MODELLING OF MECHANICAL SYSTEM VOLUME 2 Episode 6 ppsx

... 6 ℓ 0 − 12 6 ℓ 0 6 ℓ 4γℓ 2 06 ℓ 2 ℓ 2 −10 0 1 0 0 0 − 12 6 ℓ 0 12 6 ℓ 0 6 ℓ 2 ℓ 2 06 ℓ 4γℓ 2        ⇒ K (2) = K ℓ     1000 0 12 6 ℓ 6 ℓ 0 6 ℓ 12 2 ℓ 2 0 6 ℓ 2 ℓ 2 4γℓ 2     Then, ... found to be: K (1) α = K ℓ     4γℓ 2 6 ℓS 6 ℓC 2 ℓ 2 6 ℓS C 2 + 12 S 2 CS( 12 −1) 6 ℓS 6 ℓC CS( 12 −1)S 2 + 12 C 2 6 ℓC 2 ℓ 2 6 ℓS 6 ℓC 4γℓ 2  ...

Ngày tải lên: 13/08/2014, 05:22

... coefficient 46 law 44, 46 wave 40 relation of constraint 2 resonant range 22 5, 22 6 response 22 6 response spectrum 22 7 resultant stress 72 rigid body 24 , 26 2 mode 23 6 motion 8 rigid connection mode 25 6 spring ... 26 7 quasi-inertial range 22 5, 22 8 quasi-static correction 22 8, 23 5 mode 22 8 range 22 5, 22 8 Rayleigh minimum principle 29 4, 29 9 Rayle...

Ngày tải lên: 13/08/2014, 05:22

... 322 6 .2. 2.3. External loading of the edges and inhomogeneous boundary conditions 322 6 .2. 3. Surface and concentrated loadings 324 6 .2. 3.1. Loading distributed over the midplane surface 324 6 .2. 3 .2. ... 1 96 4 .2. 2.1. Longitudinal modes 1 96 4 .2. 2 .2. Torsion modes 20 0 4 .2. 2.3. Flexure (or bending) modes 20 0 4 .2. 2.4. Bending coupled with shear modes 20 5 4 .2....

Ngày tải lên: 13/08/2014, 05:22

... get: X 2 = U 2 sin θ 2 e iψ 2 ; Z 2 = U 2 cos θ 2 e iψ 2 ; ψ 2 = ω  t − x sin θ 2 − z cos θ 2 c L  (σ zz ) 2 = −iωU 2 c L  λ +2G(cos θ 2 ) 2  e iψ 2 ; (σ zx ) 2 = +iωU 2 c L G sin 2 2 e iψ 2 ; ... that: λ +2G(cos θ) 2 G = λ +2G(1 −(sin θ) 2 ) G = λ +2G(1 −(γ sin β) 2 ) G = γ 2 (1 2( sin β) 2 ) = γ 2 cos 2 The system [1.1 12] is thus...

Ngày tải lên: 13/08/2014, 05:22

... as:  x+dL /2 x−dL /2  (S) r ×  ρ ∂ 2  ξ ∂t 2 − ∂  t 1 ∂x  dS dx =  x+dL /2 x−dL /2  (S) (r ×  f (e) )dS dx +  M (e) (x; t)dL [2. 20] Using the relations [2. 1], [2. 8], and [2. 9], the following ... In terms of local quantities it reduces to: ρ ∂ 2  ξ ∂t 2 − ∂  t 1 ∂x =  f (e) (x, y, z; t) ρ ∂ 2 ξ j ∂t 2 − ∂σ xj ∂x = f (e) j (x, y, z; t); (j = 1, 2, 3) [2....

Ngày tải lên: 13/08/2014, 05:22

... GS   ∂Y s ∂x  2 +  ∂Z s ∂x  2  dx + 1 2  L 0  GJ T  ∂ψ x ∂x  2 +  EI z  ∂ 2 Y b ∂x 2  2  +  EI y  ∂ 2 Z b ∂x 2  2  dx [3 .2] The kinetic energy E κ is: E κ = 1 2  L 0 ρS{ ˙ X 2 + ( ˙ Y s + ˙ Y b ) 2 + ( ˙ Z s + ˙ Z b ) 2 }dx + 1 2  L 0 ρ(J ˙ ψ 2 x + I y ˙ ψ 2 y + ... as: E es = 1 2  L 0 GSκ  ∂Z s ∂x  2 dx [3 .21 ] The bending str...

Ngày tải lên: 13/08/2014, 05:22

... +E n I n  ℓ n 0  ∂ 2 Z n ∂x 2  2 dx =[X I Z I Z ′ I X J Z k Z ′ J ]        K 11 K 12 K 13 K 14 K 15 K 16 K 21 K 22 K 23 K 24 K 25 K 26 K 31 K 32 K 33 K 34 K 35 K 36 K 41 K 42 K 43 K 44 K 45 K 46 K 51 K 52 K 53 K 54 K 55 K 56 K 61 K 62 K 63 K 64 K 65 K 66               X I Z I Z ′ I X J Z J Z ′ J        where ... is...

Ngày tải lên: 13/08/2014, 05:22

... follows:    2 L + ̟ 2 1 − ̟ 2 2 L 2 L 2 L 2 L 2 L + ̟ 2 2 − ̟ 2 2 L 2 L 2 L 2 L 2 L + ̟ 2 3 − ̟ 2 2 L 2 L 2 L 2 L 2 L + ̟ 2 4 − ̟ 2      q 1 q 2 q 3 q 4   =   0 0 0 0   by ... 1, 2 If four modes are retained in the projection, the following homogeneous system to be solved is:    2( γ L + ̟ 2 ) 2 L 2 L 2 L 2 L 2...

Ngày tải lên: 13/08/2014, 05:22

... or odd Ehπ 2 4  n 2 η + m 2 η 2  α 2 n,m +  n 2 η + m 2 2η  β 2 n,m  otherwise Ehπ 2 4  n 2 η + m 2 η 2  α 2 n,m +  n 2 η + m 2 2η  β 2 n,m + 8n 2 m 2 π 2 (n 2 − m 2 ) 2 α n,m β n,m  where ... system: 4Eh M      π 2 4  n 2 + m 2 η 2 2  −  ω ′ n,m  2 2n 2 m 2 η 2 (n 2 − m 2 ) 2 2n 2 m 2 η 2 (n 2 −...

Ngày tải lên: 13/08/2014, 05:22

... Z ε xx =−z ∂ 2 Z ∂x 2 + 1 2  ∂Z ∂x  2 + z 2 2   ∂ 2 Z ∂x 2  2 +  ∂ 2 Z ∂x∂y  2  ε xy =−z ∂ 2 Z ∂x∂y + z 2 2 ∂ 2 Z ∂x∂y  ∂ 2 Z ∂x 2 + ∂ 2 Z ∂y 2  + 1 2  ∂Z ∂x ∂Z ∂y  ε yy =−z ∂ 2 Z ∂y 2 + 1 2  ∂Z ∂y  2 + z 2 2   ∂ 2 Z ∂y 2  2 +  ∂ 2 Z ∂x∂y  2  [6. 89] In ... m 2 ) 2 ; α n,m = β n,m out -of- phase modes: f n,m = c...

Ngày tải lên: 13/08/2014, 05:22