By Reza N. Jazar

ISBN-10: 1461441595

ISBN-13: 9781461441595

ISBN-10: 1461441609

ISBN-13: 9781461441601

*Advanced Vibrations: a contemporary Approach* is gifted at a theoretical-practical point and explains mechanical vibrations strategies intimately, focusing on their sensible use. similar theorems and formal proofs are supplied, as are real-life purposes. scholars, researchers and practising engineers alike will savor the straightforward presentation of a wealth of themes together with yet no longer restricted to useful optimization for designing vibration isolators, and temporary, harmonic and random excitations.

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**Additional info for Advanced Vibrations: A Modern Approach**

**Sample text**

173) These equations indicate the parametric path of motion of the particle. If the frequencies ω1 and ω2 are commensurable, the path of the motion will be closed. The frequencies ω1 and ω2 are commensurable when their ratio is a rational fraction, ω1 /ω2 = m/n {m, n ∈ N }. The path of motion in this case is called the Lissajous curve. If the frequencies ω1 and ω2 are not commensurable, the path of motion will be open, which means the moving particle will never pass twice through the same point with the same velocity.

132) The dynamic system is called the harmonic oscillator. 135) This motion may be described by a moving point on an ellipse in the (x, x)-plane ˙ with semi-axis ωC on x˙ and C on x axes. Such a motion is a libration motion between x = ±C. Integration of Eq. 69) is linear and superposition is the necessary and sufficient condition for linearity. So, a system is linear if it is superposable, and any superposable system is linear. We can mathematically define the superposition principle as follows.

170) or where k1 ω2 = m The solution of Eqs. 173) These equations indicate the parametric path of motion of the particle. If the frequencies ω1 and ω2 are commensurable, the path of the motion will be closed. The frequencies ω1 and ω2 are commensurable when their ratio is a rational fraction, ω1 /ω2 = m/n {m, n ∈ N }. The path of motion in this case is called the Lissajous curve. If the frequencies ω1 and ω2 are not commensurable, the path of motion will be open, which means the moving particle will never pass twice through the same point with the same velocity.

### Advanced Vibrations: A Modern Approach by Reza N. Jazar

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