etd@IISc Collection:http://hdl.handle.net/2005/272014-10-20T23:58:29Z2014-10-20T23:58:29ZClosed-form Solutions For Rotating And Non-rotating Beams : An Inverse Problem ApproachSarkar, Korakhttp://hdl.handle.net/2005/18322012-12-04T05:59:07Z2012-12-03T18:30:00ZTitle: Closed-form Solutions For Rotating And Non-rotating Beams : An Inverse Problem Approach
Authors: Sarkar, Korak
Abstract: Rotating Euler-Bernoulli beams and non-homogeneous Timoshenko beams are widely used to model important engineering structures. Hence the vibration analyses of these beams are an important problem from a structural dynamics point of view. The governing differential equations of both these type of beams do not yield any simple closed form solutions, hence we look for the inverse problem approach in determining the beam property variations given certain solutions.
Firstly, we look for a rotating beam, with pinned-free boundary conditions, whose eigenpair (frequency and mode-shape) is same as that of a uniform non-rotating beam for a particular mode. It is seen that for any given mode, there exists a flexural stiffness function (FSF) for which the ith mode eigenpair of a rotating beam with uniform mass distribution, is identical to that of a corresponding non-rotating beam with same length and mass distribution. Inserting these derived FSF's in a finite element code for a rotating pinned-free beam, the frequencies and mode shapes of a non-rotating pinned-free beam are obtained. For the first mode, a physically realistic equivalent rotating beam is possible, but for higher modes, the FSF has internal singularities. Strategies for addressing these singularities in the FSF for finite element analysis are provided. The proposed functions can be used as test functions for rotating beam codes and also for targeted destiffening of rotating beams.
Secondly, we study the free vibration of rotating Euler-Bernoulli beams, under cantilever boundary condition. For certain polynomial variations of the mass per unit length and the flexural stiffness, there exists a fundamental closed form solution to the fourth order governing differential equation. It is found that there are an infinite number of rotating beams, with various mass per unit length variations and flexural stiffness distributions, which share the same fundamental frequency and mode shape. The derived flexural stiffness polynomial functions are used as test functions for rotating beam numerical codes. They are also used to design rotating cantilever beams which may be required to vibrate with a particular frequency.
Thirdly, we study the free vibration of non-homogeneous Timoshenko beams, under fixed-fixed and fixed-hinged boundary conditions. For certain polynomial variations of the material mass density, elastic modulus and shear modulus, there exists a fundamental closed form solution to the coupled second order governing differential equations. It is found that there are an infinite number of non-homogeneous Timoshenko beams, with various material mass density, elastic modulus and shear modulus distributions, which share the same fundamental frequency and mode shape. They can be used to design non-homogeneous Timoshenko beams which may be required for certain engineering applications.2012-12-03T18:30:00ZParametric Analysis Of A Free Piston Stirling Engine For Spacecraft Power Applications With A Radioisotope Heat SourceBhaskaran, Ramprasadhttp://hdl.handle.net/2005/23392014-07-11T05:11:55Z2014-07-10T18:30:00ZTitle: Parametric Analysis Of A Free Piston Stirling Engine For Spacecraft Power Applications With A Radioisotope Heat Source
Authors: Bhaskaran, Ramprasad
Abstract: Stirling engines are promising candidates for applications where air breathing engines cannot be used. Self contained engines capable of operating independently of the environment are required to convert thermal energy into electric power, or to perform other necessary functions. These are ideally suited for power generation onboard spacecrafts with radioisotope heat source. These engines can power interplanetary missions to Mars and beyond.
The problem of parametric analysis, sensitivity and numerical optimization of Stirling cycle engine is discussed and applied to a specific example of a 2kWe free piston Stirling engine. Stirling cycle simulation programs are generated with emphasis and adaptations peculiar to free piston design for space use. Design algorithms are generated in MatLab and optimization toolbox is used for the parametric analysis adopted in this thesis.
A free piston beta Stirling engine with a linear alternator configuration has been studied for the interdependency and performance effects of various important operational parameters. The analysis has been carried out in order to optimize the primary parameters, weight vis a vis envelope (length and diameter) and stroke of the engine, to make it suitable for space use. The major cycle parameters considered are operating pressure, linear speed, dead space ratio and swept volume ratio, classified as secondary parameters. The whole analysis has been carried out at a cycle temperature ratio of 0.4 for a heat source temperature of 873 K, typical of a radioisotope heat source.
The optimization is carried out for the defined design requirements viz. envelope of 50 × 50 cm , stroke of less than 10 cm, and heat source temperature of 873 K. The process of parametric optimization of the primary parameters viz engine envelope and stroke are carried out with respect to the secondary parameters. Iterations are carried out on the design programs in MatLab. The results indicate that the three primary parameters have a different set each, of the secondary parameter values when optimized to the design requirement.
