Download PDF by François Axisa (Eds.): Discrete Systems

By François Axisa (Eds.)

ISBN-10: 1417526432

ISBN-13: 9781417526437

ISBN-10: 1903996511

ISBN-13: 9781903996515

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Extra resources for Discrete Systems

Example text

As expected, this produces the same equation as that obtained by the balance of moments. Moreover, as an interesting by-product, the balance of forces method provides us with the reaction of constraint, which is found to be: T = Mg cos 0 + MRS"- T comprises a nonlinear stiffness force induced by the weight and a centrifugal force, which is induced by the rotation of P around O. To conclude on this basic example, we must emphasize that elimination of the reactions of constraint in the case of systems having several degrees of freedom is generally much less simple than in the case of SDOF systems.

12. Conventional representation of a viscous damper According to the considerations which shall be developed in Chapter 2 concerning mechanical energy, any real system interacts with others in such a way that it can either lose or gain mechanical energy. Many kinds of physical processes can be responsible for such interactions, for instance those which are described in Mechanical systems and equilibrium of forces 19 Volumes 3 and 4, devoted to fluid-structure coupled systems. From the mathematical viewpoint, viscous damping is the simplest model that can be conceived for taking into account such irreversible exchanges of energy.

Axis is assumed to rotate at the constant angular velocity Ok about the fixed point O. 32]. 34] is known as a Coriolis force, which acts in the tangential direction, and the second term is known as a centrifugal force which acts radially in the outward direction from the centre of rotation. 4, in relation with transformations of reference frames. 4 Applications to a few basic systems EXAMPLE 1 . - The simple pendulum .... 19. 19. It consists of a rigid body tied to a fixed point O by a non-extensible string, which is supposed to move in a vertical plane.

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Discrete Systems by François Axisa (Eds.)

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