Пвлов_PROCHNOST_2_FULL+PROTECTION
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m 2ϕ dM = − jz τ 2 dz,
. m0 m – ;
jzm – & .
/ 12 . 1. & 0 ,
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+ [Q |
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(α + ϕ)]′ + R + t − my |
= 0.1) |
(1.3.3) |
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2. & 0 , ,
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+ [Qy (α + ϕ)]′ + H − t(α + ϕ) = 0. |
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(1.3.4) |
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3. z , # , |
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M z |
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m |
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2) |
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+ (Qy x) |
− (Qx y) − Hy0 + |
− jz |
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(1.3.5) |
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+ (M x x ) |
− (M y y ) |
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ϕ = 0. |
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4. & 0 , ,
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Qoy |
− R + t0 |
− m0 y |
0 = 0. |
(1.3.6) |
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z |
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. t = pdx, |
t0 = p0dx0 , |
= pxdx – |
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b |
b0 |
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; b0 b – .
1)2 z, – τ .
2)z # , # .
3
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M y |
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0 |
M x0 |
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Qy = − |
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Qx = − |
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Qy = − |
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(1.3.7) |
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R (1.3.6) (1.3.4) (1.3.2), (1.3.3)
(1.3.5):
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(α + ϕ]'+ |
Qy0 |
+ (t |
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+ t) − (m |
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+ m)y |
= 0, |
(1.3.8) |
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M z |
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+ (M x x') |
− (M y y')'+(Qy x)'−(Qx y)'+ |
Qx |
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y0 − |
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− [Qy (α + ϕ]' y0 − t(α + ϕ)y0 + − |
m |
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(1.3.9) |
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jz |
ϕ = 0. |
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* , M x = EI x y", |
M y = EI y x", |
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M x0 = EI x0 y0" , |
M z = GI ϕ', |
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#:
+ {Ay"}"+{[B(yα + yϕ )"]'(α + ϕ )}'+[Dy"]"−(t0 + t) + (m0 + m)y = 0,
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( ϕ |
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) − (B − A)[y(α + ϕ )]" y"+(Ay")ϕ ' y − t(α |
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(1.3.10) |
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+ ϕ )y + |
− jz |
ϕ = 0. |
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. = Ix – ; = I |
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; =GI – ; |
D = EIx0 – |
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! |
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«#»( |
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) , (1.3.10)
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(A + D)yIV + B{[ y(α + ϕ )]'"(α + ϕ )}'−(t |
0 |
+ t) + (m |
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+ m) y = 0, |
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ϕ"−( − A)[y(α + ϕ)]" y"+ Ay'"ϕ' y − t(α + ϕ)y + |
m |
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– jz |
ϕ = 0. |
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(1.3.11)
. [16]
y = f (τ ) y(z),
(1.3.12)
ϕ = θ (τ )ϕ (z),
. (1.3.11)
L(y, ϕ) = 0, M (y, ϕ) = 0
l |
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Lydz = 0, |
Mϕdz = 0. |
(1.3.13) |
0 |
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* (1.3.13) # ,
'
z = 0 y0 = y0 = ϕ0 = 0,
'
z = l yl"= y '"l = ϕ l' = 0
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f + f (a |
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+ a |
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θ + a |
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θ 2 ) = 0, |
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(1.3.12), : |
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(1.3.14) |
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b |
θ + b θ + f 2 |
(b + b θ) = 0. |
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l |
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2dz, |
a = (m |
+ m) (y)2dz, |
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b |
= jm ϕ |
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a3=(A+ D+α 2B) (y") |
2dz, |
b5 =C (ϕ')2dz, |
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a4 = αB{(2y'ϕ" y + y2ϕ '")l + |
b6 = α (B − A) (y")2ϕdz, |
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0 |
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+ [2(y")2ϕ + 3y" y'ϕ '+ y"ϕ ' y]dz}, |
b7 = (B − A) y"ϕ (yϕ )"dz + |
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a5 = B[(2y'ϕ"ϕy + y2ϕ '"ϕ )l + (yϕ )"(ϕy')'dz], |
+ A y" (ϕ ' yϕ )'dz. |
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! (1.3.14),
ω .
*
y(z) = 1− coskz, |
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cosωτ , |
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f (τ ) = f |
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ϕ (z) = sin kz, |
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cos2 |
(1.3.15) |
θ (τ ) = f |
θ |
ωτ . |
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. f θ – ; k = π , l – . 2l
* & 1-4 (1.3.14) [4], [14].
*
L(τ) = 0, M (τ) = 0,
:
2π / ω |
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2π / ω |
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(τ) cos2 ωτ dτ = 0. |
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L |
(τ) cos ωτ dτ = 0, |
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M |
(1.3.16) |
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* : |
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2 |
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− 8a ω 2 |
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5a θ |
+ 6a θ |
+ 8a |
3 |
= 0, |
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1 |
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(1.3.17) |
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2(3b − 4b ω 2θ ) + f |
2 (6b |
+ 5b |
θ ) = 0. |
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0 (1.3.17) ω, θ f . + 1.3.4
- α ,
(1.3.17) D=B» A:
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ω 2 |
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= 1 − 0,477 |
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θ − 0,876 |
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θ . |
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ω0 |
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1 + α 2 |
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1 + α 2 |
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. ω02 = |
a3 |
– |
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a |
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Mξ |
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Mη |
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Mζ |
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æξ = |
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; æ η = |
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; τ ζ |
= |
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(2.1.1 ) |
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EJ |
ξ |
EJη |
GJ |
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, &-& 0. 7 ξ , |
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ηζ1 |
ξ ζ1 ; |
τζ |
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ξ η ; ζ − ; EJξ, EJη −
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ξ η ζ 1 . |
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ξη1ζ $ |
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