The fmincon solver of MatLab in the optimization tool box is selected in order to validate the optimization results. The solver is used to find a minimum of a constrained nonlinear multivariable function defining the primary parameters. The results obtained concur with the optimization results generated by the design algorithm. Further, the interdependency amongst the primary and secondary parameters is studied by generating MatLab plots for all possible combinations among the various parameters.
The effect of variations in the pressure and linear speed on the system envelope and stroke are more pronounced at lower range values of the pressure and speed and the variations of the primary parameter values are constant at higher ranges. The effect of dead space ratio and swept volume ratio (>1.0) is not pronounced.
The requirements in the environment of space place a number of constraints upon a Stirling engine/alternator design that are not present in terrestrial applications. High specific power is achieved by designing the engine for higher pressure and frequency operation than a terrestrial Stirling engine, and by using light weight materials where appropriate. Cylinder is the heart of the engine and it forms a major proportion of the total system mass. Mass and heat loss estimates and analysis have been carried out on the cylinder for various materials of construction. Based on the analysis feasibility exists for a Cu-Ni combination. The system would have a mass of 7kg with a specific power estimate of 0.28kW/kg and a conduction heat loss to mass ratio of 159W/kg.
The system obtained by numerical analysis is modeled in system simulation software SIMULATIONX. The simulation of the system is studied and a sensitivity analysis performed in order to assess the parametric interdependency of the whole free piston Stirling engine system. The system sensitivity to piston and displacer mass is studied using the simulation model.
Sensitivity results indicate that there is a range of mass values within which the system is operational, mass values outside the range makes the system non-functional. Also the range is a function of various parameters and detailed analysis is required in this direction in order to further optimize all the functional parameters. Engineering approximation is carried out using the curve fitting toolbox in MatLab to generate design equations in order to provide preliminary design data for the designer, further a scaling study is carried out at various power levels in order to assess the sensitivity of system geometry at various power levels.2014-07-10T18:30:00ZWave Propagation In Hyperelastic WaveguidesRamabathiran, Amuthan Arunkumarhttp://hdl.handle.net/2005/23272014-06-20T10:05:37Z2014-06-19T18:30:00ZTitle: Wave Propagation In Hyperelastic Waveguides
Authors: Ramabathiran, Amuthan Arunkumar
Abstract: The analysis of wave propagation in hyperelastic waveguides has significant applications in various branches of engineering like Non-Destructive Testing and Evaluation, impact analysis, material characterization and damage detection. Linear elastic models are typically used for wave analysis since they are sufficient for many applications. However, certain solids exhibit inherent nonlinear material properties that cannot be adequately described with linear models. In the presence of large deformations, geometric nonlinearity also needs to be incorporated in the analysis. These two forms of nonlinearity can have significant consequences on the propagation of stress waves in solids. A detailed analysis of nonlinear wave propagation in solids is thus necessary for a proper understanding of these phenomena.
The current research focuses on the development of novel algorithms for nonlinear finite element analysis of stress wave propagation in hyperelastic waveguides. A full three-dimensional(3D) finite element analysis of stress wave propagation in waveguides is both computationally difficult and expensive, especially in the presence of nonlinearities. By definition, waveguides are solids with special geometric features that channel the propagation of stress waves along certain preferred directions. This suggests the use of kinematic waveguide models that take advantage of the special geometric features of the waveguide. The primary advantage of using waveguide models is the reduction of the problem dimension and hence the associated computational cost. Elementary waveguide models like the Euler-Bernoulli beam model, Kirchoﬀ plate model etc., which are developed primarily within the context of linear elasticity, need to be modified appropriately in the presence of material/geometric nonlinearities and/or loads with high frequency content. This modification, besides being non-trivial, may be inadequate for studying nonlinear wave propagation and higher order waveguide models need to be developed. However, higher order models are difficult to formulate and typically have complex governing equations for the kinematic modes. This reflects in the relatively scarce research on the development of higher order waveguide models for studying nonlinear wave propagation. The formulation is difficult primarily because of the complexity of both the governing equations and their linearization, which is required as part of a nonlinear finite element analysis. One of the primary contributions of this thesis is the development and implementation of a general, flexible and efficient framework for automating the finite element analysis of higher order kinematic models for nonlinear waveguides. A hierarchic set of higher order waveguide models that are compatible with this formulation are proposed for this purpose. This hierarchic series of waveguide models are similar in form to the kinematic assumptions associated with standard waveguide models, but are different in the sense that no conditions related to the stress distribution specific to a waveguide are imposed since that is automatically handled by the proposed algorithm. The automation of the finite element analysis is accomplished with a dexterous combination of a nodal degrees-of-freedom based assembly algorithm, automatic differentiation and a novel procedure for numerically computing the finite element matrices directly from a given waveguide model. The algorithm, however, is quite general and is also developed for studying nonlinear plane stress configurations and inhomogeneous structures that require a coupling of continuum and waveguide elements. Significant features of the algorithm are the automatic numerical derivation of the finite element matrices for both linear and nonlinear problems, especially in the context of nonlinear plane stress and higher order waveguide models, without requiring an explicit derivation of their algebraic forms, automatic assembly of finite element matrices and the automatic handling of natural boundary conditions. Full geometric nonlinearity and the hyperelastic form of material nonlinearity are considered in this thesis. The procedures developed here are however quite general and can be extended for other types of material nonlinearities. Throughout this thesis, It is assumed that the solids under investigation are homogeneous and isotropic.
