By Fanchi
ISBN-10: 1555631134
ISBN-13: 9781555631130
Normal Engineering, quantity I of the recent Petroleum Engineering guide, has been designed to offer fabric that's wanted through all practising petroleum engineers. It comprises chapters on arithmetic, homes of fl uids, rock homes, rock/fl uid interactions, economics, the legislation, and the social context of fossil strength
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104) There are two roots to this equation, which means that there are two natural frequencies. The solution therefore must be in terms of the two frequencies. Substituting the first natural frequency back into the equation of motion solution gives the result of the first natural frequency: (k1 + k2 − ω21m1)C11 − k2C21 = 0............................................... 105) and ( ) −k2C11 + k2 − ω21m2 C21 = 0. 106) The ratio of C11 to C21, known as the mode shape, for the first natural frequency is: Print Search Contents Home Chapter 2 Bookmarks Help I-28 Petroleum Engineering Handbook—Vol.
Outer diameter, L, in. modulus of elasticity, m/Lt2, psia excitation function cyclic frequency, 1/t, cycle/sec function of t first differential function axial force, mL/t2, lbf damping force, mL/t2, lbf friction force, mL/t2, lbf hysteretic force, mL/t2, lbf Print Search Contents Home Chapter 2 Bookmarks Help I-38 Petroleum Engineering Handbook—Vol. 3 spring constant, m/t2, lbf/in. equivalent spring constant, m/t2, lbf/in. wave number, 1/L, 1/ft stiffness matrix, m/t2, lbf/in. total length, L, ft mass, m, lbm mass polar moment of inertia, mL, lbf-sec2 mass matrix, m, lbm exponent generic value generic value generic constant iterated generic constant response function time, seconds torque, mL2/t2, lbf-ft displacement function in terms of time, t displacement, L, in.
46 is an approximation because we are neglecting all of the terms in ET , which is called the truncation error. In the limit as the increment Δx approaches zero, the truncation error approaches zero, and the finite difference approaches the definition of the derivative. The finite difference in Eq. 46 is called a forward difference. Other differences are possible. Two that we use next are the backward difference, f ( xi ) − f ( xi − Δx) df , ................................................... 47) ≈ dx Δx and the centered difference, f ( xi + Δx) − f ( xi − Δx) df ≈ .
Petroleum Engineering Handbook General Engineering by Fanchi
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