Chandramouli Padmanabhan
IIT Madras, Mechanical Engineering, Faculty Member
This paper presents numerical simulation studies on the vibration and acoustic response-characteristics of an isotropic cylindrical shell under a thermal environment using commercial softwares ANSYS and SYSNOISE. First, the critical... more
This paper presents numerical simulation studies on the vibration and acoustic response-characteristics of an isotropic cylindrical shell under a thermal environment using commercial softwares ANSYS and SYSNOISE. First, the critical buckling temperature is obtained, followed by modal and harmonic response analyses considering pre-stress due to the thermal field in the cylindrical shell, with the critical buckling temperature as a parameter. The vibration response predicted is then used to compute the sound radiation. It is found that there is a significant change in the vibration mode shapes and ring frequency towards the lowest natural frequency with an increase in temperature. There is a sudden increase in overall sound power level near the critical buckling temperature and significant changes in mode shapes with temperature does not affect the overall sound power level.
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In recent years graphical dynamic system simulation has become very important in the design and development stage, as new strategies can be examined without expensive measurements. This paper describes the development of a real time... more
In recent years graphical dynamic system simulation has become very important in the design and development stage, as new strategies can be examined without expensive measurements. This paper describes the development of a real time simulation model for ...
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Analysis of brushless D.C. motor (BDCM) torque pulsations is an essential step in the diagnosis and control of vibration and noise generated by many electro-mechanical devices. The broad band spectral content of the torque pulsations, as... more
Analysis of brushless D.C. motor (BDCM) torque pulsations is an essential step in the diagnosis and control of vibration and noise generated by many electro-mechanical devices. The broad band spectral content of the torque pulsations, as predicted by a mathematical model which accounts for various complex effects, can often be obtained only by numerical integration which is time consuming while permitting little understanding of the dynamic interactions. Prior analytical approaches, such as the Fourier series technique or the d-q axis theory, are limited by the simplifying assumptions needed to compute the torque spectrum. This paper develops a new semi-analytical formulation for the analysis of nonlinear, time-varying BDCM’s which involve both spatial and temporal domains. A modified multi-term harmonic balance method, based on a transformation of the dual-domain problem to a spatial domain formulation, is developed here specifically to compute the magnitude of several harmonics of the pulsating torque. The interacting effects of key parameters, like dynamic eccentricity, magnetic saturation and open stator slots, on the time-varying inductances and rotor flux density distribution are included explicitly in the formulation. The predicted spectra compare very well with those obtained by direct time domain numerical integration. Yet, the proposed method is computationally efficient especially when the model dimension is reduced. It also provides better insight into the high frequency dynamics of the sample case.
Research Interests: Engineering, Harmonic Analysis, Computer Science, Modeling, Density, and 15 moreFourier Analysis, Dynamic Analysis, Nonlinear Systems, Space Time, Dynamic systems, Nonlinear system, Analytical Methods, Dynamic Systems, Harmonics, Dimensions, Time Domain, Fourier Series, Harmonic Balance, Frequency Domain, and Stator
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Achieving broadband noise attenuation at low frequencies is still a significant challenge. Helmholtz resonators offer good low-frequency noise attenuation but are effective only over a narrow band; the cavity volume required at these... more
Achieving broadband noise attenuation at low frequencies is still a significant challenge. Helmholtz resonators offer good low-frequency noise attenuation but are effective only over a narrow band; the cavity volume required at these frequencies is also larger. This article proposes a new broadband acoustic metamaterial (AMM) absorber, which uses polyurethane (PU) foam embedded with small-size resonators tuned to different frequencies. The AMM design is achieved in three phases: (1) develop a transfer-matrix-based one-dimensionalmodel for a resonator with intruded neck; (2) use this model to develop a novel band broadeningmethod, to select appropriate resonators tuned to different frequencies; and (3) construct a unit cell metamaterial embedded with an array of resonators into PU foam. A small-size resonator tuned to 415 Hz is modified, by varying the intrusion lengths of the neck, to achieve natural frequencies ranging from 210 to 415 Hz. Using the band broadening methodology, 1 unit cell metamaterial is constructed; its effectiveness is demonstrated by testing in an acoustic impedance tube. The broadband attenuation characteristics of the constructed unit cell metamaterial are shown to match well with the predicted results. To demonstrate further the effectiveness of the idea, a metamaterial is formed using 4 periodic unit cells and is tested in a twin room reverberation chamber. The transmission loss is shown to improve significantly, at low frequencies, due to the inclusion of the resonators.
