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Mechanics of Solids 2011 Part 3

Tham khảo tài liệu 'mechanics of solids 2011 part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 1-28 Section 1 In the general case deforming the spring from position X1 to x2 U 1 k x2 - x1 Notation for Potential Energy The change in the potential energy V of a system is U -AF Note that negative work is done by a system while its own potential energy is increased by the action of an external force or moment. The external agent does positive work at the same time since it acts in the same direction as the resulting displacement. Potential Energy at Equilibrium For equilibrium of a system 0 dq where q an independent coordinate along which there is possibility of displacement. For a system with n degrees of freedom 3F 0 i 1 2 . n dqt Equilibrium is stable if d2V dq2 0. Equilibrium is unstable if dV dq2 0. Equilibrium is neutral only if all derivatives of V are zero. In cases of complex configurations evaluate derivatives of higher order as well. Moments of Inertia The topics of inertia are related to the methods of first moments. They are traditionally presented in statics in preparation for application in dynamics or mechanics of materials. Moments of Inertia of a Mass The moment of inertia dIX of an elemental mass dM about the X axis Figure j.2.28 is defined as dIx r2 dM y2 z2 dM where r is the nearest distance from dM to the X axis. The moments of inertia of a body about the three coordinate axes .