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LECTURE 14: DEVELOPING THE ... - Texas A&M University

211 LECTURE 14: DEVELOPING THE EQUATIONS OFMOTION FOR TWO-MASS VIBRATION EXAMPLESF igure a. Two-mass, linear vibration system with springconnections. b. Free-body diagrams. c. Alternative ( )( )Equations of Motion Assuming: The connecting spring is in tension, and the connecting spring-force magnitude is . From figure :with the resultant differential equations:Equations of Motion Assuming: The spring is in compression, and the connecting-spring forcemagnitude is . From figure :Rearranging these differential equations gives Eqs.( ). 213( )Steps for obtaining the correct differential equations ofmotion:a.

Multiple-degree-of-freedom (MDOF) vibration problems can be coupled by either the stiffness (linear spring-mass system) or inertia (double pendulum) matrices. c. For a neutrally stable system, the inertia and stiffness matrices should be symmetric and the diagonal elements should be positive. d. Free vibrations of a MDOF vibration problem leads ...

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rotorlab.tamu.edu

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