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A tracked vehicle employs a special transmission to generate a speed difference between the inner and outer tracks for steering. In this paper, the dynamic model of one of the most widely used steering transmissions called double... more
A tracked vehicle employs a special transmission to generate a speed difference between the inner and outer tracks for steering. In this paper, the dynamic model of one of the most widely used steering transmissions called double differential steering has been derived and integrated with a multi-body tracked vehicle model. A simplified multi-body model for tracks has been proposed to reduce the computational and numerical difficulties arising from a detailed three-dimensional multi-body model. The accuracy of the proposed model is demonstrated by extensive comparison with a detailed multi-body model developed using the Tracked Vehicle module of the commercial software ADAMS. Simulations are carried out using the integrated tracked vehicle model to demonstrate the effects of changes in three-dimensional vehicle dynamic performance with design changes in powertrain systems.
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An efficient numerical method for examining the stability of linear time varying systems modeled by finite element (FE) methods is presented in this paper. Parametric instability of pipes conveying pulsating fluid flow is studied using... more
An efficient numerical method for examining the stability of linear time varying systems modeled by finite element (FE) methods is presented in this paper. Parametric instability of pipes conveying pulsating fluid flow is studied using multivariable FloquetLyapunov theory. In order to ...
Research Interests: Engineering, Mathematics, Finite element method, Finite Element, Numerical Method, and 13 moreComputation, Instability, Lyapunov Stability Theory, Mathematical Sciences, Model Reduction, Fluid flow, Parametric excitation, Parametric Statistics, Finite Elements Analysis, Degree of Freedom, Lyapunov theory, Linear time-varying system, and Floquet theory
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In this talk, a semi-analytical framework, based on the scaled boundary finite element method (SBFEM), is proposed, to study interior acoustic problems in the mid-frequency range. The SBFEM shares the advantages of both the finite element... more
In this talk, a semi-analytical framework, based on the scaled boundary finite element method (SBFEM), is proposed, to study interior acoustic problems in the mid-frequency range. The SBFEM shares the advantages of both the finite element method (FEM) and the boundary element method (BEM). Like the FEM, it does not require the fundamental solution (Green's function) and similar to the BEM only the boundary is discretized, thus reducing the spatial dimensionality by one. The solution within the domain is represented analytically, while on the boundary, it is represented by finite elements. Different choices of boundary representations, such as Lagrange and NURBS description will be discussed. The proposed framework is validated using closed-form solutions and direct comparisons are made with conventional FEM based on Lagrangian description; this will be demonstrated using two two-dimensional cavities available from the literature. The improved accuracy and reduced computational time can be attributed to the semi-analytical formulation combined with the boundary discretization.
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In this paper a hybrid active noise control of a cavity with poro-elastic material has been investigated. It has been found that the noise reduction achieved with active noise control in the cavity without poro-elastic material is not... more
In this paper a hybrid active noise control of a cavity with poro-elastic material has been investigated. It has been found that the noise reduction achieved with active noise control in the cavity without poro-elastic material is not significantly altered with the presence of poro-elastic materials. This is shown to be independent of the porous material and its thickness and is true both at lower and mid-frequency ranges. Further, it is seen that macro perforations do not alter the sound absorption performance of the poro-elastic material in the presence of active noise control. The results clearly indicate that one can choose a smaller thickness of the porous material when active noise control is used in a cavity for noise suppression.
