# Ch1-2(3)c - MAE351 Mechanical Vibrations Lecture 2(Chap 1.3...

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1 MAE351 Mechanical Vibrations Lecture 2 (Chap. 1.3) 1 Basic Mechanical Elements of Vibrations x m c k 2 m = mass k = stiffness c = damping (Courtesy of Dr. D. Russell)

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2 Viscous Damping All real systems dissipate energy when they vibrate. To account for this, we must consider damping. The most simple form of damping (from a mathematical point of view) is called viscous damping. A viscous damper (or dashpot ) produces a force that is proportional to velocity. Damper ( c ) x : Mostly, a mathematically motivated form allows a solution to the resulting equations of motion that predicts reasonable (observed) amounts of energy dissipation. 3 F c Damping Elements Damper = without mass or elasticity Relative velocity between two ends of the damper force F cx c = damping constant (Ns/m) F c F 1 x 2 x 4 Several important and usual types of damping: • Viscous damping … viscous damper or dashpot • Coulomb damping … dry friction or slide damping (rubbing) • Material damping … solid or hysteretic or structural damping • Radiation damping … sound radiation
3 Resistance by the fluid medium Example cases: • Fluid film between sliding surfaces • Fluid flow around a piston in a cylinder • fluid flow through an orifice F x Physics of Viscous Damping fluid flow through an orifice • fluid film around a journal in a bearing h y F (damping force) A, surface area x y ux h homogeneous, viscous fluid Model: 5 Shear stress, : du x dy h   Shear force at bottom surface of the moving plate: A F Ax c x h    . A c damping const h  standstill plate Differential Equation Including Damping For this damped single degree of freedom system, the force acting on the mass is due to the spring and the dashpot, i.e., F M =F k +F c .

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Ch1-2(3)c - MAE351 Mechanical Vibrations Lecture 2(Chap 1.3...

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