8- My + Cy + Ky = f () t 8. C f () t ( t) = Ψq( t) () t = Ψq () t () t = Ψq () t = ( q q ) ; = [ ] y y y q Ψ φ φ φ = ( ϕ, ϕ, ϕ,3 ) 8. ψ Ψ MΨq + Ψ CΨq + Ψ KΨq = Ψ f ( t) Ψ MΨ = I; Ψ CΨ = C; Ψ KΨ = Λ; q + hωq + ω q = f / m; ( = ) 8.3 f f () t = ϕ f () t = ϕ f () t + ϕ f () t + ϕ f () t +, j j,,,3 3 j= 8.4
8- (8.3) (8.) m y() t = φ f ( τ) g ( t τ) dτ = = t 0 ( ) = φ f τ e h ω t τ dτ t hω( t τ) ( ) ( ) 0 hωm 8.5 ω h r (8.) My + Cy + Ky = I Fe r pt 8.6 I r 0 ( 0,0,, 0) I r = 8.7 pt ω ω ϕr, Fe / m q + h q + q = ; ( = ) 8.8 pt + ω + ω = Fe q h q q 8.9
8-3 q F = e ω p + hω p pt 8.0 (8.8)(8.0) F ϕ r. = ω p + hωp m y = φ e pt 8. ω = k / m y = = ( ) + ω = r. pt A B φ e k = ( + ) F ϕ φ p p h k ω ϕ F r. e pt 8. p p h A = = p p p p { ( ) } + 4 ( ) { ( ) } + 4 ( ) ω ω ω ω ( ) ( ) ω ω ; B h h 8.3 ( ) = [(, ) + (, ) ] = = y p Aa B a 8.4 a F k F m, = ϕ, r ϕ, / = ϕ, r ϕ, /( ω ) 8.5
8-4 My + Cy + Ky = MI x y 8.6 q y ( t) = Ψq( t) 8.7 y () t = Ψq () t y () t = Ψq () t q = q q ; Ψ = φ φ ( ) [ ] Ψ q + hωq + ω q = β y; ( = ) 8.8 β j x m jϕ, j β = φ MI = 8.9 j mj j= mj m β φ I x I x 8.0 βϕ, = ( = ) = y q () t q + hωq + ωq = y; ( = ) 8. = () t y = β φ q 8.
8-5 t q () t = y( τ) g ( t τ) dτ 0 ( ) t hω( t τ) q() t = y( τ ) e h ( ) 0 ω t τ dτ hω 8.3 (8.)8.3 q () t = π / ω h V B V = m ( y + y) B = 8.4 (8.)
8-6 M V = m β ϕ ( q + y) B, = = = M( q + y) = M = ( mϕ ) β, = 8.5 8.6 m / m (8.9) m ϕ M m m m m, = ( ϕ, ) β = ( ) β = β = m = m = β φ M βφ 8.7 (8.5) q + y M (8.7) M β φ x x x x = = m = I MI = I Mβ φ = I M( β φ + β φ + ) I x 8.8 βϕ, = = = ( ) (8.8) I x m = βφ M βφ = βφ M βφ = = = = (8.7) m = M = = 8.9
8-7 M B M = m( y + y) B = 8.30 y M = m β ϕ ( q + y) B, = = M / M mβ ϕ M = M ( q + y), B = = M = M ( q + y) = 8.3 mβ ϕ = M =, 8.3 (8.6) = = mϕ =, m ϕ, 8.33 (8.3) M B q + y M (8.3) m = MIx = Mβφ = = = = j= mϕ β j j, j M / M (8.3)
8-8 mβϕ j j, j m = M = M = = j= M = 8.34 6 6 m =.0 0 kg, m =.0 0 kg, h = 3.5 m, h = 7.0m φ = (.0,.946) φ = (.0, 0.54) m ϕ β = = j= j, j j= m j= m ϕ m j, j jϕ, j m m 0.0 0.946..946 β = = = = 0.654 4.787 0.0 0 0.54. 0.486 β = = = = 0.3845.64 4 4 ϕ,+ ϕ, + 4 4 mϕ,+ mϕ, 0 + 0.946 m 4 4 ϕ,+ mϕ, 4 4 mϕ,+ mϕ, 0 + 0 0.54 β φ β φ.0 0.65 = 0.654=.946.98.0 0.385 = 0.3845= 0.54 0.98
8-9 M = β φ Mβ φ M M 4.0 0 0.65 = 0 ( 0.65.98) 0.0.98 = + = 4.0 0 (0.65.98 ) 3669 ( ) kg.0 0 0.385 0.0 0.98 4 = 0 0.385 0.98 = + = 4.0 0 (0.385 0.98 ) 3749 kg M + M = 3669 + 3749 = 4008kg m + m = = mϕ =, m ϕ, ϕ ϕ.0 0 ( 3.5.946 7.9) = = = 5.8m m 4,+ m, + m 4 ϕ,+ m ϕ,.0 0 ( +.946) ϕ ϕ.0 0 ( 3.5 0.54 7.9) = = = 0.0m m 4,+ m, 4 mϕ,+ mϕ,.0 0 ( 0.54) m = M = = = = 4 5 m =.0 0 (3.5 + 7.0) =. 0 M = 3669 5.8 3749 0.0 =. 0 5
8-0 (abolute um)(8.) y βϕ S (, h ) max, D = 8.35 S D (root um quare(rss),quare root of um of quare) y βϕ S (, h ) max, D = 8.36 (8.35)(8.36) y max ( y, RSS + y, ABS ) 8.37 δ β ( ϕ ϕ ) S (, h ) max,, D = 8.38
8-6 6 m =.0 0 kg, m =.0 0 kg, h = 3.5 m, h = 7.0m φ = (.0,.946) φ = (.0, 0.54) = 0.4ec = 0.078ec h = 0.05 k G = 0. S = k = = cm D 90 G 90 0.4 0..04 S = k = = cm D 90 G 90 0.078 0. 0. RSS8. y y ABS { βφ} SD { βφ } = + 0.65 0.385 =.04 + 0..98 0.98 0.64 0.04 0.683 = + = cm.46 0.0.68 S D
8- y y RSS { βφ SD} { βφ SD} = + 0.64 + 0.04 0.64 = = cm.46 + 0.0.46 δ δ ABS { β( ϕ, ϕ, ) } S { β( ϕ, ϕ, ) } = + D D 0.65 0.385 =.04 + 0. 0.58 0.583 0.640 0.04 0.68 = + = cm 0.605 0.064 0.669 S δ δ RSS { β( ϕ, ϕ, ) SD} { β( ϕ ϕ, ) SD} 0.640 + 0.04 0.64 = = cm 0.605 + 0.064 0.608 = +