Browsing by Author "Marathe, Amol"

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Asymmetric Mathieu equations
(RSC, 2006-02) Marathe, Amol
An inverted pendulum with asymmetric elastic restraints (e.g. a one-sided spring), when subjected to harmonic vertical base excitation, on linearizing trigonometric terms, is governed by an asymmetric Mathieu equation. This system is parametrically forced and strongly nonlinear (linearization for small motions is not possible). However, solutions are scaleable: if x(t) is a solution, then so is αx(t) for any real α>0. We numerically study the stability regions in the parameter plane of this system for a fixed degree of asymmetry in the elastic restraints. A Lyapunov-like exponent is defined and numerically evaluated to find these regions of stable and unstable behaviour. These numerics indicate that there are infinitely many possibilities of instabilities in this system that are missing in the usual or symmetric Mathieu equation. We find numerically that there are periodic solutions at the boundaries of stable regions in the parameter plane, analogous to the symmetric Mathieu equation. We compute and plot several of these solution branches, which provide a relatively simpler means of computing the stability transition curves of this system. We prove theoretically that such periodic solutions must exist on all stability boundaries. Our theoretical results apply to the asymmetric Hill's equation, of which the pendulum system is a special case. We demonstrate this with numerical studies of a more general asymmetric Mathieu equation.
Computing Melnikov Curves for Periodically Perturbed Piecewise Smooth Oscillators
(World Scientific, 2015) Marathe, Amol
Curves dividing the parameter plane into regions according to the presence or absence of homoclinic or heteroclinic tangle corresponding to the periodically perturbed saddle of the piecewise smooth oscillator are studied using Melnikov analysis. The analysis is not simplified by choosing the discontinuity plane at a convenient location. Separatrix of the unperturbed system is parametrized exactly in a piecewise manner. Switching times, i.e. parameter values at which the separatrix crosses the discontinuity plane, are obtained. Switching times split the Melnikov integral into various subintegrals which are evaluated either exactly using term-wise integration of the infinite series of the integrand or approximately using a finite-term series approximation of the integrand, the latter being computationally an extensive task. Integral evaluations though approximate, are purely analytical expressions in terms of special functions such as digamma and hypergeometric. Melnikov plots show that the boundary between three regions in the parameter plane differ qualitatively in case of parametric and external excitations, however; adding self-excitation to the external one does not much alter the boundary qualitatively and quantitatively.
Condition Monitoring of Misaligned Rotor System Using Acoustic Sensor by Response Surface Methodology
(ASME, 2022) Jalan, Arun Kumar; Marathe, Amol
Misalignment is among the most common causes of vibrations in rotary machinery. Modern machinery is complicated and installing a sensor might be tricky at times. As a result, noncontact type sensors are critical in such situations. The present study investigates the influence of combinations between speed, load, and fault severity upon system vibration by employing acoustic sensor. Although acoustic sensor is used in angular fault diagnosis, however, this is the first attempt to combine the noncontact type of sensor and response surface methodology (RSM) to study the influence of misalignment upon system vibration and the factors that induce system vibrations in a misaligned rotor system. To investigate the effect of these interactions on system performance, RSM with root-mean-square (RMS) as a response factor is used. Design of experiments is used to prepare experiments, while analysis of variance (ANOVA) is used to analyze the results. Speed has a significant impact on RMS value in both parallel and angular types of misalignments and it severely affects the system's performance. According to the RSM findings, a change in load influences vibration amplitude. With increasing defect severity, the change in RMS value was not particularly significant. The outcome of RSM using acoustic sensor was found well aligned with the conclusion drawn using RSM study with vibrational sensor.
