Analytical approaches to vibration analysis of circular, annular and sectorial plates subjected to classical and arbitrary boundary conditions – a literature survey

Plates are one of the most important structural components used in many industries like aerospace, marine and various other engineering fields and thus motivate designers and engineers to study the vibration characteristics of these structures. A lot of research work and studies have been done to study its vibration characteristics. This paper is a review of existing literature on vibration analysis of circular, annular and sector plates. The aim of this paper is to compile prominent studies related to circular, annular and sector plates subjected to classical and arbitrary boundary conditions under different supports and loadings. This review also identifies the analytical methods and approaches used to study the vibration characteristics of circular, annular and sector plates based on classical plate theories, Mindlin plate theory and higher order shear deformation theories. Few important citations related to functionally graded circular, annular and sector plates have also been included. Apart from helping researchers and engineers to identify relevant literature quickly and easily, this review will also help them to apply some of these analytical methods to study the vibration characteristics of other 2D and 3D built up and coupled structures

Dynamic analysis of functionally graded material bars by using novel weak form quadrature element method

This paper presents an efficient approach to simulate frequency and wave propagations in functionally graded material (FGM) bars by using novel weak form quadrature element method (WQEM). Based on Mindlin-Herrmann rod theory, a time domain N-node quadrature bar element is proposed. Detailed formulations are given. Dynamic problems of FGM bars are investigated by using the proposed weak form quadrature bar element. Comparisons are made with results obtained by using frequency domain spectral element method (SEM) and by using strong form differential quadrature method (DQM) to verify the developed quadrature bar element. It is shown that one 21-node bar element can yield very accurate frequencies and that the proposed element can efficiently simulate the wave propagation in FGM bars. Compared to results based on the simple rod theory, the results based on Mindlin-Herrmann rod theory should be more reliable, especially for the wave forms and group velocity

Analytical approaches to vibration analysis of circular, annular and sectorial plates subjected to classical and arbitrary boundary conditions – a literature survey

Plates are one of the most important structural components used in many industries like aerospace, marine and various other engineering fields and thus motivate designers and engineers to study the vibration characteristics of these structures. A lot of research work and studies have been done to study its vibration characteristics. This paper is a review of existing literature on vibration analysis of circular, annular and sector plates. The aim of this paper is to compile prominent studies related to circular, annular and sector plates subjected to classical and arbitrary boundary conditions under different supports and loadings. This review also identifies the analytical methods and approaches used to study the vibration characteristics of circular, annular and sector plates based on classical plate theories, Mindlin plate theory and higher order shear deformation theories. Few important citations related to functionally graded circular, annular and sector plates have also been included. Apart from helping researchers and engineers to identify relevant literature quickly and easily, this review will also help them to apply some of these analytical methods to study the vibration characteristics of other 2D and 3D built up and coupled structures

Analytical approaches to vibration analysis of circular, annular and sectorial plates subjected to classical and arbitrary boundary conditions – a literature survey

Plates are one of the most important structural components used in many industries like aerospace, marine and various other engineering fields and thus motivate designers and engineers to study the vibration characteristics of these structures. A lot of research work and studies have been done to study its vibration characteristics. This paper is a review of existing literature on vibration analysis of circular, annular and sector plates. The aim of this paper is to compile prominent studies related to circular, annular and sector plates subjected to classical and arbitrary boundary conditions under different supports and loadings. This review also identifies the analytical methods and approaches used to study the vibration characteristics of circular, annular and sector plates based on classical plate theories, Mindlin plate theory and higher order shear deformation theories. Few important citations related to functionally graded circular, annular and sector plates have also been included. Apart from helping researchers and engineers to identify relevant literature quickly and easily, this review will also help them to apply some of these analytical methods to study the vibration characteristics of other 2D and 3D built up and coupled structures

Identification of leaky Lamb waves for waveguides sandwiched between elastic half-spaces using the Spectral Collocation Method

In non-destructive evaluation guided wave inspections, the elastic structure to be inspected is often embedded within other elastic media and the ensuing leaky waves are complex and non-trivial to characterise; we consider the canonical example of an elastic waveguide surrounded by other elastic materials that demonstrates the fundamental issues with characterising the leaky waves in such systems. Due to the complex wavenumber solutions required to represent them, leaky waves pose significant challenges to existing numerical methods, while methods that spatially discretise the field to retrieve them suffer from the exponential growth of their amplitude far into the surrounding media. We present a spectral collocation method yielding an accurate and efficient identification of these modes, leaking into elastic half-spaces. We discretise the elastic domains and, depending on the exterior bulk wavespeeds, select appropriate mappings of the discretised domain to complex paths, in which the numerical solution decays and the physics of the problem are preserved. By iterating through all possible radiation cases, the full set of dispersion and attenuation curves are successfully retrieved and validated, where possible, against the commercially available software DISPERSE. As an independent validation, dispersion curves are obtained from finite element simulations of time-dependent waves using Fourier analysis

Machine Learning Aided Stochastic Elastoplastic and Damage Analysis of Functionally Graded Structures

