3 2 mathematical modeling of mechanical systems

Mathematical Modeling of Biological Systems, Volume I pptx

... · PI3K]i V PIP2 Ns kass [PIP2 ]i [PTEN]cyto PIP2 Ns kdiss [PIP2 · PTEN]i PI3K·Rec(i)+PIP2 (i) → PI3K·Rec(i)+PIP3 (i) PI3K kcat [Rec·PI3K]i [PIP2 ]i PI3K PTEN·PIP2 (i)+PIP3 (i) → PTEN·PIP2 (i)+PIP2 ... (i)+PIP2 (i) PTEN kcat [Rec·PTEN]i [PIP3 ]i PTEN K M +[PIP3 ]i KM √D 3Ssite PIP2 (i)→PIP2 (j) √D 3Ssite PIP3 (i)→PIP3 (j) ′ ′ +[PIP2 ]i [PIP2 ]i − [PIP2 ] j + [PIP3 ]i − [PIP3 ] j + Table 3. 2 Physical ... 6 23 Springer, Berlin, pp 1 53 178 (20 03) 24 Rozi, A., Jia, Y.: A theoretical study of effects of cytosolic Ca2+ oscillations on activation of glycogen phosphorylase Biophys Chem., 106, 1 93 20 2...

388
246
0

.MODELLING OF MECHANICAL SYSTEMS VOLUME 2..MODELLING OF MECHANICAL SYSTEMS VOLUME 2Structural docx

Danh mục: Kĩ thuật Viễn thông

... 6 .2 .3. 3 Point loads 28 9 29 0 2 93 29 9 30 3 30 4 30 5 30 7 30 7 31 1 31 2 31 2 31 3 31 3 31 3 31 4 31 6 31 6 31 6 31 7 31 8 31 9 31 9 32 2 32 2 32 4 32 4 32 5 32 6 xii ... 5 .3. 4.4 Uniform plate stretching 23 5 23 7 23 8 24 0 24 0 2 43 24 5 24 7 24 8 25 4 25 6 25 9 26 0 26 0 26 0 26 2 26 2 26 2 2 63 2 63 2 63 26 5 26 5 26 5 26 6 26 7 27 0 27 0 27 2 2 73 27 5 27 5 ... 177 180 186 188 189 190 190 190 1 93 196 196 20 0 20 0 20 5 20 7 20 7 20 9 21 0 21 0 21 1 2 13 2 13 21 4 21 7 21 8 22 0 22 0 22 1 22 2 22 2 22 4 22 9 23 1 23 1 23 2 x Contents 4.4.1 .2 Truncation stiffness for a free-free...

521
379
0

Dynamics of Mechanical Systems 2009 Part 2 potx

Danh mục: Kĩ thuật Viễn thông

... (2. 8 .3) in the forms: A1 A ⋅ (B × C) = B1 C1 B1 = − A1 C1 A2 B2 C2 B2 A2 C2 A3 B1 B3 = C1 C3 A1 B3 A1 A3 = − C1 C3 B1 B2 C2 A2 B3 C1 C3 = A1 A3 B1 A2 C2 B2 C2 A2 B2 A3 C1 C3 = − B1 B3 A1 C3 A3 ... B = A1B1 + A2 B2 + A3 B3 (2. 8.1) and n1 A × B = A1 B1 n2 A2 B2 n3 A3 B3 (2. 8 .2) where the Ai and Bi (i = 1, 2, 3) are the ni components of A and B By comparing Eqs (2. 8.1) and (2. 8 .2) , we see ... Eq (2. 6 .21 ), C • A is: C ⋅ A = ( 4)(7 ) + (60)( 2) + ( 23 ) ( 4) = (2. 7 .26 ) C ⋅ B = ( 4)(1) + (60) (3) + ( 23 ) ( −8) = (2. 7 .27 ) Similarly, C · B is c From Eq (2. 7. 23 ) , B × A is: n1 B×A = n2 2 n3 −8...

