# NCSU MAE 208 - MOTION IN A STABILITY REGION (29 pages)

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## MOTION IN A STABILITY REGION

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## MOTION IN A STABILITY REGION

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Lecture Notes

Pages:
29
School:
North Carolina State University
Course:
Mae 208 - Engineering Dynamics
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MOTION IN A STABILITY REGION PART II 5 MOTION IN A STABILITY REGION PART II Figure 5 1 MAE 461 DYNAMICS AND CONTROLS MOTION IN A STABILITY REGION PART II This section begins by showing how to find the steady state response of a one degree of freedom system acted on by a periodic excitation The periodic excitation has a period T or equivalently 2 a frequency The periodic excitation is T represented as a linear combination of harmonic functions The linear combination of harmonic functions is called a Fourier series Once a periodic excitation is expressed as a Fourier series the steady state response of a system acted on by a periodic excitation is found By the principle of linear superposition the response of the system to the periodic excitation is a linear combination of the responses of the harmonic functions that make up the Fourier series After showing how to represent a periodic excitation by a Fourier series and how to determine the associated response it s shown how to represent a periodic excitation by a complex Fourier series The complex Fourier series is used to develop a method of finding the steady state response to a non periodic excitation Excitations are generally non periodic Earthquakes and wind produce non periodic excitations on buildings Wind road surfaces and tracks and guides produce non periodic excitations on vehicle systems Like the periodic excitation the non periodic excitation is represented as a linear combination of harmonic functions However instead of its frequencies being multiples of the frequency of an excitation there is a continuous range of frequencies The nonperiodic excitation is an integral of harmonic functions instead of a discrete sum of them The integral of harmonic functions is called the Fourier integral The coefficients in the integral are called the frequency response The frequency MAE 461 DYNAMICS AND CONTROLS MOTION IN A STABILITY REGION PART II response represents the amplitude of the response as a function of the

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