http://etd.ncsi.iisc.ernet.in:80 The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material. Wed, 19 Jun 2013 00:07:57 GMT 2013-06-19T00:07:57Z http://hdl.handle.net/2005/1832 Title: 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. Mon, 03 Dec 2012 18:30:00 GMT http://hdl.handle.net/2005/1832 2012-12-03T18:30:00Z http://hdl.handle.net/2005/2042 Title: A Computational Study Of Ion Crystals In Paul Traps Authors: Kotana, Appala Naidu Abstract: In this thesis we present a computational study of “ion crystals”, the interesting patterns in which ions arrange themselves in ion traps such as Paul and Penning traps. In ion crystals the ions are in equilibrium due to the balance of the repulsive forces between the ions and the overall tendency of the ion trap to pull ions towards the trap centre. We have carried out a detailed investigation of ion crystals in Paul traps by solving their equations of motion numerically. We also propose a model called the spring–mass model to explain the formation of ion crystals. This model is far more efficient than direct numerical simulation for predicting ion crystal structures. Finally, we demonstrate that there is a power law relating distance of an ion from the trap centre in ion crystals to the applied RF voltage amplitude. Mon, 10 Jun 2013 18:30:00 GMT http://hdl.handle.net/2005/2042 2013-06-10T18:30:00Z http://hdl.handle.net/2005/1931 Title: 1-D And 3-D Analysis Of Multi-Port Muffler Configurations With Emphasis On Elliptical Cylindrical Chamber  Authors: Mimani, Akhilesh Abstract: The flow-reversal elliptical cylindrical end chamber mufflers of short length are used often in the modern day automotive exhaust systems. The conventional 1-D axial plane wave theory is not able to predict their acoustical attenuation performance in view of the fact that the chamber length is not enough for the evanescent 3-D modes generated at the junctions to decay sufficiently for frequencies below the cut-off frequency. Also, due to the large area expansion ratio at the inlet, the first few higher order modes get cut on even in the low frequency regime. This necessitates a 3-D FEM or 3-D BEM analysis, which is cumbersome and time consuming. Therefore, an ingenious 1-D transverse plane wave theory is developed by considering plane wave propagation along the major-axis of the elliptical section, whereby a 2-port axially short elliptical and circular chamber muffler is characterized by means of the transfer matrix [T] or impedance matrix [Z]. Two different approaches are followed: (1) a numerical scheme such as the Matrizant approach, and (2) an analytical approach based upon the Frobenius series solution of the Webster’s equation governing the transverse plane wave propagation. The convective effects of mean flow are neglected; however the dissipative effects at the ports are taken into account. The TL predicted by this 1-D transverse plane wave analysis is compared with that obtained by means of the 3-D analytical approach and numerical (FEM/BEM) methods. An excellent agreement is observed between this simplified 1-D approach and the 3-D approaches at least up to the cut-on frequency of the (1, 1) even mode in the case of elliptical cylindrical chambers, or the (1, 0) mode in the case of circular cylindrical chambers, thereby validating this 1-D transverse plane wave theory. The acoustical attenuation characteristics of such short chamber mufflers for various configurations are discussed, qualitatively as well as quantitatively. Moreover, the Frobenius series solution enables one to obtain non-dimensional frequencies for determining the resonance peak and trough in the TL graph. The use of this theory is, however, limited to configurations in which both the ports are located along the major axis in the case of elliptical chambers and along the same diameter for circular chambers. The method of cascading the [T] matrices of the 2-port elements cannot be used to analyze a network arrangement of 2-port elements owing to the non-unique direction of wave propagation in such a network of acoustic elements. Although, a few papers are found in the literature reporting the analysis of a network of 2-port acoustic elements, no work is seen on the analysis of a network of multi-port elements having more than two external ports. Therefore, a generalized algorithm is proposed for analyzing a general network arrangement of linear multi-port acoustic elements having N inlet ports and M outlet ports. Each of these multi-port elements constituting the network may be interconnected to each other in an arbitrary manner. By appropriate book-keeping of the equations obtained by the [Z] matrix characterizing each of the multi-port and 2-port elements along with the junction laws (which imply the equality of acoustic pressure and conservativeness of mass velocity at a multi-port junction), an overall connectivity matrix is obtained, whereupon a global [Z] matrix is obtained which characterizes the entire network. Generalized expressions are derived for the evaluation of acoustic performance evaluation parameters such as transmission loss (TL) and insertion loss (IL) for a multiple inlet and multiple outlet (MIMO) system. Some of the characteristic properties of a general multi-port element are also studied in this chapter. The 1-D axial and transverse plane wave analysis is used to characterize axially long and short chambers, respectively, in terms of the [Z] matrix. Different network arrangements of multi-port elements are constructed, wherein the TL performance of such MIMO networks obtained on the basis of either the 1-D axial or 1-D