50
381
0

Dynamics of Mechanical Systems 2009 Part 3 pptx

Danh mục: Kĩ thuật Viễn thông

... s1c2 c3 + c1s3 )n + ( − s1c2 s3 + c1c3 )n and n1 = c2N1 + c1s2N − s1s2N n = s2c3N1 + (c1c2c3 − s1s3 )N + ( s1c2c3 + c1s3 )N (4 .3. 14) n = − s2 s3N1 + ( − c1c2 s3 − s1c3 )N + ( − s1c2 s3 + c1c3 ... orientation of B in R (see Figure 4 .3. 7) Hence, the unit vectors are related by the expressions: N1 = c2n1 + s2c3n − s2 s3n N = − c1s2n1 + (c1c2c3 − s1s3 )n + ( − c1c2c3 − s1c3 )n (4 .3. 13) N = − s1s2n1 ... S V L = 22 .38 1n x − 1.571n y + 2. 721 n z ft sec (4.9.17) and S ( ) − 0.88n ) × (0. 433 n a L = −19 .36 n y + ( −5. 529 )n y × 0. 433 n y + 0 .25 n z [ +(6 .28 3n x − 0.88n z ) × (6 .28 3n x z y + 0 .25 n z )]...

50
251
0

Modeling of Combustion Systems A Practical Approach 2 pptx

Danh mục: Kĩ thuật Viễn thông

... 19. 93 2. 258 2. 258 2. 258 2. 258 2. 258 2. 258 2. 258 2. 258 2. 258 2. 258 2. 201 2. 180 2. 127 2. 1 13 2. 089 2. 045 1.996 1.948 1.8 82 1. 833 9.91 13. 40 22 .36 24 .70 28 .55 35 .64 43. 39 50.87 60. 63 67.76 24 .07 23 . 59 ... 32 2. 1 2. 075 2. 125 2. 1 82 2. 23 7 20 1 /2" 20 3/ 4" 21 " 21 1/4" 20 .5000 20 .7500 21 .0000 21 .25 00 64.4 03 65.188 65.974 66.759 33 0.1 33 8 .2 34 6.4 35 4.7 2. 2 92 2 .34 8 2. 405 2. 4 63 21 1 /2" 21 3/ 4" 22 " 22 1/4" 21 .5000 ... 106 .2 101.6 96.1 90.8 86.6 80.5 6. 52 7.11 9.84 12. 88 14.58 15.74 19 .24 21 . 52 26.04 31 .5 36 .9 41.1 47.1 3. 34 3. 34 3. 34 3. 34 3. 34 3. 34 3. 34 3. 34 3. 34 3. 34 3. 34 3. 34 3. 34 3. 25 3. 24 3. 21 3. 17 3. 14 3. 13...

17
318
0

Modeling of Combustion Systems A Practical Approach 3 docx

Danh mục: Kĩ thuật Viễn thông

... W/m2 W/m2 K J/mol kJ/kg Mass [M] 1 –1 –1 1 1 1 Exponents Length Time θ [L] [θ] 3 3 3 2 2 –1 –1 –1 –1 1 1 1 1 2 2 2 Temperature [T] 2 2 2 2 2 2 2 2 –1 –1 –1 2 2 2 3 2 2 2 3 2 ... 4187 J 3. 968 Btu/hr 1.1 62 J/sec 0.1 124 Btu/ft3 4187 J/m3 2. 205 lb 0.0 027 8 g/sec-cm 0.6 72 lb/hr-ft 0.0 62 43 lb/ft3 34 13 Btu/hr 1 .34 1 hp 660.6 kcal/hr 31 7 .2 Btu/hr-ft2 176 .2 Btu/hr-ft2-°F 0.4 536 kg ... cal/cm2-sec = cal/cm-sec-°C = cal/g = cal/g-°C = centipoise = cm2/sec = ft = ft2/sec = g/cm3 = hp = 25 2.0 cal 1055 J 0.00890 cal/cm3 0. 037 3 MJ/m3 0.00 039 31 hp 0 .25 20 kcal/hr 0 .2 931 W 0 .2 93 MW 0.0 031 53...

4
303
0

Mathematical modeling of transport phenomena in electrochemical energy storage systems

Danh mục: Y - Dược

... , 29 430 3, 21 23 , 20 10 ix àà, à, , , , 30 431 2, 21 23 , 20 10 àà, , , à, , 20 11, , 26 1, 20 11 àà, , , à, ààà : , 20 11, , 26 ... [21 ] , , , [22 ] à [19] à [ 23 ] [24 ] à àà à, [25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 ], [2, 3, ... (3. 18) (3. 19) 3. 1 22 = 0, = ; = ; = > > > > () < = > > > > () : (3. 20 ) (3. 21 ) = 0 (,,) 3. 1.6 (3. 22 ) à, , = > > > > (, ) < > > > >0 : ; (3. 23 ) ...

