Free vibration analysis of two-dimensional functionally graded structures by a meshfree boundary–domain integral equation method

A type of complete systems of orthogonal functions in L2[a,b] space is introduced into the construction of Green's function of annular plate. A brief and effective method is derived to study the free vibration of annular plates by using the integral equation method. The results obtained not only reveal its briefness and high precision, but also provide a reliable premise for the vibration analysis of more complex annular plates.

Download Full-text

A two-dimensional free vibration analysis of functionally graded sandwich beams under thermal environment

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406212440669 ◽

2012 ◽

Vol 226 (12) ◽

pp. 2860-2873 ◽

Cited By ~ 10

Author(s):

AR Setoodeh ◽

M Ghorbanzadeh ◽

P Malekzadeh

Keyword(s):

Free Vibration ◽

Shear Deformation ◽

Vibration Analysis ◽

Thermal Environment ◽

Free Vibration Analysis ◽

Functionally Graded ◽

Mode Shapes ◽

Geometrical Parameters ◽

Sandwich Beams ◽

Two Dimensional

In this article, free vibration analysis of elastically supported sandwich beams with functionally graded face sheets subjected to thermal environment is presented. In order to accurately include the transverse shear deformation and the inertia effects, two-dimensional elasticity theory is used to formulate the problem. The layerwise theory in conjunction with the differential quadrature method is employed to discretize the governing equations in the thickness and axial directions, respectively. The material properties of functionally graded face sheets are assumed to be temperature-dependent and graded in the thickness direction according to a power-law distribution. For the purpose of comparison, the problem under consideration is also solved using two-dimensional finite element method and the first-order shear deformation theory. The accuracy, convergence, and versatility of the method are demonstrated by comparing the results with those of the two aforementioned approaches and also with the existing solutions in literature. Eventually, some new numerical results are presented which depict the effects of different material and geometrical parameters on natural frequencies and mode shapes of the beam.

Download Full-text

Free vibration characteristics of functionally graded structures by an isogeometrical analysis approach

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406213508757 ◽

2013 ◽

Vol 228 (9) ◽

pp. 1512-1530 ◽

Cited By ~ 3

Author(s):

Alireza Hassanzadeh Taheri ◽

Mohammad Hossein Abolbashari ◽

Behrooz Hassani

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Free Vibration ◽

Material Properties ◽

Isogeometric Analysis ◽

Vibration Analysis ◽

Functionally Graded ◽

Analysis Method ◽

Graded Structures ◽

Functionally Graded Structures

An improved methodology based on isogeometric analysis (IGA) approach is suggested to investigate the free vibration characteristics of functionally graded structures. The proposed method, which can be considered as an extension of the isogeometric analysis method to inhomogeneous elasticity, employs a fully isogeometric formulation for construction of the geometry, approximation of the solution as well as modelling the variations of material properties. The gradations of material properties are captured using the same NURBS basis functions employed for geometric and computational modelling by utilization of an interpolation technique. It will be seen that the proposed NURBS-based analysis method constitutes an efficient tool for studying integrated modelling and vibration analysis of functionally graded structures. Some numerical examples of 2D plane elasticity problems are presented and the effects of different types of unidirectional and bidirectional material profiles on dynamic characteristics of functionally graded structures are investigated. The obtained numerical results are verified with available exact elasticity solutions or the results of commercial finite element method software. It is shown that the difficulties encountered in free vibration analysis of functionally graded structures using the conventional finite element method are considerably circumvented by adopting the proposed procedure.

Download Full-text