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ABSTRACT Earlier works on the smooth and discontinuous (SD) oscillator concentrated mainly on the time domain analysis using analytical, semi-analytical and numerical integration methods. In this paper, the frequency domain analysis of... more
ABSTRACT Earlier works on the smooth and discontinuous (SD) oscillator concentrated mainly on the time domain analysis using analytical, semi-analytical and numerical integration methods. In this paper, the frequency domain analysis of the SD oscillator subjected to harmonic excitation which is as important and giving further insight into the dynamics is carried out. Multi Harmonic Balance Method (MHBM) in combination with arc length continuation is used to obtain the periodic solutions and their branches in the frequency domain for different values of the smoothing parameter α and exciting frequency ω . Stability of the periodic motions and bifurcation behavior are analyzed using Floquet theory. For the discontinuous case, the oscillator is treated as a Filippov system and an event driven numerical integration method is used to obtain the response. For α>1α>1, the dynamics of the SD oscillator is similar to that of the hardening Duffing oscillator, for α=1α=1, it is like that of the Ueda oscillator and for 0<α<10<α<1 it is like that of the Duffing oscillator with double well potential. The SD oscillator exhibits period 1 solutions, higher order periodic solutions, chaotic solutions through symmetry breaking bifurcations, period doubling and boundary crises in different parameter ranges. Chaos is observed over a larger frequency range interspersed by narrow windows of higher order periodic solutions.
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I. INTRODUCTION ONLINER system identification problems have given birth to a variety of techniques. The use of chaotic response for identification is one of them. Chaotic response of dynamical systems has fascinated researchers for many... more
I. INTRODUCTION ONLINER system identification problems have given birth to a variety of techniques. The use of chaotic response for identification is one of them. Chaotic response of dynamical systems has fascinated researchers for many years. However the use of ...
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Research Interests: Engineering, Geology, Mechanics, Vibration, Turbine, and 3 moreNonlinear system, Damper, and Harmonic Balance
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The effectiveness of macro perforated porous materials to control noise levels inside a cavity is investigated. This is done using a finite element formulation based on the BiotAllard theory that accounts for sound propagation in a... more
The effectiveness of macro perforated porous materials to control noise levels inside a cavity is investigated. This is done using a finite element formulation based on the BiotAllard theory that accounts for sound propagation in a poro-elastic medium. Earlier investigations have ...
Research Interests: Engineering, Mechanical Engineering, Acoustics, Materials Science, Architecture, and 14 moreFinite element method, Finite Element, Low Frequency, Classical Physics, Noise reduction, Macro, Finite Element Model, Perforation, Noise Control, Porous Material, Porous Medium, Applied Acoustics, Acoustic Analysis, and Higher order
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This paper proposes a new procedure for formulating the gear rattle type problem analytically before attempting a numerical solution. This step is necessary due to the nature of the mathematical formulation with vibro-impacts, which is... more
This paper proposes a new procedure for formulating the gear rattle type problem analytically before attempting a numerical solution. This step is necessary due to the nature of the mathematical formulation with vibro-impacts, which is non-analytical and hence causes numerical “stiffness”. The procedure is essentially an “intelligent” pre-processing stage and is based on our vast experience in simulating such systems. Important concepts such as order reduction, gear contact ratio, appropriate choice of non-dimensionalization parameters are illustrated through several examples.
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This paper proposes a new procedure for formulating the gear rattle type problem analytically before attempting a numerical solution. This step is necessary due to the nature of the mathematical formulation with vibro-impacts, which is... more
This paper proposes a new procedure for formulating the gear rattle type problem analytically before attempting a numerical solution. This step is necessary due to the nature of the mathematical formulation with vibro-impacts, which is nonanalytical and hence ...
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Although non-linear systems subject to combined parametric and external excitations have been examined in some depth, very few of these investigations have addressed the influence of a mean (time-invariant) load on the system response. In... more
Although non-linear systems subject to combined parametric and external excitations have been examined in some depth, very few of these investigations have addressed the influence of a mean (time-invariant) load on the system response. In particular, the importance of the mean load effect has been highlighted in the study of whirling asymmetric shafts, where significant changes in system response and stability occur under the influence of gravity. The present paper intends to characterize the specific effect of mean load on the dynamic behavior of a single degree-of-freedom Hill’s oscillator with a clearance type non-linearity while also being subjected to a periodic base displacement excitation. The parametric continuation technique and method of harmonic balance are used for this purpose. Issues discussed include the coupling between the mean load and the dynamic response amplitude, interaction between the parametric excitation effect and the clearance non-linearity and comparison between time-invariant and time-varying systems.