transverse plane wave theory are compared with 3-D FEA carried on a commercial software. The versatility of this algorithm is that it can deal with more than two external or terminal ports, i.e., one can have multiple inlets and outlets in a complicated acoustic network. A generalized approach/algorithm is presented to characterize rigid wall reactive multi-port chamber mufflers of different geometries by means of a 3-D analytical formulation based upon the modal expansion and the uniform piston-driven model. The geometries analyzed here are rectangular plenum chambers, circular cylindrical chamber mufflers with and without a pass tube, elliptical cylindrical chamber mufflers, spherical and hemispherical chambers, conical chamber mufflers with and without a co-axial pass tube and sectoral cylindrical chamber mufflers of circular and elliptical cross-section as well as sectoral conical chamber mufflers. Computer codes or subroutines have been developed wherein by choosing appropriate mode functions in the generalized pressure response function, one can characterize a multi-port chamber muffler of any of the aforementioned separable geometrical shapes in terms of the [Z] matrix, subsequent to which the TL performance of these chambers is evaluated in terms of the scattering matrix [S] parameters by making use of the relations between [Z] and [S] matrices derived earlier. Interestingly, the [Z] matrix approach combined with the uniform piston-driven model is indeed ideally suited for the 3-D analytical formulation inasmuch as regardless of the number of ports, one deals with only one area discontinuity at a time, thereby making the analysis convenient for a multi-port muffler configuration with arbitrary location of ports. The TL characteristics of SISO chambers corresponding to each of the aforementioned geometries (especially the elliptical cylindrical chamber) are analyzed in detail with respect to the effect of chamber dimensions (chamber length and transverse dimensions), and relative angular and axial location of ports. Furthermore, the analysis of SIDO (i.e., single inlet and double outlet) chamber mufflers is given special consideration. In particular, we examine (1) the effect of additional outlet port (second outlet port), (2) variation in the relative angular or axial location of the additional or second outlet port (keeping the location of the inlet port and the outlet ports of the original SISO chamber to be constant) and (3) the effect of interchanging the location of the inlet and outlet ports on the TL performance of these mufflers. Thus, design guidelines are developed for the optimal location of the inlet and outlet ports keeping in mind the broadband attenuation characteristics for a single inlet and multiple outlet (SIMO) system. The non-dimensional limits up to which a flow-reversal elliptical (or circular) cylindrical end chamber having an end-inlet and end-outlet configuration is acoustically short (so that the 1-D transverse plane wave theory is applicable) and the limits beyond which it is acoustically long (so that the 1-D axial plane wave theory is applicable) is determined in terms of the ratio or equivalently, in terms of the ratio. Towards this end, two different configurations of the elliptical cylindrical chamber are considered, namely, (1) End-Offset Inlet (located along the major-axis of the ellipse) and End-Centered Outlet (2) End-Offset Inlet and End-Offset Outlet (both the ports located on the major-axis of the ellipse and at equal offset distance from the center). The former configuration is analyzed using 3-D FEA simulations (on SYSNOISE) while the 3-D analytical uniform piston-driven model is used to analyze the latter configuration. The existence of the higher order evanescent modes in the axially long reversal chamber at low frequency (before the cut-on frequency of the (1, 1) even mode or (1, 0) mode) causes a shift in the resonance peak predicted by the 1-D axial plane wave theory and 3-D analytical approach. Thus, the 1-D axial plane wave analysis is corrected by introducing appropriate end correction due to the modified or effective length of the elliptical cylindrical chamber. An empirical formulae has been developed to obtain the average non-dimensional end correction for the aforementioned configurations as functions of the expansion ratio, (i.e., ), minor-axis to major-axis ratio, (i.e., ) and the center-offset distance ratio, (i.e., ). The intermediate limits between which the chamber is neither short nor long (acoustically) has also been obtained. Furthermore, an ingenious method (Quasi 1-D approach) of combining the 1-D transverse plane wave model with the 1-D axial plane wave model using the [Z] matrix is also proposed for the end-offset inlet and end-centered outlet configuration. A 3-D analytical procedure has also been developed which also enables one to determine the end-correction in axially long 2-port flow-reversal end chamber mufflers for different geometries such as rectangular, circular and elliptical cylindrical as well as conical chambers, a priori to the computation of TL. Using this novel analytical technique, we determine the end correction for arbitrary locations on the two end ports on the end face of an axially long flow-reversal end chamber. The applicability of this method is also demonstrated for determination of the end corrections for the 2-port circular cylindrical chamber configuration without and with a pass tube, elliptical cylindrical chambers as well as rectangular and conical chambers. Tue, 19 Feb 2013 18:30:00 GMT http://hdl.handle.net/2005/1931 2013-02-19T18:30:00Z