Abstract
In this paper, the flexural vibration frequency in the antisymmetric mode of a thick plate as a function of the amplitude of the vibration and the axial force applied is investigated. With this aim, the theory of geometrically nonlinear deformation of second order and an optimized three-dimensional Ritz method are used. The plate is homogeneous, elastically linear, free from any constraints, and subjected to axial forces uniformly distributed on two of its opposite sides. Several approaches are discussed. First, the problem based on finite stress and infinitesimal strains is solved. Second, the deformation energy is assumed as the energy in the initial state plus the vibration energy of small or large amplitude. Third, without assumptions about the size of the deformation and of the vibration amplitude, the theory of nonlinear deformation is employed. Finally, numerical calculations for free vibration are compared with experimental results, including their systematic uncertainties.
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Francisco J. Nieves received his Ph.D. degree in Physics from University of Seville in 1999. He is currently an Associate Professor at Department of Applied Physics II at the School of Architecture in University of Seville. His main subjects are mechanical vibrations and acoustics.
Ana Bayón is currently an Associate Professor of Applied Physics at the Energy and Mining Engineering School of Madrid. She received the Ph.D. in 1992 from the Technical University of Madrid (UPM). Her research interests include mechanical vibrations, optical detection of ultrasounds, and elastic characterization of materials. She is a Fellow of the Acoustical Society of America (ASA).
Francisco Gascón received his Master of Science at the University of Zaragoza in 1958, and his Ph.D. in 1962. He has carried out research at the C. F. E. Fontenay-aux-Roses (France), the L’École Nationale Supérieure d'Électrotechnique (ENSEEIHT), and the Clarendon Laboratory (Oxford). He got a full professorship in Applied Physics at the Mining Engineering School (Technical University of Madrid). In 2009 he assumed Emeritus status at the University of Sevilla. His main research fields are speckle interferometry and vibration analysis.
Rafael Medina is currently an Associate Professor of Applied Physics at the Energy and Mining Engineering School of Madrid. He received the Ph.D. in 1989 from the Technical University of Madrid (UPM). His research has been developed mainly in mechanical vibrations and wave propagations in materials.
Félix Salazar studied Physics at the Complutense University of Madrid (1987), and received the Ph.D. degree from the Technical University of Madrid (UPM) in 1992. He was awarded the Ph.D. Prize in the academic course 1993-94. In 1995 he was appointed as Associate Professor of Applied Physics at the Mining Engineering School of Madrid (ETSIM). His main research subjects are random electromagnetic fields (speckle) and vibration analysis. He is a Fellow of the Deutsche Gesellschaft für angewandte Optik (DGaO), Arbeitskreis der Hochschullehrer für Messtechnik (AHMT), and the Optical Society of America (OSA).
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Nieves, F.J., Bayón, A., Gascón, F. et al. Nonlinear bending vibration of a prestressed thick plate. J Mech Sci Technol 32, 1505–1517 (2018). https://doi.org/10.1007/s12206-018-0304-8
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DOI: https://doi.org/10.1007/s12206-018-0304-8