Linear and non-linear vibration analysis of moderately thick isosceles triangular FGPs using a triangular finite p-element

Abstract

Background: The geometrically non-linear formulation based on Von-Karman's hypothesis is used to study the free vibration isosceles triangular plates by using four types of mixtures of functionally graded materials (FGMs -AL/ AL 2 O 3 , SUS304/Si 3 N 4 , Ti-AL-4V/Aluminum oxide, AL/ZrO 2 ). Material properties are assumed to be temperature dependent and graded in the thickness direction according to power law distribution. Methods: A hierarchical finite element based on triangular p-element is employed to define the model, taking into account the hypotheses of first-order shear deformation theory. The equations of non-linear free motion are derived from Lagrange's equation in combination with the harmonic balance method and solved iteratively using the linearized updated mode method.