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The focus of the current study is on the dynamics of rubbing between the rotor and stator parts in a rotating machine. Rub is a malfunction associated with the physical contact of rotating and stationary parts, which are otherwise not in... more
The focus of the current study is on the dynamics of rubbing between the rotor and stator parts in a rotating machine. Rub is a malfunction associated with the physical contact of rotating and stationary parts, which are otherwise not in contact. Because of the nonlinear nature of the problem the simulation time is significant even for small size systems. The rubbing is localized in space, either at the seal locations or at the interface between the rotor blade and stator. Since the nonlinearity is localized, reduced models can be developed for efficient computation. The objective of the present study is to develop a computationally efficient methodology for analyzing the rotor stator rub, by applying model reduction techniques using component mode synthesis, solving the reduced problem using harmonic balance method and time variational method. A hypersphere-based continuation algorithm is used for tracing the unstable branches and a backward differentiation formula based predictor is used for the Newton–Raphson update. The numerical results are validated by performing experiments.
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Dry friction dampers are passive devices used to reduce the resonant vibration amplitudes in turbine bladed systems. In shrouded turbine blade systems, in addition to the stick- slip motion induced by dry friction during the contact state... more
Dry friction dampers are passive devices used to reduce the resonant vibration amplitudes in turbine bladed systems. In shrouded turbine blade systems, in addition to the stick- slip motion induced by dry friction during the contact state in the tangential direction, the interface also undergoes intermittent separation in the normal direction. The problem can thus be treated as a combination of impact and friction. In this work, the dynamics of dry friction damped oscillators which are representative models of dry friction damped bladed system is investigated. A one dimensional contact model which is capable of modeling the interface under constant and variable normal load is used. The steady state periodic solutions are obtained by multi - harmonic balance method (MHBM). Frequency response plots are generated for different values of normal load using the arc length continuation procedure. The MHBM solutions are validated using numerical integration. A single degree of freedom (dof)...
Research Interests: Engineering, Geology, Mechanics, Vibration, Turbine, and 3 moreNonlinear system, Damper, and Harmonic Balance
A method is presented to determine the forced responses of piezoelectric cylinders using weighted sums of only certain exact solutions to the equations of motion and the Gauss electrostatic conditions. One infinite set of solutions is... more
A method is presented to determine the forced responses of piezoelectric cylinders using weighted sums of only certain exact solutions to the equations of motion and the Gauss electrostatic conditions. One infinite set of solutions is chosen such that each field variable is expressed in terms of Bessel functions that form a complete set in the radial direction. Another infinite set of solutions is chosen such that each field variable is expressed in terms of trigonometric functions that form a complete set in the axial direction. Another solution is used to account for the electric field that can exist even when there is no vibration. The weights are determined by using the orthogonal properties of the functions and are used to satisfy specified, arbitrary, axisymmetric boundary conditions on all the surfaces. Special cases including simultaneous mechanical and electrical excitation of cylinders are presented. All numerical results are in excellent agreement with those obtained using the finite element software ATILA. For example, the five lowest frequencies at which the conductance and susceptance of a stress-free cylinder, of length 10 mm and radius 5 mm, reach a local maximum or minimum differ by less than 0.01% from those computed using ATILA.
Research Interests: Mathematics, Physics, Finite Element, Medicine, Multidisciplinary, and 15 moreFinite Element Analysis, Mathematical Analysis, Piezoelectric material, Equation of Motion, Boolean Satisfiability, Cylinder, Boundary Condition, Boundary Value Problem, Electric Field, Axial Symmetry, Acoustic Waves, Exact solution methods, The The, Trigonometric Functions, and Cylindrical Coordinate System
... denoted by and , respectively, ie,(14a,14b) and(14c,14d). The boundary condition on T zz in Eq. (14a) is satisfied by using the orthogonal property of J 0 (k rn a). Substituting Eq. (14a) in Eq. (12), multiplying both sides by rJ 0 (k... more
... denoted by and , respectively, ie,(14a,14b) and(14c,14d). The boundary condition on T zz in Eq. (14a) is satisfied by using the orthogonal property of J 0 (k rn a). Substituting Eq. (14a) in Eq. (12), multiplying both sides by rJ 0 (k rn.