172
347
0

03 analysis of mechanical systems using interval computations applied to finite element methods o dessombz

Danh mục: Báo cáo khoa học

... i 2 )k2 −(1 + i 2 )k2 (1 + iη1 )k1 0 0 + e1 0 −(1 + i 2 )k2 (1 + i 2 )k2 + (1 + i 3 )k3 +e2 1 0 (1 + i 2 )k2 −(1 + i 2 )k2 m1 + e3 −ω 1 m2 (1 + i 3 )k3 −(1 + i 2 )k2 (1 + i 2 )k2 H1 H2 = f1 f2 ... by:   2EI −EI  9l 3l2  d = F ( 32 )  −EI 2EI  θ M 3l2 3l3 And from a numerical point of view, the stiﬀness matrix is an interval matrix: [4 033 .68, 436 9.68] [−6554. 52, −6050. 52] [−6554. 52, −6050. 52] ... t3 is (t0 + δt )3 = t3 + 3 t.t2 + 3t0 δt2 + δt3 0 (38 ) The matrix equation (37 ) becomes : t3 [K](1 + iη) − ω t0 [M ] + δt 3. t2 [K](1 + iη) − ω [M ] 0 + 3t0 δt2 + δt3 [K](1 + iη) {H} = {F } (39 )...

21
424
0

Tài liệu Activity 3.2: Identifying Sources of Information doc

Danh mục: Hệ điều hành

... 18 Activity 3. 2: Identifying Sources of Information Exercise 1: Identifying Sources of Information ! Develop a list of sources of information Review the information ... the following table, list examples for each source of information You will discuss your results in a class discussion Sources Examples Artifacts Systems People ...

2
346
0

Vibration of mechanical systems

Danh mục: Cơ khí - Chế tạo máy

... Matrices 23 7 23 7 20 1 2 03 20 9 21 2 21 2 22 0 22 4 22 4 22 7 22 8 22 8 23 1 23 9 24 2 Contents 5.1 .3 Modal Decomposition Case I: Undamped System (C = 0) Case II: Proportional or Rayleigh Damping 5 .2 Continuous Systems ... Potential Energies of the Beam Exercise Problems xi 24 5 24 6 24 9 25 0 25 0 25 1 25 5 25 8 26 1 26 5 26 5 26 7 26 9 27 1 2 73 27 9 27 9 2 83 28 6 29 1 29 5 APPENDIX A: EQUIVALENT STIFFNESSES (SPRING CONSTANTS) OF BEAMS, ... 1 .3. 12, the total PE in the system is PEtot = 1 k1 x + k2 x1 2 (1 .3. 33) where from Figure 1 .3. 13, x1 = r3 θ (1 .3. 34) Substituting Equation 1 .3. 34 into Equation 1 .3. 33 and using Equation 1 .3. 23 , ...

330
800
0

stochastic modeling of manufacturing systems advances in design, performance evaluation, and control issues - g. liberopoulos

Danh mục: Kế hoạch kinh doanh

... Information Scheduling General Outsource Process Systems Control C11 I 12 S 13 G14 O15 C21 I 22 S 23 G24 O25 C31 I 32 S 33 G34 O35 C41 I 42 S 43 G44 I 52 S 53 G45 Fig 10 Path through IBIS network In fact, ... not just one Refer to Figure 11 for an illustration of this process J MacGregor Smith 18 11 i 12 i1 i i2 i 22 11 i 21 12 21 i1 i2 i i 22 i3 32 31 Fig 11 Many explanations possible for i The paradox ... units of cycle time For the case of M > 2machine serial lines, the following formula had been derived (Enginarlar et al., 20 03a): e(1 Q)(eQ + e)(eQ + 2e) (2 Q) ì Q(2e 2eQ + eQ2 + Q 2) ...

