lecture notes for vibrations and accoustics

8/19/2019 Lecture Notes for Vibrations and accoustics

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Vibration and Acoustics (MECH 3420)

Department of Mechanical Engineering

University of Manitoba

Instructor:

Ali Khosrozadeh

Chapter 4:

Vibration Under General ForcingConditions

Lecture Notes 4

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4: Vibration Under General Forcing ConditionsIntroduction

• In Chapter 3, we considered the response of single-degree-of-

freedom systems subjected to harmonic excitation. However,

many practical systems are subjected to several types of forcing

functions that are not harmonic. The general forcing functions

may be periodic (harmonic or nonharmonic) or nonperiodic.

• If the forcing function is periodic but not harmonic, it can be

replaced by a sum of harmonic functions using the harmonicanalysis procedure. Using the principle of superposition, the

response of the system can then be determined by superposing

the responses of the individual harmonic forcing functions.

• The response of a system subjected to any type of nonperiodic

force can be found using the Convolution integral, Laplace

transform, and Numerical methods.

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4.2 Response Under a General Periodic Force

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First-ordersystems:

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Study example 4.5

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4.3 Response Under a Periodic Force of Irregular Form


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4.4 Response Under a Nonperiodic Force

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4.5 Convolution Integral


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EX. In a structure under an impact hammer (See Ex. 4.7 and 4.8),find the response of the system for:

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Ex. 4.12 Determine the response of the compacting machine when a

linearly varying force is applied due to the motion of the cam.

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lecture notes for vibrations and accoustics

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