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Harris' Shock and Vibration Handbook Part 2

Tham khảo tài liệu 'harris' shock and vibration handbook part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | VIBRATION OF A RESILIENTLY SUPPORTED RIGID BODY 3.15 FIGURE 3.2 Three-scale method of locating the center-of-gravity of a body. The vertical forces F1 F2 F3 at the scales result from the weight of the body. The vertical line located by the distances a0 and b0 see Eqs. 3.10 passes through the center-of-gravity of the body. body while it is balanced particularly where the height of the body is great relative to a horizontal dimension. If a perfect point or edge support is used the equilibrium position is inherently unstable. It is only if the support has width that some degree of stability can be achieved but then a resulting error in the location of the line or plane containing the center-of-gravity can be expected. Another method of locating the center-of-gravity is to place the body in a stable position on three scales. From static moments the vector weight of the body is the resultant of the measured forces at the scales as shown in Fig. 3.2. The vertical line through the center-of-gravity is located by the distances a0 and b0 _F a0 77 77 _a1 F1 F2 F3 b0 77 77. b1 F1 F2 F3 3.10 This method cannot be used with more than three scales. MOMENT AND PRODUCT OF INERTIA Computation of Moment and Product of Inertia.2 3 The moments of inertia of a rigid body with respect to the orthogonal axes X Y Z fixed in the body are Ixx J Y2 Z2 dm Iyy ị X2 Z2 dm Izz J X2 Y2 dm 3.11 where dm is the infinitesimal element of mass located at the coordinate distances X Y Z and the integration is taken over the mass of the body. Similarly the products of inertia are Ixy I XY dm Ixz I XZ dm Iyz I YZ dm 3.12 It is conventional in rigid body mechanics to take the center of coordinates at the center-of-mass of the body. Unless otherwise specified this location is assumed and the moments of inertia and products of inertia refer to axes through the center-of-mass of the body. For a unique set of axes the products of inertia vanish. These axes are called the principal inertial axes of