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article · Journal of low frequency noise, vibration and active control

Free vibration of a microbeam resting on Pasternak’s foundation via the Green–Naghdi thermoelasticity theory without energy dissipation

201619 citationsOpen accessKafr el-Sheikh University

In plain language

This research investigates the free vibration characteristics of a thermoelastic microbeam resonator supported by an elastic foundation. Using the Green and Naghdi generalized thermoelasticity theory without energy dissipation, the study establishes a governing frequency equation for a simply supported microbeam mounted on a Winkler-Pasternak elastic foundation. It demonstrates how varying the length-to-thickness ratio and changing the parameters of the elastic foundation affect the natural frequencies of the device. The calculated natural vibration frequencies are illustrated graphically and accompanied by tabulated data intended for future comparative evaluations.

Key takeaways

  • A governing frequency equation is established for a simply supported thermoelastic microbeam on Winkler-Pasternak foundations using Green-Naghdi theory without energy dissipation.
  • The length-to-thickness ratio directly influences the natural frequencies of the microbeam resonator.
  • Elastic foundation parameters alter the vibrational characteristics of the microbeam.
  • Natural vibration frequencies are tabulated and graphically illustrated to serve as reference data for future studies.

Why it matters

Microbeam resonators are miniature components whose vibration patterns dictate their operational behaviour. Understanding how dimensions and underlying support structures alter these natural frequencies helps engineers accurately predict mechanical responses in miniaturised thermal and elastic systems.

Commercialisation angle

This is early-stage theoretical modelling of microbeam resonators. While the calculations could inform engineers designing micro-electromechanical systems, the abstract does not indicate an application pathway or specify target commercial users.

AI-generated from the published abstract. Always read the original work before citing.

Abstract

This article investigates the effect of length-to-thickness ratio and elastic foundation parameters on the natural frequencies of a thermoelastic microbeam resonator. The generalized thermoelasticity theory of Green and Naghdi without energy dissipation is used. The governing frequency equation is given for a simply supported microbeam resting on Winkler–Pasternak elastic foundations. The influences of different parameters are all demonstrated. Natural vibration frequencies are graphically illustrated and some tabulated results are presented for future comparisons.

Research topics

  • Thermoelastic and Magnetoelastic Phenomena
  • Nonlocal and gradient elasticity in micro/nano structures
  • Composite Structure Analysis and Optimization

Sustainable Development Goals

Read the original research

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DOI: 10.1177/0263092316676405

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