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Vibration analysis of FGM beams incorporating surface energy immersed in fluids under photothermal excitation

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Abstract

In this study, the dynamic response of FGM (functionally graded materials) beam with surface effect immersed in fluids under high-frequency photothermal excitation is investigated theoretically. The governing equations of FGM beams are derived under Euler–Bernoulli beam theory. The cubical assumption is adopted to describe stress along thickness of FGM beam. In consideration of photothermal force and hydrodynamic load, the solution of forced vibration is obtained by means of the Fourier series expansion of variables. Theoretical analysis shows that the volume fraction and surface effect have an important influence on the response of beams immersed in different fluids; for the FGM material, an optimal material distribution proportion can maximize the response of beams. Among the parameters of the surface effect, the influence of surface residual is greater than surface elastic modulus and surface density. The influence of fluids on resonant frequencies is much more significant than surface effect. This study can provide some references to the application of micro- and nano-FGM structures in Micro-Electro-Mechanical System and Nano-Electro-Mechanical System.

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References

  1. Song, Y.Q., Cretin, B., Todorovic, D.M., Vairac, P.: Study of laser excited vibration of silicon cantilever. J. Appl. Phys. 104, 104909 (2008)

    Article  Google Scholar 

  2. Song, Y.Q., Cretin, B., Todorovic, D.M., Vairac, P.: Study of photothermal vibrations of semiconductor cantilevers near the resonant frequency. J. Phys. D. Appl. Phys. 41(15), 155106 (2008)

    Article  Google Scholar 

  3. Wang, G.F., Feng, X.Q.: Effects of surface elasticity and residual surface tension on the natural frequency of microbeams. Appl. Phys. Lett. 90, 231904 (2007)

    Article  Google Scholar 

  4. Gu, Q.F., Krauss, G., Gramm, F., Cervellino, A., Steurer, W.: Unexpected high stiffness of Ag and au nano-particles. Phys. Rev. Lett. 100, 045502 (2008)

    Article  Google Scholar 

  5. Yao, Y., Chen, S.: Surface effect in the bending of nanowires. Mech. Mater. 100, 12–21 (2016)

    Article  Google Scholar 

  6. Sader, J.E.: Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope. J. Appl. Phys. 84(1), 64–76 (1998)

    Article  Google Scholar 

  7. Chon, J.W.M., Mulvaney, P., Sader, J.E.: Experimental validation of theoretical models for the frequency response of atomic force microscope cantilever beams immersed in fluids. J. Appl. Phys. 87(8), 3978–3988 (2000)

    Article  Google Scholar 

  8. Eysden, C., Sader, J.E.: Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope: Arbitrary mode order. J. Appl. Phys. 101, 044908 (2007)

    Article  Google Scholar 

  9. Aureli, M., Porfiri, M.: Low frequency and large amplitude oscillations of cantilevers in viscous fluids. Appl. Phys. Lett. 96, 164102 (2010)

    Article  Google Scholar 

  10. Aureli, M., Basaran, M.E., Porfiri, M.: Nonlinear finite amplitude vibrations of sharp-edged beams in viscous fluids. J. Sound Vibr. 331(7), 1624–1654 (2012)

    Article  Google Scholar 

  11. Hu, L., Yan, H., Zhang, W.M., Zou, H.X., Peng, Z.K., Meng, G.: Theoretical and experimental study on dynamic characteristics of V-shaped beams immersed in viscous fluids: from small to finite amplitude. J. Fluids Struct. 82, 215–244 (2018)

    Article  Google Scholar 

  12. Zhu, Hz., Wu, J.H.: Free vibration of partially fluid-filled or fluid-surrounded composite shells using the dynamic stiffness method. Acta Mech 231, 3961–3978 (2020). https://doi.org/10.1007/s00707-020-02734-3