Experimental Investigation Using Response Surface Methodology for Condition Monitoring of Misaligned Rotor System
(ASME, 2021-08) Marathe, Amol; Jalan, Arun Kumar
Misalignment is one of the key reasons for vibrations in most of the rotating system. The present study focuses on interactions among speed, load, and defect severity by investigating their effect on the system vibration. Response surface methodology (RSM) with root-mean-square (RMS) as a response factor is used to understand the influence of such interactions on the system performance. Experiments are planned using design of experiments, and analysis is carried out using analysis of variance (ANOVA). It is observed that speed has a remarkable effect on RMS value in both parallel and angular types of misalignment and affects the system performance. RSM results revealed that a change in load has less impact on vibration amplitude in case of horizontal and vertical directions, but there is a significant variation in RMS value in axial direction for both types of misalignment. A slight increase in the RMS value with an increase in defect severity is observed in the axial direction. These observations will help to understand the misalignment defect and its effect in a better way.
Minimal Modeling for Passive Flow Control via a Poro-elastic Coating
(Springer, 2016-04) Marathe, Amol
Minimal models are obtained for vortex-shedding, both from a smooth aerofoil, and from an aerofoil coated with a porous layer of flow-compliant feather-like actuators. The latter is a passive way to achieve flow control. The minimal-order model for a smooth aerofoil is extracted by analyzing the frequencies present in the flow over this aerofoil, and phenomena such as the presence of super-harmonics of these flow frequencies and existence of limit cycle behaviour for this system. Next, the minimal model for the poro-elastically coated aerofoil is realized by linearly coupling the minimal-order model for vortex-shedding from the smooth aerofoil with an equation for the poro-elastic coating, here modeled as a linear damped oscillator. The various coefficients in both of these models, derived using perturbation techniques, not only lead to solutions from the models that match very well with results from expensive and time-consuming computational models, but also aid in our understanding of the physics of this fluid-structure interaction problem. In particular, the minimal model for a coated aerofoil indicates the presence of distinct regimes that are dependent on the flow and coating characteristics and in this process, provide insight into the selection of optimal coating parameters, to enable flow control at low Reynolds numbers.
Modeling the immune response to Salmonella during typhoid
(OUP, 2021-05) Marathe, Amol; Marathe, Sandhya
Several facets of the host immune response to Salmonella infection have been studied independently at great depths to understand the progress and pathogenesis of Salmonella infection. The circumstances under which a Salmonella-infected individual succumbs to an active disease, evolves as a persister or clears the infection are not understood in detail. We have adopted a system-level approach to develop a continuous-time mechanistic model. We considered key interactions of the immune system state variables with Salmonella in the mesenteric lymph node to determine the final disease outcome deterministically and exclusively temporally. The model accurately predicts the disease outcomes and immune response trajectories operational during typhoid. The results of the simulation confirm the role of anti-inflammatory (M2) macrophages as a site for persistence and relapsing infection. Global sensitivity analysis highlights the importance of both bacterial and host attributes in influencing the disease outcome. It also illustrates the importance of robust phagocytic and anti-microbial potential of M1 macrophages and dendritic cells (DCs) in controlling the disease. Finally, we propose therapeutic strategies for both antibiotic-sensitive and antibiotic-resistant strains (such as IFN-γ therapy, DC transfer and phagocytic potential stimulation). We also suggest prevention strategies such as improving the humoral response and macrophage carrying capacity, which could complement current vaccination schemes for enhanced efficiency
Multiple scales analysis of early and delayed boundary ejection in Paul traps
(Elsevier, 2007-03) Marathe, Amol
We use the method of multiple scales to elucidate dynamics associated with early and delayed ejection of ions in mass selective ejection experiments in Paul traps. We develop a slow flow equation to approximate the solution of a weakly nonlinear Mathieu equation to describe ion dynamics in the neighborhood of the stability boundary of ideal traps (where the Mathieu parameter ). The method of multiple scales enables us to incorporate higher order multipoles, extend computations to higher orders, and generate phase portraits through which we view early and delayed ejection. Our use of the method of multiple scales is atypical in two ways. First, because we look at boundary ejection, the solution to the unperturbed equation involves linearly growing terms, requiring some care in identification and elimination of secular terms. Second, due to analytical difficulties, we make additional harmonic balance approximations within the formal implementation of the method. For positive even multipoles in the ion trapping field, in the stable region of trap operation, the phase portrait obtained from the slow flow consists of three fixed points, two of which are saddles and the third is a center. As the value of an ion approaches , the saddles approach each other, and a point is reached where all nonzero solutions are unbounded, leading to an observation of early ejection. The phase portraits for negative even multipoles and odd multipoles of either sign are qualitatively similar to each other and display bounded solutions even for , resulting in the observation of delayed ejection associated with a more gentle increase in ion motion amplitudes, a mechanism different from the case of the positive even multipoles.
