A cell-based smoothed three-node Mindlin plate element (CS-MIN3) based on the first-order shear deformation theory (FSDT) was recently proposed to improve the performance of the existing three-node Mindlin plate element (MIN3) for static and dynamic analyses of Mindlin plates. In this paper, the CS-MIN3 is extended to the C0-type higher-order shear deformation plate theory (C0-HSDT) and incorporated with damping-spring systems for dynamic analyses of Mindlin plates on the viscoelastic foundation subjected to a moving vehicle. The plate-foundation system is modeled as a discretization of triangular plate elements supported by discrete springs and dashpots at the nodal points representing the viscoelastic foundation. A two-step process for transforming the weight of a four-wheel vehicle into loads at nodes of elements is presented. The accuracy and reliability of the proposed method is verified by comparing its numerical solutions with those of others available numerical results. A parametric examination is also conducted to determine the effects of various parameters on the dynamic response of the plates on the viscoelastic foundation subjected to the moving vehicle.

In this article, a free vibration analysis of the functionally graded porous piezoelectric (FGPP) microplates is firstly solved by using a combination of two variable refined plate theory (RPT), modified strain gradient theory (MSGT) and isogeometric analysis (IGA). The FGPP microplate is composed of piezoelectric material with pores, which are distributed across the plate thickness in uniform and non-uniform distributions. The modified strain gradient theory is used to capture the size effect on the natural frequency of the FGPP microplates. According to the variational principle of RPT with two variables, the governing equations are derived and solved by the IGA. The influence of the length scale parameters (LSPs), external electric voltage, power law index, length-to-thickness ratio, aspect ratio and boundary conditions (BCs) on the natural frequency of the FGPP microplates is studied. The numerical results show that a rise in the porosity coefficient makes a decrease in the microplate’s stiffness, while an increase in LSPs leads to a rise in the microplate’s stiffness.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.