Benchmark exact free vibration solutions for multilayered piezoelectric composite plates

Abstract The development of advanced finite element models suitable for analysis of smart structures depends on a comprehensive understanding of the high layerwise inhomogeneity in mechanical and electric properties present in multilayered piezoelectric composite structures. The assessment of advanced models still continues to rely only on a few well-known benchmark three-dimensional (3D) exact solutions provided by pioneer works, namely, in the 1970s by Pagano as well as Srinivas for composite plates and later in the 1990s by Heyliger and Saravanos for piezoelectric composite plates. To overcome the limited number of test cases whose 3D exact solutions have been published, the method introduced by Heyliger to derive the 3D exact solutions has been successfully implemented using symbolic computing. New benchmark 3D exact free vibration solutions are provided for piezoelectric composite plates that complete a previous work with the static solutions. Two multilayered plates using PVDF piezoelectric material are chosen as test cases under three sets of electrical boundary conditions and considering three plate aspect ratios (from thick to thin plate), in a total of 18 test cases. For each case, the frequencies of the first six thickness modes are presented, along with some representative through-thickness mode shapes.