Chapter 5
Supporting Systems/Foundations


The effective stiffness of mechanical systems is determined not only by stiffness characteristics of their components but also by designed interactions between the components. Influence of interactions is both due to elastic deformations in the connections between the interacting components (contact deformations; see Chapter 4) and due to the location, size, and shape of the connection areas (sup-porting conditions). Relatively slight changes in the supporting conditions may result in up to one to two decimal orders of magnitude changes of deformations under the specified forces, as well as in very significant changes in stress conditions of the components.

The influence of parameters of the supporting elements on effective damping of the supported component or structure is more difficult to assess. It depends not only on parameters (stiffness and damping) of the supporting elements, but also on rather complex correlations between dynamic characteristics of the supported system/component and the supporting system. In some cases, this influence can be analyzed, at least approximately, in a close form. Such cases are represented by an analysis of influence of the mounting (vibration isolation) system on dynamic stability (chatter resistance) of a machine tool, e.g., given in [1] and in Appendix 2. However, in many cases, influence of the supporting structure on the effective damping has to be analyzed by testing and by estimation.

This chapter addresses effects of the supporting systems/foundations on static stiffness/deformations of the supported systems. Some important effects of the supporting conditions on damping are discussed in Section 5.3.

  • 5.1 Influence of Support Characteristics
  • 5.2 Rational Location of Supporting/Mounting Elements
  • 5.3 Overconstrained (Statically Indeterminate) Systems
  • 5.4 Influence of Foundation on Structural Deformations
  • 5.4.1 General Considerations
  • 5.4.2 Machines Installed on Individual Foundations or on Floor Plate
  • 5.5 Deformations of Long Machine Bases
  • References

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