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Size-dependent vibration of a microplate under the action of a moving load based on the modified couple stress theory

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Abstract

This study deals with forced vibration analysis of a microplate subjected to a moving load. The formulation is developed based on the modified couple stress theory in conjunction with Kirchhoff–Love plate theory. The equations of motion of the problem are derived using Lagrange’s equations. In order to obtain the response of the microplate, the trial function for the dynamic deflection is expressed in the polynomial form. The equations of motion are solved by using the implicit time integration Newmark-β method, and then displacements, velocities and accelerations of the microplate at the considered point and time are determined. Five different sets of boundary condition are considered. For this purpose, boundary conditions are satisfied by adding some auxiliary functions to the trial functions. A parametric study is conducted to study the effects of the material length scale parameter, plate aspect ratio, boundary conditions and the moving load velocity on the dynamic response of the microplate. Also, in order to validate the present formulation and solution method, some comparisons with those available in the literature are performed. Good agreement is found. The results show that the dynamic deflections are significantly affected by the scale parameter and the load velocity.

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Authors and Affiliations

  1. Department of Civil Engineering, Faculty of Civil Engineering, Yildiz Technical University, Davutpaşa Campus, 34210, Esenler, Istanbul, Turkey

    M. Şimşek

  2. Department of Mathematics, Faculty of Science and Literature, Yildiz Technical University, Davutpaşa Campus, 34210, Esenler, Istanbul, Turkey

    M. Aydın

  3. Department of Mathematical Engineering, Chemical and Metallurgical Engineering, Yildiz Technical University, Davutpaşa Campus, 34210, Esenler, Istanbul, Turkey

    H. H. Yurtcu

  4. Mechanical Engineering Department, Texas A&M University, College Station, TX, 77843-3123, USA

    J. N. Reddy

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  1. M. Şimşek
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  2. M. Aydın
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Şimşek, M., Aydın, M., Yurtcu, H.H. et al. Size-dependent vibration of a microplate under the action of a moving load based on the modified couple stress theory. Acta Mech 226, 3807–3822 (2015). https://doi.org/10.1007/s00707-015-1437-9

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  • DOI: https://doi.org/10.1007/s00707-015-1437-9

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