    Article  MathSciNet  MATH  Google Scholar 

  13. El-Sapa, S., Mohamed, M.S., Lotfy, K., et al.: A mechanical ramp type of electron–hole semiconducting model with laser pulses and variable thermal conductivity. Acta Mech 233, 4641–4658 (2022). https://doi.org/10.1007/s00707-022-03342-z

    Article  MathSciNet  MATH  Google Scholar 

  14. Kiracofe, D., Kobayashi, K., Labuda, A., Raman, A., Yamada, H.: High efficiency laser photothermal excitation of microcantilever vibrations in air and liquids. Rev. Sci. Instrum. 82(1), 160–165 (2011)

    Article  Google Scholar 

  15. Evans, D.R., Tayati, P., An, H., Lam, P.K., Craig, V.S.J., Senden, T.J.: Laser actuation of cantilevers for picometre amplitude dynamic force microscopy. Sci. Rep. 4, 5567 (2014)

    Article  Google Scholar 

  16. Song, Y.Q., Dong, T.B., Bai, J.T., Kang, Y.F.: Photothermal response of polymer microcantilever with metal coating in fluids. Appl. Math. Model. 41, 596–603 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  17. Gu, S., Song, Y.Q., Zheng, Q.: Study on the vibration of functionally graded micro-cantilevers immersed in fluids under photothermal excitation. IOP Conf. Ser. Mater. Sci. Eng. 531, 012070 (2019)

    Article  Google Scholar 

  18. Ebrahimi, F., Salari, E.: Nonlocal thermo-mechanical vibration analysis of functionally graded nanobeams in thermal environment. Acta Astronaut. 113, 29–50 (2015)

    Article  Google Scholar 

  19. Chan, D.Q., Quan, T.Q., Phi, B.G., et al.: Buckling analysis and dynamic response of FGM sandwich cylindrical panels in thermal environments using nonlocal strain gradient theory. Acta Mech 233, 2213–2235 (2022). https://doi.org/10.1007/s00707-022-03212-8

    Article  MathSciNet  MATH  Google Scholar 

  20. Vaghefi, R.: Nonlinear bending of FG skew sandwich plates with temperature-dependent elastoplastic properties using an enhanced 3D meshless approach. Acta Mech 233, 1599–1631 (2022). https://doi.org/10.1007/s00707-022-03175-w

    Article  MathSciNet  MATH  Google Scholar 

  21. Li, L., Liao, W.H., Zhang, D., Zhang, Y.: Vibration control and analysis of a rotating flexible FGM beam with a lumped mass in temperature field. Compos. Struct. 208, 244–260 (2019)

    Article  Google Scholar 

  22. Liang, L.N., Ke, L.L., Wang, Y.S., Yang, J., Kitipornchai, S.: Flexural vibration of an atomic force microscope cantilever based on modified couple stress theory. Int. J. Struct. Stab. Dyn. 15(07), 1540025 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  23. Wang, C.M., Zhang, Y.Y., He, X.Q.: Vibration of nonlocal Timoshenko beams. Nanotechnology 18, 105401 (2007)

    Article  Google Scholar 

  24. Hosseini, S.M., Sladek, J.V.: Nonlocal coupled photo-thermoelasticity analysis in a semiconducting micro/nano beam resonator subjected to plasma shock loading: a Green-Naghdi-based analytical solution. Appl. Math. Model. 88, 631–651 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  25. Tang, F.X., Dong, F., Guo, Y.Z., Shi, S.N., Jiang, J.Z., Liu, S.: Size-dependent buckling and post-buckling analysis of the functionally graded thin plate Al–Cu material based on a modified couple stress theory. Nanomaterials 12, 3502 (2022)

    Article  Google Scholar 

  26. Tan, Z.Q., Chen, Y.C.: Size-dependent electro-thermo-mechanical analysis of multilayer cantilever microactuators by Joule heating using the modified couple stress theory. Compos. Part B-Eng. 161, 183–189 (2019)

