Transcription of Vibration Theory - Cooper Union
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Vibration Theory - Cooper Union
CHAPTER 2 BASIC Vibration THEORYR alph E. BlakeINTRODUCTIONThis chapter presents the Theory of free and forced steady-state Vibration of singledegree-of-freedom systems. Undamped systems and systems having viscous damp-ing and structural damping are included. Multiple degree-of-freedom systems arediscussed, including the normal-mode Theory of linear elastic structures andLagrange s PARTS OF VIBRATORY SYSTEMSV ibratory systems comprise means for storing potential energy (spring), means forstoring kinetic energy (mass or inertia), and means by which the energy is graduallylost (damper). The Vibration of a system involves the alternating transfer of energybetween its potential and kinetic forms. In a damped system, some energy is dissi-pated at each cycle of Vibration and must be replaced from an external source if asteady Vibration is to be maintained. Although a single physical structure may storeboth kinetic and potential energy, and may dissipate energy, this chapter considersonly lumped parameter systemscomposed of ideal springs, masses, and damperswherein each element has only a single function.
storing kinetic energy (mass or inertia), and means by which the energy is gradually lost (damper).The vibration of a system involves the alternating transfer of energy between its potential and kinetic forms. In a damped system, some energy is dissi-pated at each cycle of vibration and must be replaced from an external source if a
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