Geometric Nonlinear Finite Element and Genetic Algorithm Based Vibration Energy Harvesting from Functionally Graded Nonprismatic Piezolaminated Beams

Energy harvesting technology has the ability to create autonomous, self-powered systems which do not rely on the conventional battery for their operation. The term energy harvesting is the process of converting the ambient energy surrounding a system into some useful electrical energy using certain materials. Among several energy conversion techniques, the conversion of ambient vibration energy to electrical energy using piezoelectric materials has great deal of importance which encompasses electromechanical coupling between mechanical and electrical domains. The energy harvesting systems are designed by incorporating the piezoelectric materials in the host structure located in vibration rich environment. The work presented in this dissertation focuses on upgrading the concept of energy harvesting in order to engender more power than conventional energy harvesting designs. The present work deals with first the finite element (FE) formulation for coupled thermo-electro-mechanical analysis of vibration energy harvesting from an axially functionally graded (FG) non-prismatic piezolaminated cantilever beam. A two noded beam element with two degrees of freedom (DOF) at each node has been used in the FE formulation. The FG material (i.e. non-homogeneity) in the axial direction has been considered which varies (continuously decreasing from root to tip of such cantilever beam) using a proposed power law formula. The various cross section profiles (such as linear, parabolic and cubic) have been modelled using the Euler-Bernoulli beam theory and Hamilton‘s principle is used to solve the governing equation of motion. The simultaneous variation of tapers (both width and height in length directions) is incorporated in the mathematical formulation. The FE formulation developed in the present work has been compared with the analytical solutions subjected to mechanical, electrical, thermal and thermo-electro-mechanical loading. Results obtained from the present work shows that the axially FG nonprismatic beam generates more output power than the conventional energy harvesting systems. Further, the work has been focussed towards the nonlinear vibration energy harvesting from an axially FG non-prismatic piezolaminated cantilever beam. Geometric nonlinear based FE formulation using Newmark method in conjunction with Newton-Raphson method has been formulated to solve the obtained governing equation. Moreover, a real code GA based constrained optimization technique has also been proposed to determine the best possible design variables for optimal power harvesting within the allowable limits of ultimate stress of the beam and voltage of the PZT sensor. It is observed that more output power can be obtained based on the present optimization formulation within the allowable limits of stress and voltage than that of selection of design variables by trial and error in FE modelling

Vibration and buckling of composite twisted Panels subjected to hygrothermal loading

The twisted composite cantilever have significant applications in aeronautical and aerospace industry civil, naval and other high-performance engineering applications due to their light weight, high-specific strength and stiffness, excellent thermal characteristics, ease in fabrication and other important specialties These structural members are often exposed to various service loads during their entire service life. The presence of temperature and moisture concentration in the environment may greatly reduce the stiffness and strength of the structures and may affect some design parameter such as vibration and stability characteristics of the structures. To avoid these typical problems caused by vibrations and stability, it is important to find out natural frequency, static stability of the composite laminated twisted cantilever panels under hygrothermal conditions. Therefore the vibration and stability behavior of laminated composite twisted panels subjected to hygrothermal conditions are studied in the present investigation. A simple laminated model is developed for the vibration and stability analysis of laminated composite pre-twisted cantilever panel subjected to hygrothermal conditions. A computer program based on FEM in MATLAB environment is developed to perform all necessary computations. Here an eight noded isoparametric quadratic shell element with five degrees of freedom per node is used based on FSDT theory with hygrothermal loading. Element elastic stiffness matrices, mass matrices, geometric stiffness matrix due to hygrothermal loads and load vectors are derived using the principle of minimum potential energy. The influences of various parameters such as angle of twist, aspect ratio, ply-orientation, geometry and number of layers of laminate are studied on the vibration and buckling characteristics of laminated pre twisted cantilever panels for different temperatures and moisture concentrations

Stability analysis of FGM plates by using layer wise displacement model

In this paper, the stability analysis of simply supported functionally graded material (FGM) plate under mechanical in–plane compressive loads is analyzed. The displacement model based on Generalized Laminate Plate Theory (GLPT) assumes piece–wise linear variation of in–plane displacements, constant transverse displacement, non–linear strain–displacement relations (in von Karman sense) and linear material properties. The properties of FGMs are assumed to be constant in xy–plane and vary through thickness by a power law function in terms of volume fraction of the constituents. The mathematical model includes the quadratic variation of transverse shear stresses within each layer of the plate. The principle of virtual displacements (PVD) is used to derive Euler–Lagrange differential equations of linearized buckling problem. Closed form solution is derived following the Navier’s technique and solving the eigenvalue problem. The 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 modulus ratio have significant effect on critical buckling loads of FGM plates

Vibration and Buckling of Composite Twisted Panels Subjected to Hygrothermal Environment

The twisted cantilever panels have significant applications in wide chord turbine blades, compressor blades, fan lades, aircraft or marine propellers, helicopter blades, and particularly in gas turbines . These structural members are often subjected to various environmental loads during their service life. The presence of temperature and moisture concentration may significantly reduce the stiffness and strength of the structures and may affect some design parameter such as vibration and stability characteristics of the structures. To avoid the typical problems caused by vibrations and stability, it is important to determine natural frequency, critical buckling load of the composite laminated pre twisted cantilever panels under hygrothermal conditions. Therefore the vibration and buckling behavior of laminated composite twist ed panels subjected to hygrothermal loadings are studied in the present investigation. The present study deals with the free vibration and buckling analysis of pre- twisted cantilever laminated composite panels subjected to hygrothermal loading using Finite element method. A computer program based on FEM in MATLAB environment is developed to perform all necessary computations. Here eight noded isoparametric quadratic shell element with five degrees of freedom per node is used based on FSDT theory with hygrothermal loading. The influences of various parameters such as angle of twist, aspect ratio and lamination parameters are examined on the vibration and buckling characteristics of laminated twisted panels subjected to hygrothermal loads. Numerical results a re presented to show the effects of pre- twist angles, geometry and lamination details on the vibration and buckling characteristics of twisted plates

