J+ l9 [$ x7 r& J# W2 ^3 A
aa1 = Det[BB]3 J3 z. B) q, a/ p0 q
Plot[aa1, {\[Omega], -10, 10}]3 b2 U I A* q; J$ w/ K7 k. i
ss = FindRoot[aa1 == 0, {\[Omega], 2}][[1]]1 e( s4 ]( g( }6 q4 j
7 {4 g# t F( [) u4 h s. q( G) w/ T
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