364
411
0

Báo cáo hóa học: " Research Article A Variational Approach to the Modeling of MIMO Systems" docx

Danh mục: Báo cáo khoa học

... into the form Pe,sup δmin = − Γ|υ |2 δmin 2 = e−(δmin /2 ) ( 32 ) δmin 2 Pe δmin = erf c π = √ ∞ δmin /2 exp − x2 dx (33 ) So, the theoretical total probability of errors Pe can be ex∞ pressed as ... > δmin /2 The cdf of |υ |2 is F|υ |2 (u) = P(|υ |2 < u) or equivalently as F|υ |2 (u) = Γu/σ (1) = − exp(−u/σ ) For the upper bound Pe,sup (δmin ) = P(|υ |2 > (δmin /2) 2 ), the probability of errors ... theory to practice: an overview of MIMO space-time coded wireless systems, ” IEEE Journal on Selected Areas in Communications, vol 21 , no 3, pp 28 1 30 2, 20 03 [3] V Erceg, K V S Hari, M S Smith,...

10
548
0

MODELLING OF MECHANICAL SYSTEMS VOLUME : Structural Elements pot

Danh mục: Kĩ thuật Viễn thông

... 6 .2 .3. 3 Point loads 28 9 29 0 2 93 29 9 30 3 30 4 30 5 30 7 30 7 31 1 31 2 31 2 31 3 31 3 31 3 31 4 31 6 31 6 31 6 31 7 31 8 31 9 31 9 32 2 32 2 32 4 32 4 32 5 32 6 xii ... 5 .3. 4.4 Uniform plate stretching 23 5 23 7 23 8 24 0 24 0 2 43 24 5 24 7 24 8 25 4 25 6 25 9 26 0 26 0 26 0 26 2 26 2 26 2 2 63 2 63 2 63 26 5 26 5 26 5 26 6 26 7 27 0 27 0 27 2 2 73 27 5 27 5 ... 177 180 186 188 189 190 190 190 1 93 196 196 20 0 20 0 20 5 20 7 20 7 20 9 21 0 21 0 21 1 2 13 2 13 21 4 21 7 21 8 22 0 22 0 22 1 22 2 22 2 22 4 22 9 23 1 23 1 23 2 x Contents 4.4.1 .2 Truncation stiffness for a free-free...

521
337
0

Modelling of Mechanical Systems Structural Elements Francois Axisa potx

Danh mục: Kĩ thuật Viễn thông

... 6 .2 .3. 3 Point loads 28 9 29 0 2 93 29 9 30 3 30 4 30 5 30 7 30 7 31 1 31 2 31 2 31 3 31 3 31 3 31 4 31 6 31 6 31 6 31 7 31 8 31 9 31 9 32 2 32 2 32 4 32 4 32 5 32 6 xii ... 5 .3. 4.4 Uniform plate stretching 23 5 23 7 23 8 24 0 24 0 2 43 24 5 24 7 24 8 25 4 25 6 25 9 26 0 26 0 26 0 26 2 26 2 26 2 2 63 2 63 2 63 26 5 26 5 26 5 26 6 26 7 27 0 27 0 27 2 2 73 27 5 27 5 ... 177 180 186 188 189 190 190 190 1 93 196 196 20 0 20 0 20 5 20 7 20 7 20 9 21 0 21 0 21 1 2 13 2 13 21 4 21 7 21 8 22 0 22 0 22 1 22 2 22 2 22 4 22 9 23 1 23 1 23 2 x Contents 4.4.1 .2 Truncation stiffness for a free-free...

521
337
0

DYNAMICS of MECHANICAL SYSTEMS ppt

Danh mục: Kĩ thuật Viễn thông

... rad deg m2 cm2 m2 cm2 in .2 ft2 ft2 in .2 cm2 ft2 in .2 m2 Nm (or J) Nm (or J) in lb ft lb ft lb in lb N lb 3. 048 3. 048 1 .20 0 3. 105 3. 28 0 3. 937 1.000 1.018 8 .33 3 2. 540 2. 540 2. 587 3. 28 0 3. 937 1.000 ... 5.1 53 1.940 1.000 1.940 1.000 1 .35 5 1 .20 0 1. 129 8 .33 3 7 .37 5 8.850 1 .35 5 7 .37 5 1.818 1 .35 5 3. 030 2. 259 7.456 7 .37 5 4. 425 1 .34 1 5.500 3. 300 6.894 1.440 4.788 6.944 1.450 2. 088 3. 048 3. 048 1.097 1 .20 0 ... lb/in .2 (or psi) lb/ft2 m/sec cm/sec km/hr in./sec mi/hr (or mph) m/sec cm/sec km/hr 3. 048 3. 048 1 .20 0 2. 540 2. 540 8 .33 3 3. 28 0 3. 937 1.000 3. 28 0 3. 937 1.000 5 .28 0 1.609 6 .2 13 1.459 6.8 52 5.1 53 5.153...