Index of NACA Technical Publications, 1949 - May, 1951

The Preface to the Index of NACA Technical Publications, 1915-1949, mentioned that regular supplements would be issued in the future. This is the first such Supplement and covers those documents issued through May of 1951. Similar arrangement is used in both Indexes. First, there is a classified listing of the subject categories; second, a chronological listing of NACA publications under each subject category; third, an alphabetical index to the subject categories; and finally, an author index. The latter feature was not included in the basic 1915-1949 Index but has been issued separately and is available upon request. Immediately following this Preface is an Explanatory Chart of NACA Publications Series Designations which may be of use in identifying references to NACA documents encountered in the literature

Engine structures: A bibliography of Lewis Research Center's research for 1980-1987

This compilation of abstracts describes and indexes the technical reporting that resulted from the scientific and engineering work performed and managed by the Structures Division of the NASA Lewis Research Center from 1980 through 1987. All the publications were announced in the l980 to 1987 issues of STAR (Scientific and Technical Aerospace Reports) and or IAA (International Aerospace Abstracts). Included are research reports, journal articles, conference presentations, patents and patent applications, and theses

Three dimensional coupling between elastic and thermal fields in the static analysis of multilayered composite shells

This new work aims to develop a full coupled thermomechanical method including both the temperature profile and displacements as primary unknowns of the model. This generic full coupled 3D exact shell model permits the thermal stress investigation of laminated isotropic, composite and sandwich structures. Cylindrical and spherical panels, cylinders and plates are analyzed in orthogonal mixed curved reference coordinates. The 3D equilibrium relations and the 3D Fourier heat conduction equation for spherical shells are coupled and they trivially can be simplified in those for plates and cylindrical panels. The exponential matrix methodology is used to find the solutions of a full coupled model based on coupled differential relations with respect to the thickness coordinate. The analytical solution is based on theories of simply supported edges and harmonic relations for displacement components and sovra-temperature. The sovra-temperature magnitudes are directly applied at the outer faces through static state hypotheses. As a consequence, the sovra-temperature description is assumed to be an unknown variable of the model and it is calculated in the same way as the three displacements. The final system is based on a set of coupled homogeneous differential relations of second order in the thickness coordinate. This system is reduced in a first order differential relation system by redoubling the number of unknowns. Therefore, the exponential matrix methodology is applied to calculate the solution. The temperature field effects are evaluated in the static investigation of shells and plates in terms of displacement and stress components. After an appropriate preliminary validation, new benchmarks are discussed for several thickness ratios, geometrical data, lamination sequences, materials and sovra-temperature values imposed at the outer faces. Results make evident the accordance between the uncoupled thermo-mechanical model and this new full coupled thermo-mechanical model without the need to separately solve the Fourier heat conduction relation. Both effects connected with the thickness layer and the related embedded materials are included in the conducted thermal stress analysis

Electrowetting: from basics to applications

Electrowetting has become one of the most widely used tools for manipulating tiny amounts of liquids on surfaces. Applications range from 'lab-on-a-chip' devices to adjustable lenses and new kinds of electronic displays. In the present article, we review the recent progress in this rapidly growing field including both fundamental and applied aspects. We compare the various approaches used to derive the basic electrowetting equation, which has been shown to be very reliable as long as the applied voltage is not too high. We discuss in detail the origin of the electrostatic forces that induce both contact angle reduction and the motion of entire droplets. We examine the limitations of the electrowetting equation and present a variety of recent extensions to the theory that account for distortions of the liquid surface due to local electric fields, for the finite penetration depth of electric fields into the liquid, as well as for finite conductivity effects in the presence of AC voltage. The most prominent failure of the electrowetting equation, namely the saturation of the contact angle at high voltage, is discussed in a separate section. Recent work in this direction indicates that a variety of distinct physical effects¿rather than a unique one¿are responsible for the saturation phenomenon, depending on experimental details. In the presence of suitable electrode patterns or topographic structures on the substrate surface, variations of the contact angle can give rise not only to continuous changes of the droplet shape, but also to discontinuous morphological transitions between distinct liquid morphologies. The dynamics of electrowetting are discussed briefly. Finally, we give an overview of recent work aimed at commercial applications, in particular in the fields of adjustable lenses, display technology, fibre optics, and biotechnology-related microfluidic devices

Non-linear forced vibration analysis of axially functionally graded tapered beam with various end conditions

In the present thesis a study of large amplitude forced vibration of axially functionally graded beams is carried out by considering various boundary conditions and loading condition. The governing differential equation for the system is derived by using Hamilton’s principle and the solution to the nonlinear set of equations is generated by implementing a substitution technique. The results of the nonlinear analysis are plotted as characteristics curve i.e. non-dimensional frequency response curve for different classical flexural boundary conditions with different variation of material and geometric parameters. For each boundary condition, variation of material properties (i.e. elastic modulus & density) in the axial direction of the beam is considered with different taper profile of thickness. The variation of material properties taken under consideration are homogenous material, linear variation of both elasticity and density, exponential variation both elasticity and density, linear variation of elasticity with quadratic variation of density. Four different taper profiles are taken into account, namely, uniform, linear, exponential, and parabolic, for thickness variation, while the width of the beam is kept constant