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Research Papers

A Mechanical Fourier Series Generator: An Exact Solution

[+] Author and Article Information
Izhak Bucher

Mechanical Engineering, Technion, Haifa 32000, Israelbucher@technion.ac.il

J. Vib. Acoust 131(3), 031012 (Apr 23, 2009) (9 pages) doi:10.1115/1.3085892 History: Received July 01, 2008; Revised January 06, 2009; Published April 23, 2009

A vibrating system is constructed such that its natural frequencies are exact integer multiples of a base frequency. This system requires little energy to produce a periodic motion whose period is determined by the base frequency. The ability to amplify integer multiples of a base frequency makes this device an effective mechanical Fourier series generator. The proposed topology makes use of symmetry to assign poles and zeros at optimal frequencies. The system zeros play the role of suppressing the energy at certain frequencies while the poles amplify the input at their respective frequencies. An exact, non-iterative procedure is adopted to provide the stiffness and mass values of a discrete realization. It is shown that the spatial distributions of mass and stiffness are smooth; thus it is suggested that a continuous realization of a mechanical Fourier series generator is a viable possibility. A laboratory experiment and numerical examples are briefly described to validate the theory.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Topology of the spring mass series

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Figure 2

Right: A dissected left half of Fig. 1 with N+1DOF; left: left half of Fig. 1, clamped at the middle thus leaving N DOF

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Figure 3

Frequency response magnitude for a 2N+1=5DOF structure scaled for ω0=15,000 Hz

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Figure 4

Stiffness and mass elements for a 25DOF MFSG

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Figure 5

Antisymmetric and symmetric eigenvectors of a 25DOF MFSG

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Figure 6

Pictorial realization of a 25DOF MFSG

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Figure 7

Frequency response amplitude of a 25DOF MFSG

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Figure 8

Photograph of a miniature DFG

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Figure 9

Antisymmetric (left) and symmetric (right) modes of the miniature structure FE model

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Figure 10

Measured and computed by finite element and frequency response amplitude

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