Multiple scales analysis of out-of-plane and in-plane vibrations of a wind turbine blade
(ARXIV, 2020) Marathe, Amol
Steady-state response of an isolated horizontal axis wind turbine blade undergoing out-of-plane and in-plane vibrations are studied considering the two cases separately. Equations of motion for both cases are sought by modeling the blade as cantilevered Euler-Bernoulli beam and applying the Lagrangian formulation. Taking into account the effects of blade rotation on gravitational and aerodynamic forces and allowing the blade to undergo large deformations, various nonlinearities arise in the system resulting in superharmonic resonances. Taking practically relevant numerical values of parameters, we suitably order the parameters for their smallness. We then obtain the frequency responses corresponding to primary and superharmonic resonances by applying the method of multiple scales up to fourth and third orders for out-of-plane and in-plane cases respectively. Comparisons are drawn with the results obtained using the method of harmonic balance.
Natural Response of Non-smooth Oscillators Using Homotopy Analysis Combined with Galerkin Projections
(Springer, 2022-11) Marathe, Amol
Several problems from mechanical engineering, e.g., vibrations of a spring–mass system with unequal restraints, pendulum with impact, a gear-pair with backlash and friction, etc. are modeled using second-order differential equations involving discontinuous mathematical functions such as signum, Heaviside, modulus, etc. Several perturbation-like methods such as parameter expansion, homotopy perturbation, modified Lindstedt–Poincaré, and variational iteration have been applied successfully to get the periodic solution as well as the approximate analytical estimate of the natural frequency. The chief limitation of all the methods mentioned above is the poor approximation with the large value of the perturbation parameter.
Nonlinear Dynamical Systems, Their Stability, and Chaos : Lecture notes from the FLOW-NORDITA Summer School on Advanced Instability Methods for Complex Flows, Stockholm, Sweden, 2013
(Springer, 2022-01) Marathe, Amol
In condition monitoring, accurate fault identification is an essential task for designing a proper maintenance strategy. Misalignment is one of the main faults in rotary machinery, because 70% of the failure occurs due to misalignment. Conventionally, the diagnosis of misalignment is carried out through vibration measurements. Especially, the presence of strong 2x vibration peak is generally accepted. Both angular and parallel misalignment shows peak at 2x, therefore, distinguishing misalignment type by using vibration signals alone is a difficult activity. This paper discusses classification of misalignment i.e., angular and parallel by using a diagnostic medium such as the acoustic emission and the rotor vibration signal. Vibro-acoustic sensors are used to collect data from the misaligned rotor system at two different loading, three different speed and three defect severity conditions. Time domain features are extracted and graded according to their significance using t test (One-way ANOVA) technique. Extracted features are used to train different algorithms. The outcome obtained using support vector machine (SVM) is 100% accurate. Vibro-acoustic sensor data fusion technique is employed to classify various forms of misalignment under different operating conditions. This work also intended to explore using a small amount of training data using different algorithms. The proposed method outperforms fault classification using vibration signal and acoustic signal separately.
Robot vision-based control strategy to suppress residual vibration of a flexible beam for assembly
(Emerald, 2023-04) Rout, Bijay Kumar; Marathe, Amol
Industrial robots are extensively used in the robotic assembly of rigid objects, whereas the assembly of flexible objects using the same robot becomes cumbersome and challenging due to transient disturbance. The transient disturbance causes vibration in the flexible object during robotic manipulation and assembly. This is an important problem as the quick suppression of undesired vibrations reduces the cycle time and increases the efficiency of the assembly process. Thus, this study aims to propose a contactless robot vision-based real-time active vibration suppression approach to handle such a scenario.
