CAPITOLUL 1

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70 2 K34 d34 = = 0, 6 K Probleme rezolvate. Sisteme cu 1 GLD – vibraţii forţate Pab 1 ⋅ 2l ⋅ l 2 M23 = = = l = 1, 11111Nm 2 2 l ( 3l) 9 2 2 Pa b 1 ⋅ ( 2l) ⋅ l 4 M32 = = = l = 2, 22222Nm 2 2 l ( 3l) 9 Verificarea diagramei M: ∑ ∫ 3 2 M1M l 2l dx = − ⋅ 1, 111067 ⋅ 1 + ( −2 ⋅ 1, 111067 ⋅ 1 + EI 3EI 6EI l + 2 ⋅ 1, 975324 ⋅ + 1 ⋅ 1, 975324 − 3 1 l 1 − ⋅ 1, 111067) + ( 2 ⋅ 1, 975324 ⋅ − 3 6EI 3 l = ( 7, 901296 − 7, 90094) 6EI ε T 1.11067 1.975324 M,M 1 ⋅ 1, 481481) = 3 1.111067 1.481481 1 2l l Fig.2.13 1.481481 0.7074 7, 901296 − 7, 90094 −3 % = ⋅ 100 = 4, 5 ⋅ 10 < 0,1 7, 901296 Calculăm coeficientul de flexibilitate:
STABILITATEA ŞI DINAMICA CONSTRUCŢIILOR 71 δ = 1 1/3 1 l 2l l 2l ∑ ∫ Fig.2.14 M l 2l dx = ⋅ 1, 111067 ⋅ 1, 111067 + EI 3EI 6EI 2 + 2 ⋅ ( 1, 975324) − l − 2 ⋅ 1, 111067 ⋅ 1, 975324) + 6EI − 2 ⋅ 1, 975324 ⋅ 1, 481481 + + = l 6EI ⋅ 2 ⋅ ( 1, 481481) 27, 16049927 l 6EI + 2 ⋅ ( 0, 74074) 2 ⋅ ( 1, 975324) 2 2 2 ω = δ=2,155595⋅10 -6 mN -1 1 mδ = 10, 7693radS 2 2 ⋅ ( 2 ⋅ ( 1, 111067) + 2 ⋅ ( 1, 481481) − 2 ⋅ 1, 481481 ⋅ 2. Determinarea factorului de amplificare dinamică, µ. −1 µ ∗ 1 = = 1, 72072 2 2 7 2 2 7 ( 1 − ) + 4( 0, 05) 2 2 10, 4693 10, 7693 F µ ∗ Fo=1,72072⋅10 4 d = N 3. Determinarea răspunsului în eforturi 2 0, 74074 Cunoscând mărimea forţei dinamice se determină forţele maxime şi minime:
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CONSTANTIN IONESCU STABILITATEA ŞI
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4 Cuprins 3.4. Vibraţii forţate p
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1.1.Generalităţi CAPITOLUL 1 STAB
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8 Stabilitatea şi Dinamica Constru
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10 1.2.4. Modelarea sistemelor Stab
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12 Stabilitatea şi Dinamica Constr
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14 1.2.6. Sistem dinamic (vibrant)
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16 a. m k a. m k x(t) x(t) c 1GLD b
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18 Stabilitatea şi Dinamica Constr
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Page 22 and 23: 22 a. x(t) F(t) m b. u(t) Sisteme c
Page 24 and 25: 24 b. pentru situaţia aplicării i
Page 26 and 27: 26 Sisteme cu un grad de libertate
Page 30 and 31: 30 a. b. m a. k ∆ =1 b. k m MS
Page 34 and 35: 34 ∗ Sisteme cu un grad de libert
Page 38 and 39: 38 1.1.3 1.1.2 1 EI=const 1.1.5. m
Page 40 and 41: 40 Probleme rezolvate. Sisteme cu 1
Page 42 and 43: 42 1/2 ω = 1 mδ l/2 − Probleme
Page 44 and 45: 44 Aplicaţia 1.3 (fig.1.3) 1. Tras
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Page 48 and 49: 48 nodul 7: ⎧ ⎪∑ x = 0; ⎨
Page 50 and 51: 50 b) forţa elastică c) forţa pe
Page 52 and 53: 52 m( ω F 0 2 Sisteme vibrante cu
Page 54 and 55: 54 xF ( t) Sisteme vibrante cu 1GLD
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Page 60 and 61: 60 2.2. 2.3. 2.4 Problema 2.2 EI=co
Page 62 and 63: 62 Breviar teoretic 1. Forţe Probl
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Page 72 and 73: 72 6.27166⋅10 4 2.448⋅10 4 Fig.