777
344
0

Dynamics of Mechanical Systems 2009 Part 1 ppsx

Danh mục: Kĩ thuật Viễn thông

... rad deg m2 cm2 m2 cm2 in .2 ft2 ft2 in .2 cm2 ft2 in .2 m2 Nm (or J) Nm (or J) in lb ft lb ft lb in lb N lb 3. 048 3. 048 1 .20 0 3. 105 3. 28 0 3. 937 1.000 1.018 8 .33 3 2. 540 2. 540 2. 587 3. 28 0 3. 937 1.000 ... 5.1 53 1.940 1.000 1.940 1.000 1 .35 5 1 .20 0 1. 129 8 .33 3 7 .37 5 8.850 1 .35 5 7 .37 5 1.818 1 .35 5 3. 030 2. 259 7.456 7 .37 5 4. 425 1 .34 1 5.500 3. 300 6.894 1.440 4.788 6.944 1.450 2. 088 3. 048 3. 048 1.097 1 .20 0 ... lb/in .2 (or psi) lb/ft2 m/sec cm/sec km/hr in./sec mi/hr (or mph) m/sec cm/sec km/hr 3. 048 3. 048 1 .20 0 2. 540 2. 540 8 .33 3 3. 28 0 3. 937 1.000 3. 28 0 3. 937 1.000 5 .28 0 1.609 6 .2 13 1.459 6.8 52 5.1 53 5.153...

50
251
0

Dynamics of Mechanical Systems 2009 Part 4 docx

Danh mục: Kĩ thuật Viễn thông

... validity of Eq (6 .3. 17): ? 160n1 − 30 n − 168n = 32 n1 − 42n − 1 32 n + (12n + 4n ) × (3n1 + 24 n + 24 n ) = 32 n1 − 42n − 1 32 n − 36 n + 28 8n1 + 12n − 96n1 = 160n1 − 30 n − 168n Equation (6 .3. 17) is ... (l 2) 2 sin 2 − (l 2) 2 cos 2 N Z (5.6.14) Similarly, the velocity of acceleration of O3 is: ˙ ˙˙ vO3 = lθ1n11 + l θ2n 21 (5.6.15) ˙˙ 2 ˙˙ 2 aO3 = l θ1n11 − lθ1 n 13 + l θ2n 21 − lθ2n 23 ... in Eqs (5 .3. 26 ) and (5 .3. 27 ), we immediately obtain Eqs (5 .3. 22 ) and (5 .3. 23 ) Finally, observe that by differentiating in Eqs (5 .3. 22 ) and (5 .3. 23 ) we obtain Eqs (5 .3. 24 ) and (5 .3. 25 ) 5.4 Instant...

50
417
0

Dynamics of Mechanical Systems 2009 Part 5 pps

Danh mục: Kĩ thuật Viễn thông

... I 22 + I 33 (7.7. 13) I II = I 22 I 33 − I 32 I 23 + I11I 33 − I 31 I 13 + I11I 22 − I 12 I 21 (7.7.14) I III = I11I 22 I 33 − I11I 32 I 23 + I 12 I 31 I 23 − I 12 I 21 I 33 + I 21 I 32 I 13 − I 31 I 13 ... as: 05 93_ C07_fm Page 20 4 Monday, May 6, 20 02 2: 42 PM 20 4 Dynamics of Mechanical Systems D = d11n1n1 + d12n1n + d13n1n + d21n 2n1 + d22n 2n + d23n 2n (7.4.6) + d31n 3n1 + d22n 3n + d33n 3n = dij ... operations: D ab = (a n 1 + a2n + a3n )(b1n1 + b2n + b3n ) = a1b1n1n1 + a1b2n1n + a1b3n1n + a2b1n 2n1 + a2b2n 2n + a2b3n 2n (7.4.5) + a3b1n 3n1 + a3b2n 2n + a3b3n 3n where the unit vector products...

50
232
0