Static and free vibration analysis of functionally graded porous sandwich beams

Functionally graded sandwich materials are composite materials used to build a variety of structures. These structures are used in ships industries, marine, automotive, high building structures, energy engineering applications, and many more. Finite element method is used to analyze the static response of the functionally graded porous (FGP) sandwich beam is subjected to uniformly distributed load along the beam span. The core of the beam is made from functionally graded porous material while the top and bottom layers are made from isotropic homogenous materials. Uniform distribution and symmetric material constitutive relationships (SMCR) are used as two different types of porous material. Shear deformation is considered in the analysis by utilizing beam189 in ANSYS which is a finite element package program. This element method is based on the first-order shear deformation theory. The influence of porosity coefficient, boundary conditions, and type of the porous material on the static response for the considered structures is presented in details. The results demonstrate that the porosity coefficient has an important impact on the static response of the FGP sandwich beams. The porosity made in these materials may negatively affect some of behaviour aspects and properties like stiffness, and strength, nonetheless it may provide superior performance in other fields like vibration reduction, thermal isolation, energy absorption, and others characteristics. A discussion based on dynamic analysis theories is performed about the effect of porosity on the measured natural frequencies for functionally graded porous (FGP) sandwich beams. The mechanical properties of the FGP sandwich beams are mutually changing with the porosity in the thickness direction. The free vibration of the beam is examined with the effect of porosity variations. The analysis is carried out for four different beam supporting types (pinned–pinned, fixed – fixed, fixed – free, fixed–pinned). Various porosity ratios are considered with a range from (0.1 – 0.9). Total of two hundred sixty – four beam's samples divided to four groups. Forty–four samples are analyzed for each type of core material distribution which is the symmetric material constitutive relationships (SMCR), and uniform core material in addition to forty-four samples for nonsymmetric cross section materials, and forty – four beams for Plane183 method. The results obtained from the dynamic analysis show that the porosity constant has a significant effect on the natural frequencies of the FGP sandwich beams