Frequency detuning effects for a parametric amplifier

S. Neumeyer*, V.S. Sorokin, M. H. M. van Gastel, J. J. Thomsen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

Frequency tuned parametric amplifiers may experience changes in both the two-to-one frequency ratio between the parametric and the direct excitation, and between the direct excitation frequency and the systems natural frequency. These effects are investigated theoretically using a Duffing-Mathieu equation as the model system, and investigated experimentally using a macro cantilever beam as the model object. The approximate analytical steady-state vibration amplitudes are derived using the method of varying amplitudes, and compared with results of direct numerical integration, showing good agreement. Theoretical predictions reveal that for detuned superthreshold parametric amplification some of the amplitude-frequency curves appear to collapse. Experiments show that a drop in the maximum steady-state vibration amplitude occurs for specific areas in the amplitude-excitation detuning domain, whereas for other areas frequency detuning may yield an increased maximum steady-state vibration amplitude. Thus frequency detuning is a feature which can purposefully be avoided or utilized, dependent on the usage e.g. for sensors or energy harvesters. We report experimentally obtained bistable amplified steady-state responses, which also support theoretical findings
Original languageEnglish
JournalJournal of Sound and Vibration
Volume445
Pages (from-to)77-87
ISSN0022-460X
DOIs
Publication statusPublished - 2019

Keywords

  • Parametric amplification
  • Frequency detuning
  • Nonlinearity

Cite this

Neumeyer, S. ; Sorokin, V.S. ; van Gastel, M. H. M. ; Thomsen, J. J. / Frequency detuning effects for a parametric amplifier. In: Journal of Sound and Vibration. 2019 ; Vol. 445. pp. 77-87.
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title = "Frequency detuning effects for a parametric amplifier",
abstract = "Frequency tuned parametric amplifiers may experience changes in both the two-to-one frequency ratio between the parametric and the direct excitation, and between the direct excitation frequency and the systems natural frequency. These effects are investigated theoretically using a Duffing-Mathieu equation as the model system, and investigated experimentally using a macro cantilever beam as the model object. The approximate analytical steady-state vibration amplitudes are derived using the method of varying amplitudes, and compared with results of direct numerical integration, showing good agreement. Theoretical predictions reveal that for detuned superthreshold parametric amplification some of the amplitude-frequency curves appear to collapse. Experiments show that a drop in the maximum steady-state vibration amplitude occurs for specific areas in the amplitude-excitation detuning domain, whereas for other areas frequency detuning may yield an increased maximum steady-state vibration amplitude. Thus frequency detuning is a feature which can purposefully be avoided or utilized, dependent on the usage e.g. for sensors or energy harvesters. We report experimentally obtained bistable amplified steady-state responses, which also support theoretical findings",
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Frequency detuning effects for a parametric amplifier. / Neumeyer, S.; Sorokin, V.S.; van Gastel, M. H. M.; Thomsen, J. J.

In: Journal of Sound and Vibration, Vol. 445, 2019, p. 77-87.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Frequency detuning effects for a parametric amplifier

AU - Neumeyer, S.

AU - Sorokin, V.S.

AU - van Gastel, M. H. M.

AU - Thomsen, J. J.

PY - 2019

Y1 - 2019

N2 - Frequency tuned parametric amplifiers may experience changes in both the two-to-one frequency ratio between the parametric and the direct excitation, and between the direct excitation frequency and the systems natural frequency. These effects are investigated theoretically using a Duffing-Mathieu equation as the model system, and investigated experimentally using a macro cantilever beam as the model object. The approximate analytical steady-state vibration amplitudes are derived using the method of varying amplitudes, and compared with results of direct numerical integration, showing good agreement. Theoretical predictions reveal that for detuned superthreshold parametric amplification some of the amplitude-frequency curves appear to collapse. Experiments show that a drop in the maximum steady-state vibration amplitude occurs for specific areas in the amplitude-excitation detuning domain, whereas for other areas frequency detuning may yield an increased maximum steady-state vibration amplitude. Thus frequency detuning is a feature which can purposefully be avoided or utilized, dependent on the usage e.g. for sensors or energy harvesters. We report experimentally obtained bistable amplified steady-state responses, which also support theoretical findings

AB - Frequency tuned parametric amplifiers may experience changes in both the two-to-one frequency ratio between the parametric and the direct excitation, and between the direct excitation frequency and the systems natural frequency. These effects are investigated theoretically using a Duffing-Mathieu equation as the model system, and investigated experimentally using a macro cantilever beam as the model object. The approximate analytical steady-state vibration amplitudes are derived using the method of varying amplitudes, and compared with results of direct numerical integration, showing good agreement. Theoretical predictions reveal that for detuned superthreshold parametric amplification some of the amplitude-frequency curves appear to collapse. Experiments show that a drop in the maximum steady-state vibration amplitude occurs for specific areas in the amplitude-excitation detuning domain, whereas for other areas frequency detuning may yield an increased maximum steady-state vibration amplitude. Thus frequency detuning is a feature which can purposefully be avoided or utilized, dependent on the usage e.g. for sensors or energy harvesters. We report experimentally obtained bistable amplified steady-state responses, which also support theoretical findings

KW - Parametric amplification

KW - Frequency detuning

KW - Nonlinearity

U2 - 10.1016/j.jsv.2018.12.036

DO - 10.1016/j.jsv.2018.12.036

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JO - Journal of Sound and Vibration

JF - Journal of Sound and Vibration

SN - 0022-460X

ER -