Critical Damping in Certain Linear Continuous Dynamic Systems.
NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST
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Free damped vibrations of linear elastic structures composed of uniform beam elements with a continuous distribution of mass are studied. Axial, torsional and flexural vibrations are considered. The amount of damping, which can be either internal or external viscous type, varies among the various beam elements of the structure resulting in many critical damping possibilities. A general method is developed, which, with the aid of dynamic stiffness influence coefficients defined for every element, determines the critical damping surfaces of the system. These surfaces represent the loci of combinations of amounts of damping leading to critically damped motion and thus separating regions of partial or complete underdamping from those of overdamping. The dimension of a critical damping surface is equal to the number of independent amounts of damping present in the system, while the number of these surfaces is infinite, i.e., equal to the number of degrees of freedom of the system. Three examples are presented in detail to illustrate the proposed method for determining critical damping and demonstrate its importance. Author
- Structural Engineering and Building Technology