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Abstract
The present study examines the vibrations in micro- and nano-piezothermoelastic beams with voids. In this work, the modified couple stress theory is employed to generate closed-form formulas for deflection, volume fraction, electric potential and temperature distribution. The effects of voids, modified couple stress, beam dimensions and electric potential on energy dissipation (thermoelastic damping) are examined for beams under various boundary conditions. We have established analytical formulas for frequency shift, attenuation and thermoelastic damping. MATLAB software is used to get numerical results and exhibit them visually.
Disclosure statement
The authors declare that they have no competing financial and personal relationships that could have appeared to influence the work reported in this paper.
Figure 1. Geometrical structure of beam under deflection.
Figure 2. Variation of TED in a C-C microbeam with thickness in presence and absence of couple stress in context of Lord Shulman (LS) and Coupled thermoelasticity (CT) theories.
Figure 3. Variation of TED in a S-S microbeam with thickness in presence and absence of couple stress in context of LS and CT theories.
Figure 4. Variation of TED in a cantilever microbeam with thickness in presence and absence of couple stress in context of LS and CT theories.
Figure 5. Variation of TED in a C-C piezothermoelastic and thermoelastic microbeam with thickness in context of LS and CT theories.
Figure 6. Variation of TED in a S-S piezothermoelastic and thermoelastic microbeam with thickness in context of LS and CT theories.
Figure 7. Variation of TED in a cantilever piezothermoelastic and thermoelastic microbeam with thickness in context of LS and CT theories.
Figure 8. Variation of TED in C-C microbeam in presence and absence of voids in context of LS and CT theories.
Figure 9. Variation of TED in S-S microbeam in presence and absence of voids in context of LS and CT theories.
Figure 10. Variation of TED in cantilever microbeam in presence and absence of voids in context of LS and CT theories.
Figure 11. Variation of TED in a C-C nanobeam with thickness in presence and absence of couple stress in context of LS and CT theories.
Figure 12. Variation of TED in a S-S nanobeam with thickness in presence and absence of couple stress in context of LS and CT theories.
Figure 13. Variation of TED in a C-C piezothermoelastic and thermoelastic nanobeam with thickness in context of LS and CT theories.
Figure 14. Variation of TED in a S-S piezothermoelastic and thermoelastic nanobeam with thickness in context of LS and CT theories.
Figure 15. Variation of TED in a cantilever piezothermoelastic and thermoelastic nanobeam with thickness in context of LS and CT theories.
Figure 16. Variation of frequency shift in C-C microbeam in presence and absence of voids in context of LS and CT theories.
Figure 17. Variation of frequency shift in S-S microbeam in presence and absence of voids in context of LS and CT theories.