Support Vector Machine for Misalignment Fault Classification Under Different Loading Conditions Using Vibro-Acoustic Sensor Data Fusion
(Springer, 2022-01) Jalan, Arun Kumar; Marathe, Amol
In condition monitoring, accurate fault identification is an essential task for designing a proper maintenance strategy. Misalignment is one of the main faults in rotary machinery, because 70% of the failure occurs due to misalignment. Conventionally, the diagnosis of misalignment is carried out through vibration measurements. Especially, the presence of strong 2x vibration peak is generally accepted. Both angular and parallel misalignment shows peak at 2x, therefore, distinguishing misalignment type by using vibration signals alone is a difficult activity. This paper discusses classification of misalignment i.e., angular and parallel by using a diagnostic medium such as the acoustic emission and the rotor vibration signal. Vibro-acoustic sensors are used to collect data from the misaligned rotor system at two different loading, three different speed and three defect severity conditions. Time domain features are extracted and graded according to their significance using t test (One-way ANOVA) technique. Extracted features are used to train different algorithms. The outcome obtained using support vector machine (SVM) is 100% accurate. Vibro-acoustic sensor data fusion technique is employed to classify various forms of misalignment under different operating conditions. This work also intended to explore using a small amount of training data using different algorithms. The proposed method outperforms fault classification using vibration signal and acoustic signal separately.
Unimportance of geometric nonlinearity in analysis of flanged joints with metal-to-metal contact
(Elsevier, 2007-07) Marathe, Amol
Gasketless flanged joints with metal to metal contact offer some advantages over gasketed joints such as lower weight and better fatigue life. Design of such joints is often based on finite element analyses, and complicated by the fact that the area of contact between the flanges changes upon application of loads. Such analyses can be done using commercial software, which can incorporate geometrical nonlinearities as well as contact nonlinearities. Engineering intuition suggests that the role of geometrical nonlinearities might be small for such problems. However, many engineers continue to use the fully nonlinear analyses. Our aim in this paper is simply to put on record that significant savings in time can be obtained by “turning off” geometric nonlinearities in such analyses, with negligible loss of accuracy. To this end, a nonautomated implementation of the basic ideas is first demonstrated for a simple geometry; more automated analyses for a more general geometry follow.
Vision sensor based residual vibration suppression strategy of non-deformable object for robot-assisted assembly operation with gripper flexibility
(Emerald, 2022-06) Rout, Bijay Kumar; Marathe, Amol
Industrial robots are extensively deployed to perform repetitive and simple tasks at high speed to reduce production time and improve productivity. In most cases, a compliant gripper is used for assembly tasks such as peg-in-hole assembly. A compliant mechanism in the gripper introduces flexibility that may cause oscillation in the grasped object. Such a flexible gripper–object system can be considered as an under-actuated object held by the gripper and the oscillations can be attributed to transient disturbance of the robot itself. The commercially available robots do not have a control mechanism to reduce such induced vibration. Thus, this paper aims to propose a contactless vision-based approach for vibration suppression which uses a predictive vibrational amplitude error-based second-stage controller.
Wave attenuation in nonlinear periodic structures using harmonic balance and multiple scales
(Elsevier, 2006-02) Marathe, Amol
We study the attenuation, caused by weak damping, of harmonic waves through a discrete, periodic structure with frequency nominally within the Propagation Zone (i.e., propagation occurs in the absence of the damping). The period of the structure consists of a linear stiffness and a weak linear/nonlinear damping. Adapting the transfer matrix method and using harmonic balance for the nonlinear terms, a four-dimensional linear/nonlinear map governing the dynamics is obtained. We analyze this map by applying the method of multiple scales upto first order. The resulting slow evolution equations give the amplitude decay rate in the structure. The approximations are validated by comparing with other analytical solutions for the linear case and full numerics for the nonlinear case. Good agreement is obtained. The method of analysis presented here can be extended to more complex structures.