The subject matter of the research is developed in four stages: First, a comparison of different finite element discretization schemes is carried out using a simple rod model to choose the most efficient computational scheme to study nonlinear wave propagation. As part of this, the frequency domain Fourier spectral finite element method is extended for a special class of weakly nonlinear problems. Based on this comparative study, the Legendre spectral element method is identified as the most efficient computational tool. The efficiency of the Legendre spectral element is also illustrated in the context of a nonlinear Timoshenko beam model. Since the spectral element method is a special case of the standard nonlinear finite element Method, differing primarily in the choice of the element basis functions and quadrature rules, the automation of the standard nonlinear finite element method is undertaken next. The automatic finite element formulation and assembly algorithm that constitutes the most significant contribution of this thesis is developed as an efficient numerical alternative to study the physics of wave propagation in nonlinear higher order structural models. The development of this algorithm and its extension to a general automatic framework for studying a large class of problems in nonlinear solid mechanics forms the second part of this research. Of special importance are the automatic handling of nonlinear plane stress configurations, hierarchic higher order waveguide models and the automatic coupling of continuum and higher order structural elements using specially designed transition elements that enable an efficient means to study waveguides with local inhomogeneities. In the third stage, the automatic algorithm is used to study wave propagation in hyperelastic waveguides using a few higher order 1D kinematic models. Two variants of a particular hyperelastic constitutive law – the6-constantMurnaghanmodel(for rock like solids) and the 9-constant Murnaghan model(for metallic solids) –are chosen for modeling the material nonlinearity in the analysis. Finally, the algorithm is extended to study energy-momentum conserving time integrators that are derived within a Hamiltonian framework, thus illustrating the extensibility of the algorithm for more complex finite element formulations.
In short, the current research deals primarily with the identification and automation of finite element schemes that are most suited for studying wave propagation in hyper-elastic waveguides. Of special mention is the development of a novel unified computational framework that automates the finite element analysis of a large class of problems involving nonlinear plane stress/plane strain, higher order waveguide models and coupling of both continuum and waveguide elements. The thesis, which comprises of 10 chapters, provides a detailed account of various aspects of hyperelastic wave propagation, primarily for 1D waveguides.2014-06-19T18:30:00ZModelling And Analysis Of Fish Inspired Ionic Polymer Metal Composite Flapping FinsKarthigan, Ghttp://hdl.handle.net/2005/22822014-03-03T06:36:28Z2014-03-02T18:30:00ZTitle: Modelling And Analysis Of Fish Inspired Ionic Polymer Metal Composite Flapping Fins
Authors: Karthigan, G
Abstract: Ionic polymer metal composites (IPMC) are a new class of smart materials that have attractive characteristics such as muscle like softness, low voltage and power consumption, and good performance in aqueous environments. Therefore, there is a significant motivation for research on design and development of IPMC based biomimetic propulsion systems for underwater vehicles. In aerospace, underwater vehicles finds application for forensic studies of spaceship wrecks, missile fragments and any airplane accidents in sea and ocean terrains. Such vehicles can also survey moons and planets that house water oceans. Among biomimetic swimming systems, fish inspired swimming has gained interest since fish like swimming provides high maneuverability, high cruising speed, noiseless propulsion and efficient stabilization compared to conventional propulsion systems. In this work, the paired pectoral fin based oscillatory propulsion using IPMC for aquatic propulsor applications is studied. Dynamic characteristics of IPMC fin are analyzed using numerical simulations and optimization is used to improve the fin design. A complex hydrodynamic function is used to describe the behavior of an active IPMC fin actuator in water. The structural model of the IPMC fin is obtained by modifying the classical dynamic equation for a slender beam to account for the electromechanical dynamics of the IPMC beam in water. A quasi-steady blade element model that accounts for unsteady phenomena such as added mass effects, dynamic stall, and the cumulative Wagner effect is used to estimate the hydrodynamic performance of the flapping fin. It is shown that the use of optimization methods can lead to significant improvement in performance of the IPMC fin. Further, three fish species with high performance flapping pectoral fin locomotion are chosen and performance analysis of each fin design is conducted to discover the better configurations for engineering applications. Dynamic characteristics of IPMC actuated flapping fins having the same size as the actual fins of three different fish species, Gomphosus varius, Scarus frenatus and Sthethojulis trilineata, are also analyzed. Finally, a comparative study is performed to analyze the performance of the three different biomimetic IPMC flapping pectoral fins.2014-03-02T18:30:00Z