Benchmark exact free vibration solutions for multilayered piezoelectric composite plates
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2018 International Center for Numerical Methods in Engineering. All rights reserved. The development of advanced finite element models suitable for the analysis of smart structures depends on a comprehensive understanding of the behaviour of multilayered piezoelectric composite structures. In fact, an accurate electromechanical modelling of smart structures requires a correct description of both electrical and mechanical fields, particularly in the thickness direction. The assessment of recent and advanced models still continues to rely nowadays only on a few well-known benchmark three-dimensional (3D) exact solutions provided by pioneer works, namely, in the 1970s by Pagano [1,2] as well as Srinivas  for composite plates and later in the 1990s by Heyliger [4-6] for piezoelectric composite plates. To overcome the limited number of test cases whose 3D exact solutions have been published, the authors provided in a previous work  new additional benchmark 3D exact solutions for the static analysis of piezoelectric composite plates. The present work aims to complete this previous one by providing new benchmark 3D exact solutions for the corresponding free vibration analysis. The method introduced by Heyliger to derive the 3D exact solutions has been successfully implemented using symbolic computing and a number of new test cases for free vibration analysis are here presented. Specifically, two multilayered plates using PVDF piezoelectric material are chosen as test cases under two sets of electrical boundary conditions and considering three plate aspect ratios for thick, moderately thick and thin plate, in a total of 12 distinct test cases.