Exact solution for thermal vibration of multi-directional functionally graded porous plates submerged in fluid medium

An analytical method for analyzing the thermal vibration of multi-directional functionally graded porous rectangular plates in fluid media with novel porosity patterns is developed in this study.Mechanical properties of MFG porous plates change according to the length,width,and thickness directions for various materials and the porosity distribution which can be widely applied in many fields of engineering and defence technology.Especially,new porous rules that depend on spatial coordinates and grading indexes are proposed in the present work.Applying Hamilton's principle and the refined higher-order shear deformation plate theory,the governing equation of motion of an MFG porous rectangular plate in a fluid medium(the fluid-plate system)is obtained.The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to compute the extra mass.The GalerkinVlasov solution is used to solve and give natural frequencies of MFG porous plates with various boundary conditions in a fluid medium.The validity and reliability of the suggested method are confirmed by comparing numerical results of the present work with those from available works in the literature.The effects of different parameters on the thermal vibration response of MFG porous rectangular plates are studied in detail.These findings demonstrate that the behavior of the structure within a liquid medium differs significantly from that within a vacuum medium.Thereby,they offer appropriate operational approaches for the structure when employed in various mediums.

Nonlinear dynamic analysis of functionally graded carbon nanotube-reinforced composite plates using MISQ20 element

The main objective of this study is to further extend the mixed integration smoothed quadrilateral element with 20 unknowns of displacement(MISQ20)to investigate the nonlinear dynamic responses of functionally graded carbon nanotube-reinforced composite(FG-CNTRC)plates with four types of carbon nanotube distributions.The smooth finite element method is used to enhance the accuracy of the Q4 element and avoid shear locking without using any shear correction factors.This method yields accurate results even if the element exhibits a concave quadrilateral shape and reduces the error when the element meshing is rough.Additionally,the element stiffness matrix is established by integrating the boundary of the smoothing domains.The motion equation of the FG-CNTRC plates is solved by adapting the Newmark method combined with the Newton–Raphson algorithm.Subsequently,the calculation program is coded in the MATLAB software and verified by comparing it with other published solutions.Finally,the effects of the input parameters on the nonlinear vibration of the plates are investigated.

An isogeometric approach to static and transient analysis of fluid-infiltrated porous metal foam piezoelectric nanoplates with flexoelectric effects and variable nonlocal parameters

In this work,a novel refined higher-order shear deformation plate theory is integrated with nonlocal elasticity theory for analyzing the free vibration,bending,and transient behaviors of fluid-infiltrated porous metal foam piezoelectric nanoplates resting on Pasternak elastic foundation with flexoelectric effects.Isogeometric analysis(IGA)and the Navier solution are applied to the problem.The innovation in the present study is that the influence of the in-plane variation of the nonlocal parameter on the free and forced vibration of the piezoelectric nanoplates is investigated for the first time.The nonlocal parameter and material characteristics are assumed to be material-dependent and vary gradually over the thickness of structures.Based on Hamilton’s principle,equations of motion are built,then the IGA approach combined with the Navier solution is used to analyze the static and dynamic response of the nanoplate.Lastly,we investigate the effects of the porosity coefficients,flexoelectric parameters,elastic stiffness,thickness,and variation of the nonlocal parameters on the mechanical behaviors of the rectangular and elliptical piezoelectric nanoplates.