    Article  Google Scholar 

  27. Babaei, H., Eslami, M.R.: Thermally induced large deflection of FGM shallow micro-arches with integrated surface piezoelectric layers based on modified couple stress theory. Acta Mech 230, 2363–2384 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  28. Kiani, K.: Thermo-mechanical analysis of functionally graded plate-like nanorotors: a surface elasticity model. Int. J. Mech. Sci. 106, 39–49 (2016)

    Article  MathSciNet  Google Scholar 

  29. Song, Y.Q., Bai, J.T., Kang, Y.F.: Effect of surface elastic on the response of micro-cantilevers under photothermal excitation. Int. J. Thermophys. 36(10), 3106–3115 (2015)

    Article  Google Scholar 

  30. Attia, M.A., Mohamed, S.A.: Coupling effect of surface energy and dispersion forces on nonlinear size-dependent pull-in instability of functionally graded micro-/nanoswitches. Acta Mech 230, 1181–1216 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  31. Barretta, R., Canadija, M., Luciano, R., Marotti de Sciarra, F.: Stress-driven modeling of nonlocal thermoelastic behavior of nanobeams. Int. J. Eng. Sci. 126, 53–67 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  32. Abbas, I.A., Alzahrani, F.S., Elaiw, A.: A DPL model of photothermal interaction in a semiconductor material. Waves Random Complex Media 29(2), 1–16 (2018)

    MATH  Google Scholar 

  33. Lotfy, K., Hassan, W., El-Bary, A.A., Kadry, M.A.: Response of electromagnetic and Thomson effect of semiconductor medium due to laser pulses and thermal memories during photothermal excitation. Results Phys. 16, 102877 (2020)

    Article  Google Scholar 

  34. Hu, H.F., Yu, T.T., Le, V.L., Bui, T.Q.: Functionally graded curved Timoshenko microbeams: a numerical study using iga and modified couple stress theory. Compos. Struct. 254, 112841 (2020)

    Article  Google Scholar 

  35. Liu, S., Yu, T.T., Le, V.L., et al.: Size and surface effects on mechanical behavior of thin nanoplates incorporating microstructures using isogeometric analysis. Comput. Struct. 212, 173–187 (2019)

    Article  Google Scholar 

  36. Gurtin, M.E., Murdoch, A.I.: A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57, 291–323 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  37. Liu, C., Rajapakse, R.K.N.D.: Continuum models incorporating surface energy for static and dynamic response of nanoscale beams. IEEE Trans. Nanotechnol. 9(4), 422–431 (2010)

    Article  Google Scholar 

  38. Hosseini-Hashemi, S., Nazemnezhad, R.: an analytical study on the nonlinear free vibration of functionally graded nanobeams incorporating surface effects. Compos. Pt B-Eng. 52, 199–206 (2013)

    Article  Google Scholar 

  39. Lu, P., He, L.H., Lee, H.P., Lu, C.: Thin plate theory including surface effects. Int. J. Solids Struct. 43(16), 4631–4647 (2006)

    Article  MATH  Google Scholar 

  40. Nazarenko, L., Bargmann, S., Stolarski, H.: Energy-equivalent inhomogeneity approach to analysis of effective properties of nanomaterials with stochastic structure. Int. J. Solids Struct. 59, 183–197 (2015)

    Article  Google Scholar 

  41. Gurtin, M.E., Murdoch, A.I.: Surface stress in solids. Int. J. Solids Struct. 14, 431–440 (1978)

    Article  MATH  Google Scholar 

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Acknowledgements

This work was supported by Natural Science Foundation of China [Grant Number: 62074125].

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Authors and Affiliations

  1. State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Sen Gu, Luke Zhao & Yaqin Song

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  1. Sen Gu
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  2. Luke Zhao
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Correspondence to Yaqin Song.

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Gu, S., Zhao, L. & Song, Y. Vibration analysis of FGM beams incorporating surface energy immersed in fluids under photothermal excitation. Acta Mech 234, 2481–2495 (2023). https://doi.org/10.1007/s00707-023-03511-8

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  • DOI: https://doi.org/10.1007/s00707-023-03511-8

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