The elastoplastic and damage analyses, which serve as key indicators for the nonlinear performances of engineering structures, have been extensively investigated during the past decades. However, with the development of advanced composite material, such as the functionally graded material (FGM), the nonlinear behaviour evaluations of such advantageous materials still remain tough challenges. Moreover, despite of the assumption that structural system parameters are widely adopted as deterministic, it is already illustrated that the inevitable and mercurial uncertainties of these system properties inherently associate with the concerned structural models and nonlinear analysis process. The existence of such fluctuations potentially affects the actual elastoplastic and damage behaviours of the FGM structures, which leads to the inadequacy between the approximation results with the actual structural safety conditions. Consequently, it is requisite to establish a robust stochastic nonlinear analysis framework complied with the requirements of modern composite engineering practices. In this dissertation, a novel uncertain nonlinear analysis framework, namely the machine leaning aided stochastic elastoplastic and damage analysis framework, is presented herein for FGM structures. The proposed approach is a favorable alternative to determine structural reliability when full-scale testing is not achievable, thus leading to significant eliminations of manpower and computational efforts spent in practical engineering applications. Within the developed framework, a novel extended support vector regression (X-SVR) with Dirichlet feature mapping approach is introduced and then incorporated for the subsequent uncertainty quantification. By successfully establishing the governing relationship between the uncertain system parameters and any concerned structural output, a comprehensive probabilistic profile including means, standard deviations, probability density functions (PDFs), and cumulative distribution functions (CDFs) of the structural output can be effectively established through a sampling scheme. Consequently, by adopting the machine learning aided stochastic elastoplastic and damage analysis framework into real-life engineering application, the advantages of the next generation uncertainty quantification analysis can be highlighted, and appreciable contributions can be delivered to both structural safety evaluation and structural design fields

Free vibration analysis of FGM plates by using layer wise displacement model

In this paper, the free vibration analysis of simply supported functionally graded material (FGM) plate is analyzed. The displacement model based on Generalized Laminate Plate Theory (GLPT) assumes layer wise (LW) linear variation of in–plane displacements, constant transverse displacement, linear strain–displacement relations and linear material properties. The effective material properties of FGMs are assumed to be given by the Voigt’s rule of mixture (ROM). The Power law distribution of volume fraction is assumed through the plate thickness. The mathematical model includes the quadratic variation of transverse shear stresses within each mathematical layer of the plate. The principle of virtual displacements (PVD) is used to derive Euler–Lagrange differential equations of motions for free vibration problem. The Closed form solution is derived following the Navier’s technique and solving the eigenvalue problem. An original MATLAB computer program is coded for the numerical solution. The results reveal that the effects of side–to–thickness ratio, power–low index and material properties have significant effect on free vibration frequencies of FGM plates

Enriched finite element methods : advances & applications

This thesis presents advances and applications of the eXtended Finite Element Method (XFEM). The novelty of the XFEM is the enrichment of the primary variables in the elements intersected by the discontinuity surface by appropriate functions. The enrichment scheme carries the local behaviour of the problem and the main advantage is that the method does not require themesh to conform to the internal boundaries. But this flexibility comes with associated difficulties: (1) Blending problem; (2) Numerical integration of enrichment functions and (3) sub-optimal rate of convergence. This thesis addresses the difficulty in the numerical integration of the enrichment functions in the XFEM by proposing two new numerical integration schemes. The first method relies on conformal mapping, where the regions intersected by the discontinuity surface are mapped onto a unit disk. The second method relies on strain smoothing applied to discontinuous finite element approximations. By writing the strain field as a non-local weighted average of the compatible strain field, integration on the interior of the finite elements is transformed into boundary integration, so that no sub-division into integration cells is required. The accuracy and the efficiency of both the methods are studied numerically with problems involving strong and weak discontinuities. The XFEM is applied to study the crack inclusion interaction in a particle reinforced composite material. The influence of the crack length, the number of inclusions and the geometry of the inclusions on the crack tip stress field is numerically studied. Linear natural frequencies of cracked functionally graded material plates are studied within the framework of the XFEM. The effect of the plate aspect ratio, the crack length, the crack orientation, the gradient index and the influence of cracks is numerically studied. LATEX-ed Friday, October 14, 2011; 10:55am © Sundararajan NatarajanEThOS - Electronic Theses Online ServiceGBUnited Kingdo

Mathematical and Numerical Aspects of Dynamical System Analysis

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Recent Advances in Theoretical and Computational Modeling of Composite Materials and Structures

The advancement in manufacturing technology and scientific research has improved the development of enhanced composite materials with tailored properties depending on their design requirements in many engineering fields, as well as in thermal and energy management. Some representative examples of advanced materials in many smart applications and complex structures rely on laminated composites, functionally graded materials (FGMs), and carbon-based constituents, primarily carbon nanotubes (CNTs), and graphene sheets or nanoplatelets, because of their remarkable mechanical properties, electrical conductivity and high permeability. For such materials, experimental tests usually require a large economical effort because of the complex nature of each constituent, together with many environmental, geometrical and or mechanical uncertainties of non-conventional specimens. At the same time, the theoretical and/or computational approaches represent a valid alternative for designing complex manufacts with more flexibility. In such a context, the development of advanced theoretical and computational models for composite materials and structures is a subject of active research, as explored here for a large variety of structural members, involving the static, dynamic, buckling, and damage/fracturing problems at different scales