Page 74 and 75: 74 δ ss δ ss = δ 11 + 2δ Calcul
Page 76 and 77: 76 3. Determinarea răspunsului în
Page 78 and 79: 78 X(t) ϕ/ω=0.01782 s x0ω 2 Apli
Page 80 and 81: 80 X(t) ϕ/ω Rezolvare µ * F0δ
Page 82 and 83: PROBLEME PROPUSE 1 SISTEME CU 1GLD
Page 84 and 85: 84 m Probleme propuse. Sisteme cu 1
Page 86 and 87: 86 Fig. 1.10 F( t) = F0 sin θt Pro
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Page 90 and 91: 90 ⎡ δ11 δ12 . δ1j . δ1n ⎤
Page 92 and 93: 92 λ n + a n−1 1 λ + ....... +
Page 94 and 95: 94 [ Ω] ⎡ω ⎢ ⎢ ⎢ = ⎢
Page 96 and 97: 96 ⎧ 1 ⎫ y 1 = ⎨ ⎬ şi {} y
Page 98 and 99: 98 c. d. 1, 1 d. 1, 1 δ1 j δ41 δ
Page 100 and 101: 100 1,1 1,1 a. b. c 1 l 1 1,1 l 1 l
Page 102 and 103: CAPITOLUL 5 SISTEME VIBRANTE CU nGL
Page 104 and 105: 104 Sisteme vibrante cu nGLD. Vibra
Page 106 and 107: 106 2 [ K] − ω [ m] ) { A} = { 0
Page 108 and 109: 108 Sisteme vibrante cu nGLD. Vibra
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Page 112 and 113: 112 5.6.1. Folosirea metodei forţe
Page 114 and 115: 114 a. c. 2 R1p K Z1 Z2 K 2 R2p Z3
Page 116 and 117: 116 ⎧y⎫ ⎨ ⎬ ⎩θ⎭ [ r ]{
Page 118 and 119: 118 3.4 1 3.3 2EI 0.5l m2 Probleme
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120 [ ∆] ⎡δ11 ⎢ ⎢ δ21 ⎢
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122 εr % = det( Probleme rezolvate
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124 Probleme rezolvate. Sisteme cu
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126 δ 11 Probleme rezolvate. Siste
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128 εa εr % = ⎛ 3 ml ⎞ 94⎜
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130 2. Determinarea matricei de fle
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134 şi matricea de flexibilitate d
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136 a. c. 1. 3265 2. 4458 e. y , 2
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138 Matricea de flexibilitate se co
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142 6EI 2 a a. 6EI 2 a c. 4EI a f.
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CAPITOLUL 6 SISTEME VIBRANTE CU nGL
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STABILITATEA ŞI DINAMICA CONSTRUC
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PROBLEME PROPUSE 2 SISTEME CU n GLD
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CAPITOLUL 7 SISTEME VIBRANTE CU NGL
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9.1. Grinda încastrată CAPITOLUL
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CAPITOLUL 11 CALCULUL DE STABILITAT
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CAPITOLUL 14 CALCULUL DE ORDINUL II
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BIBLIOGRAFIE B 1. Bănuţ, V., Calc
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CAPITOLUL 1

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