Next Article in Journal
Analysis of the Chip Geometry in Dry Machining of Aeronautical Aluminum Alloys
Next Article in Special Issue
A Time Finite Element Method Based on the Differential Quadrature Rule and Hamilton’s Variational Principle
Previous Article in Journal
Supercooled Water Droplet Impacting Superhydrophobic Surfaces in the Presence of Cold Air Flow
Previous Article in Special Issue
An Equivalent Layer-Wise Approach for the Free Vibration Analysis of Thick and Thin Laminated and Sandwich Shells
Article Menu
Issue 2 (February) cover image

Export Article

Open AccessArticle
Appl. Sci. 2017, 7(2), 131; doi:10.3390/app7020131

A Numerical Investigation on the Natural Frequencies of FGM Sandwich Shells with Variable Thickness by the Local Generalized Differential Quadrature Method

1
DICAM—Department, School of Engineering and Architecture, University of Bologna, 40126, Italy
2
Advanced Computational Mechanics Laboratory, Department of Mechanical Engineering, Texas A&M University, College Station, TX, 77843, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Faris Ali
Received: 15 January 2017 / Revised: 20 January 2017 / Accepted: 23 January 2017 / Published: 27 January 2017
View Full-Text   |   Download PDF [4036 KB, uploaded 6 February 2017]   |  

Abstract

The main aim of the present paper is to solve numerically the free vibration problem of sandwich shell structures with variable thickness and made of Functionally Graded Materials (FGMs). Several Higher-order Shear Deformation Theories (HSDTs), defined by a unified formulation, are employed in the study. The FGM structures are characterized by variable mechanical properties due to the through-the-thickness variation of the volume fraction distribution of the two constituents and the arbitrary thickness profile. A four-parameter power law expression is introduced to describe the FGMs, whereas general relations are used to define the thickness variation, which can affect both the principal coordinates of the shell reference domain. A local scheme of the Generalized Differential Quadrature (GDQ) method is employed as numerical tool. The natural frequencies are obtained varying the exponent of the volume fraction distributions using higher-order theories based on a unified formulation. The structural models considered are two-dimensional and require less degrees of freedom when compared to the corresponding three-dimensional finite element (FE) models, which require a huge number of elements to describe the same geometries accurately. A comparison of the present results with the FE solutions is carried out for the isotropic cases only, whereas the numerical results available in the literature are used to prove the validity as well as accuracy of the current approach in dealing with FGM structures characterized by a variable thickness profile. View Full-Text
Keywords: functionally graded materials; free vibration analysis; local generalized differential quadrature method; higher-order structural theories; variable thickness shells functionally graded materials; free vibration analysis; local generalized differential quadrature method; higher-order structural theories; variable thickness shells
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Tornabene, F.; Fantuzzi, N.; Bacciocchi, M.; Viola, E.; Reddy, J.N. A Numerical Investigation on the Natural Frequencies of FGM Sandwich Shells with Variable Thickness by the Local Generalized Differential Quadrature Method. Appl. Sci. 2017, 7, 131.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Appl. Sci. EISSN 2076-3417 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top