http://hdl.handle.net/2005/2021 Title: Structural Modeling And Analysis Of Insect Scale Flapping Wing Authors: Mukherjee, Sujoy Abstract: Micro Air Vehicles (MAVs) are defined as a class of vehicles with their larger dimension not exceeding 15 cm and weighing 100 gm. The three main approaches for providing lift for such vehicles are through fixed, rotating and flapping wings. The flapping wing MAVs are more efficient in the low Reynolds-number regime than conventional wings and rotors. Natural flapping flyers, such as birds and insects, serve as a natural source of inspiration for the development of MAV. Flapping wing design is one of the major challenges to develop an MAV because it is not only responsible for the lift, but also propulsion and maneuvers. Two important issues are addressed in this thesis: (1) an equivalent beam-type modeling of actual insect wing is proposed based on the experimental data and (2) development of the numerical framework for design and analysis of insect scale smart flapping wing. The experimental data is used for structural modeling of the blowfly Calliphora wing as a stepped cantilever beam with nine spanwise sections of varying mass per unit lengths, flexural rigidity (EI) and torsional rigidity (GJ) values. Natural frequencies, both in bending and torsion, are obtained by solving the homogeneous part of the respective governing differential equations using the finite element method. It is found that natural frequency in bending and torsion are 3.17 and 1.57 times higher than flapping frequency of Calliphora wing, respectively. The results provide guidelines for the biomimetic structural design of insect-scale flapping wings. In addition to the structural modeling of the insect wing, development of the biomimetic mechanisms played a very important role to achieve a deeper insight of the flapping flight. Current biomimetic flapping wing mechanisms are either dynamically scaled or rely on pneumatic and motor-driven flapping actuators. Unfortunately, these mechanisms become bulky and flap at very low frequency. Moreover, mechanisms designed with conventional actuators lead to high weight and system-complexity which makes it difficult to mimic the complex wingbeat kinematics of the natural flyers. The usage of the actuator made of smart materials such as ionic polymer metal composites (IPMCs) and piezoceramics to design flapping wings is a potential alternative. IPMCs are a relatively new type of smart material that belongs to the family of Electroactive Polymers (EAP) which is also known as “artificial muscles”. In this work, structural modeling and aerodynamic analysis of a dragonfly inspired IPMC flapping wing are performed using numerical simulations. An optimization study is performed to obtain improved flapping actuation of the IPMC wing. Later, a comparative study of the performances of three IPMC flapping wings having the same size as the actual wings of three different dragonfly species Aeshna Multicolor, Anax Parthenope Julius and Sympetrum Frequens is conducted. It is found that the IPMC wing generates sufficient lift to support its own weight and carry a small payload. In addition to the IPMC, piezoelectric materials are also considered to design a dragonfly inspired flapping wing because they have several attractive features such as high bandwidth, high output force, compact size and high power density. The wings of birds and insects move through a large angle which may be obtained using piezofan through large deflection. Piezofan which is one of the simple motion amplifying mechanisms couples a piezoelectric unimorph to an attached flexible wing and is competent to produce large deflection especially at resonance. Non-linear dynamic model for the piezoelectrically actuated flapping wing is done using energy method. It is shown that flapping angle variations of the smart flapping wing are similar to the actual dragonfly wing for a specific feasible voltage. Subsequently, a comparative study of the performances of three piezoelectrically actuated flapping wings is performed. Numerical results show that the flapping wing based on geometry of dragonfly Sympetrum Frequens wing is suitable for low speed flight and it represents a potential candidate for use in insect scale micro air vehicles. In this study, single crystal piezoceramic is also considered for the flapping wing design because they are the potential new generation materials and have attracted considerable attention due to superior electromechanical properties. It is found that the use of single crystal piezoceramic can lead to considerable amount of wing weight reduction and increase of aerodynamic forces compared to conventional piezoelectric materials such as PZT-5H. It can also be noted that natural fliers flap their wings in a vertical plane with a change in the pitch of the wings during a flapping cycle. In order to capture this particular feature of the wingbeat kinematics, coupled flapping-twisting non-linear dynamic modeling of piezoelectrically actuated flapping wing is done using energy method. Excitation by the piezoelectric harmonic force generates only the flap bending motion, which in turn, induces the elastic twist motion due to interaction between flexural and torsional vibrations modes. It is found that the value of average lift reaches to its maximum when the smart flapping wing is excited at a frequency closer to the natural frequency in torsion. Moreover, consideration of the elastic twisting of flapping wing leads to an increase in the lift force. Mon, 03 Jun 2013 18:30:00 GMT http://hdl.handle.net/2005/2021 2013-06-03T18:30:00Z