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54) where d is the diameter. com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. 14 Constant circular cross-section microbar. 15 Very thin versus thin rectangular cross-section bars in terms of the moment of inertia. Example: Compare the torsional moment of inertia of a very thin constant rectangular cross-section bar (t << w) to that of a thin constant rectangular cross-section bar (t < w). If the ratio of the two moments of inertia–the one of Eq.
The eigenvectors corresponding to the mechanical system of Fig. 23 are assembled into the modal matrix of Eq. 100) 1 As a result of the definition in Eq. 101) 2+ 2 which is in diagonal form. The mass matrix [Eq. 78)] is already in diagonal form, and there is no need to calculate a transformed mass matrix. The decoupled dynamic equation of motion will therefore be .. 102) Lagrange’s equations Lagrange’s method and equations can be utilized to derive the equations of motion of a mechanical system with (generally) multiple degrees of freedom by utilizing the energy forms that define the system’s motion.
Any use is subject to the Terms of Use as given at the website. 0-07-145538-8_CH02_50_08/30/05 Basic Members: Lumped- and Distributed-Parameter Modeling and Design 50 Chapter Two The axial distribution function is determined by considering it as a first-degree polynomial (with two unknown coefficients), which has to satisfy the following boundary conditions that apply to the fixed-free member of Fig. 8) The axial stiffness is found by combining Eqs. 10) In Eq. 10), Mt(x) is the torsional moment, It(x) is the torsional moment of inertia, șx(x) is the angular deformation, and G is the shear modulus of elasticity.
