Free Vibration Analysis on Functionally Graded Material Plates with Diverse Porosity Layers

Functionally graded porous structures have gained prominence owing to their lightweight properties and exceptional energy absorption capabilities. These structures find application across diverse fields like aerospace, biomedical science, and engineering [1, 2]. Badri and Al-Kayiem [3] developed an analytical solution procedure of a simply supported plate constructed by a smart multi-layered Magneto-Thermo-Electro-Elastic functional graded material. The developed procedure has been utilized by Albarody et al. [4] to predict the transverse shear deformation behavior of Magneto-Electro-Elastic shell and by Badri and Al-Kayiem [5] to study the dynamic response, i.e., the vibrations, of a Magneto-Thermo-Elastic shell structure subjected to a closed-circuit surface condition.

Porosity, whether inherent to the manufacturing process or deliberately introduced, is a prevalent feature in materials [6]. Functionally Graded Porous Materials (FGPMs) have demonstrated remarkable traits, including substantial bending toughness, low weight, efficient sound absorption, and superior damping characteristics. Consequently, they have enjoyed extensive application in various mechanical and civil engineering Njim et al. [7]. The material used in the present study is Polylactic acid because it has emerged as a leading biomaterial in various industries and medical applications, replacing traditional petrochemical-based polymers due to the environmental and economic concerns associated with petrochemical-based polymers. Polylactic acid is a highly biodegradable thermoplastic that has been extensively researched and utilized for decades, making it one of the most exciting biopolymers in use today [8]. Much extensive research has examined this field for its increasing significance in various applications. Barati and Zenkour [9] presented a new method to investigate how porous functionally graded piezoelectric plates vibrate based on their electrical, thermal, and mechanical properties. Long et al. [10] proposed a novel finite element method to analyze the bending and free vibrations of plates with different characteristics. Vinh [11] investigated the static bending, free vibration, and buckling behavior of functionally graded sandwich panels with porosity based on a new hyperbolic shear deflection theory and a finite element model.

Merdaci et al. [12] investigated functionally graded plates (FGPs) with two unique porosity distributions. The plates were modeled using high-order shear deformation plate theory, ignoring shear correction variables. The natural frequencies of a simply supported porous smart plate were obtained through free oscillation studies using the Hamilton approach. In another study carried out by Singh and Harsha [13], the impact of porosity on the vibration and buckling responses of sandwich panels with different boundary conditions was investigated. Tran et al. [14] presented numerical simulations for analyzing the static bending and free vibration of functionally graded porous plates with varying thicknesses. Kumar et al. [15] considered the free vibration analysis of a tapered plate made of a porous functionally graded material (FGM). The plate was supported on a two-parameter elastic base that incorporates Winkler and Pasternak effects. Leite et al. [16] studied the influence of various 3D printing parameters, such as infill density, extrusion temperature, screen angle, and layer thickness, on the mechanical properties of polylactic acid, and its water absorption was also examined. Rezaei et al. [17] conducted an analytical study on the free vibration analysis of rectangular plates made of functionally graded porous materials based on FSDT. In the study presented by Ibnorachid et al. [18], a porous graded functional beam (P-FGB) was subjected to free oscillation analysis using a sophisticated high-order shear strain theory and Hamilton's principle.

Al Rjoub and Alshatnawi [19] aimed to predict the natural frequencies of a simply supported plate composed of functionally graded material (FGM) with uniform porosity distribution and lateral cracks using both analytical and artificial neural network (ANN) methods. Njim et al. [20] used a novel analytical model to conduct a free vibration analysis of a rectangular functional graded sandwich panel (FGSP) with a porous metal core and uniform top and bottom surfaces. Zghal et al. [21] conducted a study on a modified mixed finite element beam model that was used to examine the impact of porosity on the bending analysis of functionally graded (FG) beams. The material properties of the FG beams were determined based on modified power law distributions with uniform and non-uniform porosity distributions. Kurpa et al. [22] studied the effect of various parameters such as porosity distribution, volume fraction index, elastic foundation, FGM types, and boundary conditions on vibrations. The study concluded that as the volume fraction index increases, frequencies decrease for FGM-1 and FGM-3 materials, while the others show insignificant changes. Frequencies for FGM-2 were found to be lower than those for FGM-1, and FGM-3 frequencies were significantly higher than in other cases. Additionally, the frequencies for FGM-4 remained practically unchanged.

Njim et al. [23] examined the natural frequencies of rectangular sandwich plates and porosities that are functionally graded using a new approximation analytical solution to the free vibration analysis. Rezaei and Saidi [24] investigated and analyzed the free vibration in a thick rectangular porous plate saturated with an inviscid fluid.

Despite the extensive use of FGMs in advanced engineering applications, limited research has focused on the effect of different porosity distributions on the dynamic behavior of FGM plates. Most existing studies either assume uniform porosity or neglect its spatial variation across thickness. This gap makes it difficult to understand and optimize the performance of FGM sheet porous structures under vibrational loads. Therefore, this study aims to fill this gap by investigating the effects of different porosities and their locations on the natural frequencies of FGM porous laminates using ANSYS analysis. A free vibration analysis model of the FGM is built to examine the impact of various factors, including porosity ratio, different porosity locations across the plate layer, and plate thickness, on the natural frequencies of porous rectangular functionally graded plates. Compared with existing literature, the model can be constructed and has high efficiency. Additionally, the FEM model has been conducted using ANSYS software to examine the sensitivity of FEM.

This work presents the effect of porosity values and installation positions on the vibration characteristics of plate structures. Free vibration tests at different thicknesses, porosity, and locations of the porous layer for functionally graded plates were performed. The highest obtained frequency is 259.81 Hz when the porous layer is in the middle. It was observed that the distribution of porosity, as well as changes in the location of the porous layer and different heights, play a significant role in influencing mechanical properties and vibrations. Placing the porous layer in the middle of the sample may improve stress distribution and reduce edge effects, increasing the structure stiffness and subsequently raising its natural frequencies.

It is recommended to consider future works in the direction of:

1. Different porous distributions could also be implemented to study and compare with the current results. This could help identify which types of porous materials are most effective for specific applications.

2. Analyzing the economic and environmental impact of using FGMs. In addition, analyzing the mechanical and physical properties of the composite material could examine the economic and environmental benefits of using these materials in various applications. This could include factors such as reduced weight, improved energy efficiency, and reduced waste in manufacturing.