Dataset Information

Analytical Solutions Based on Fourier Cosine Series for the Free Vibrations of Functionally Graded Material Rectangular Mindlin Plates.

ABSTRACT: This study aimed to develop series analytical solutions based on the Mindlin plate theory for the free vibrations of functionally graded material (FGM) rectangular plates. The material properties of FGM rectangular plates are assumed to vary along their thickness, and the volume fractions of the plate constituents are defined by a simple power-law function. The series solutions consist of the Fourier cosine series and auxiliary functions of polynomials. The series solutions were established by satisfying governing equations and boundary conditions in the expanded space of the Fourier cosine series. The proposed solutions were validated through comprehensive convergence studies on the first six vibration frequencies of square plates under four combinations of boundary conditions and through comparison of the obtained convergent results with those in the literature. The convergence studies indicated that the solutions obtained for different modes could converge from the upper or lower bounds to the exact values or in an oscillatory manner. The present solutions were further employed to determine the first six vibration frequencies of FGM rectangular plates with various aspect ratios, thickness-to-width ratios, distributions of material properties and combinations of boundary conditions.

SUBMITTER: Huang CS

PROVIDER: S-EPMC7503694 | biostudies-literature | 2020 Aug

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Analytical Solutions Based on Fourier Cosine Series for the Free Vibrations of Functionally Graded Material Rectangular Mindlin Plates.

Huang Chiung-Shiann CS Huang S H SH

Materials (Basel, Switzerland) 20200829 17

This study aimed to develop series analytical solutions based on the Mindlin plate theory for the free vibrations of functionally graded material (FGM<b>)</b> rectangular plates. The material properties of FGM rectangular plates are assumed to vary along their thickness, and the volume fractions of the plate constituents are defined by a simple power-law function. The series solutions consist of the Fourier cosine series and auxiliary functions of polynomials. The series solutions were establish ...[more]

PMID: 32872462

Similar Datasets

Project description:The functional gradient is a concept often occurring in nature. This concept can be implemented in the design and fabrication of advanced materials with specific functionalities and properties. Functionally graded materials (FGMs) can effectively eliminate the interface problems in extremely hard-soft connections, and, thus, have numerous and diverse applications in high-tech industries, such as those in biomedical and aerospace fields. Here, using voxel-based multi-material additive manufacturing (AM, = 3D printing) techniques, which works on the basis of material jetting, we studied the fracture behavior of functionally graded soft-hard composites with a pre-existing crack colinear with the gradient direction. We designed, additively manufactured, and mechanically tested the two main types of functionally graded composites, namely, composites with step-wise and continuous gradients. In addition, we changed the length of the transition zone between the hard and soft materials such that it covered 5%, 25%, 50%, or 100% of the width (W) of the specimens. The results showed that except for the fracture strain, the fracture properties of the graded specimens decreased as the length of the transition zone increased. Additionally, it was found that specimens with abrupt hard-soft transitions have significantly better fracture properties than those with continuous gradients. Among the composites with gradients, those with step-wise gradients showed a slightly better fracture resistance compared to those with continuous gradients. In contrast, FGMs with continuous gradients showed higher values of elastic stiffness and fracture energy, which makes each gradient function suitable for different loading scenarios. Moreover, regardless of the gradient function used in the design of the specimens, decreasing the length of the transition zone from 100%W to 5%W increased the fracture resistance of FGMs. We discuss the important underlying fracture mechanisms using data collected from digital image correlation (DIC), digital image microscopy, and scanning electron microscopy (SEM), which were used to analyze the fracture surface.

Dataset Information

Analytical Solutions Based on Fourier Cosine Series for the Free Vibrations of Functionally Graded Material Rectangular Mindlin Plates.

Publications

Analytical Solutions Based on Fourier Cosine Series for the Free Vibrations of Functionally Graded Material Rectangular Mindlin Plates.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets