Sangram Redkar - Academia.edu (original) (raw)

Papers by Sangram Redkar

Research paper thumbnail of Reducibility of Periodic Quasi-Periodic Systems

International Journal of Modern Nonlinear Theory and Application, 2014

Research paper thumbnail of Failure Analysis and Reliability Study of NAND Flash- Based Solid State Drives

This research focuses on conducting failure analysis and reliability study to understand and anal... more This research focuses on conducting failure analysis and reliability study to understand and analyze the root cause of Quality, Endurance component Reliability Demonstration Test (RDT) failures and determine SSD performance capability. It addresses essential challenges in developing techniques that utilize solid-state memory technologies (with emphasis on NAND flash memory) from device, circuit, architecture, and system perspectives. These challenges include not only the performance degradation arising from the physical nature of NAND flash memory, e.g., the inability to modify data in-place read/write performance asymmetry, and slow and constrained erase functionality, but also the reliability drawbacks that limits Solid State Drives (SSDs) performance. In order to understand the nature of failures, a Fault Tree Analysis (FTA) was performed that identified the potential causes of component failures. In the course of this research, significant data gathering and analysis effort was carried out that led to a systematic evaluation of the components under consideration. The approach used here to estimate reliability utilized a sample of drives to reflect the reliability parameters (RBER, AFR, and MRR) over 1 year. It is anticipated that this study can provide a methodology for future reliability studies leading to systematic testing and evaluation procedure for SSD RDT's and critical components.

Research paper thumbnail of Unmanned Ground Vehicle Navigation Using Brain Emotional Learning Based Intelligent Controller (BELBIC)

Research paper thumbnail of Failure Analysis and Reliability Study of NAND Flash-Based Solid State Drives

Indonesian Journal of Electrical Engineering and Computer Science, 2016

Research paper thumbnail of Fuzzy logic based sensor fusion for accurate tracking

Proceedings of the 7th International Conference on Advances in Visual Computing Volume Part Ii, 2011

ABSTRACT Accuracy and tracking update rates play a vital role in determining the quality of Augme... more ABSTRACT Accuracy and tracking update rates play a vital role in determining the quality of Augmented Reality(AR) and Virtual Reality(VR) applications. Applications like soldier training, gaming, simulations & virtual conferencing need a high accuracy tracking with update frequency above 20Hz for an immersible experience of reality. Current research techniques combine more than one sensor like camera, infrared, magnetometers and Inertial Measurement Units (IMU) to achieve this goal. In this paper, we develop and validate a novel algorithm for accurate positioning and tracking using inertial and vision-based sensing techniques. The inertial sensing utilizes accelerometers and gyroscopes to measure rates and accelerations in the body fixed frame and computes orientations and positions via integration. The vision-based sensing uses camera and image processing techniques to compute the position and orientation. The sensor fusion algorithm proposed in this work uses the complementary characteristics of these two independent systems to compute an accurate tracking solution and minimizes the error due to sensor noise, drift and different update rates of camera and IMU. The algorithm is computationally efficient, implemented on a low cost hardware and is capable of an update rate up to 100 Hz. The position and orientation accuracy of the sensor fusion is within 6mm & 1.5°. By using the fuzzy rule sets and adaptive filtering of data, we reduce the computational requirement less than the conventional methods (such as Kalman filtering). We have compared the accuracy of this sensor fusion algorithm with a commercial infrared tracking system. It can be noted that outcome accuracy of this COTS IMU and camera sensor fusion approach is as good as the commercial tracking system at a fraction of the cost.

Research paper thumbnail of Order reduction of nonlinear systems with time periodic coefficients using invariant manifolds

Journal of Sound and Vibration, Jun 1, 2005

The basic problem of order reduction of nonlinear systems with time periodic coefficients is cons... more The basic problem of order reduction of nonlinear systems with time periodic coefficients is considered. First, the equations of motion are transformed using the Lyapunov-Floquet transformation such that the linear parts of new set of equations are time invariant. At this stage, the linear order reduction technique can be applied in a straightforward manner. A nonlinear order reduction methodology is also suggested through a generalization of the invariant manifold technique via ' Time Periodic Center Manifold Theory'. A ' reducibility condition' is derived to provide conditions under which a nonlinear order reduction is possible. Unlike perturbation or averaging type approaches, the parametric excitation term is not assumed to be small. An example consisting of two parametrically excited coupled pendulums is given to show potential applications to real problems. Order reduction possibilities and results for various cases including 'parametric', 'internal', 'true internal' and 'combination' resonances are discussed.

Research paper thumbnail of Order Reduction of Parametrically Excited Nonlinear Systems Subjected to External Periodic Excitations

Volume 4: 7th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B and C, 2009

The basic problem of order reduction of nonlinear systems with time periodic coefficients is cons... more The basic problem of order reduction of nonlinear systems with time periodic coefficients is considered in state space and in direct second order (structural) form. In state space order reduction methods, the equations of motion are expressed as a set of first order equations and transformed using the Lyapunov-Floquet (L-F) transformation such that the linear parts of new set of equations are time invariant. At this stage, four order reduction methodologies, namely linear, nonlinear projection via singular perturbation, post-processing approach and invariant manifold technique, are suggested. The invariant manifold technique yields a unique 'reducibility condition' that provides the conditions under which an accurate nonlinear order reduction is possible. Unlike perturbation or averaging type approaches, the parametric excitation term is not assumed to be small. An alternate approach of deriving reduced order models in direct second order form is also presented. Here the system is converted into an equivalent second order nonlinear system with time invariant linear system matrices and periodically modulated nonlinearities via the L-F and other canonical transformations. Then a master-slave separation of degrees of freedom is used and a nonlinear relation between the slave coordinates and the master coordinates is constructed. This method yields the same 'reducibility conditions' obtained by invariant manifold approach in state space. Some examples are given to show potential applications to real problems using above mentioned methodologies. Order reduction possibilities and results for various cases including 'parametric', 'internal', 'true internal' and 'true combination resonances' are discussed. A generalization of these ideas to periodic-quasiperiodic systems is included and demonstrated by means of an example.

Research paper thumbnail of A Direct Approach to Order Reduction of Nonlinear Systems Subjected to External Periodic Excitations

Journal of Computational and Nonlinear Dynamics, 2008

Research paper thumbnail of Order Reduction of Nonlinear Systems With Periodic-Quasiperiodic Coefficients

Volume 1: 20th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C, 2005

Research paper thumbnail of Analysis and simulation of Wiseman hypocycloid engine

Research paper thumbnail of Order Reduction of Nonlinear Time Periodic Systems Using Invariant Manifolds

Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C, 2003

The basic problem of order reduction of nonlinear systems with time periodic coefficients is cons... more The basic problem of order reduction of nonlinear systems with time periodic coefficients is considered. First, the equations of motion are transformed using the Lyapunov-Floquet transformation such that the linear parts of new set of equations are time invariant. At this stage, the linear order reduction technique can be applied in a straightforward manner. A nonlinear order reduction methodology is also suggested through a generalization of the invariant manifold technique via 'Time Periodic Center Manifold Theory'. A 'reducibility condition' is derived to provide conditions under which a nonlinear order reduction is possible. Unlike perturbation or averaging type approaches, the parametric excitation term is not assumed to be small. An example consisting of two parametrically excited coupled pendulums is given to show potential applications to real problems. Order reduction possibilities and results for various cases including 'parametric', 'internal', 'true internal' and 'combination' resonances are discussed. r

Research paper thumbnail of Some Techniques for Order Reduction of Nonlinear Time Periodic Systems

Design Engineering, Volumes 1 and 2, 2003

This work reports new approaches for order reduction of nonlinear systems with time periodic coef... more This work reports new approaches for order reduction of nonlinear systems with time periodic coefficients. First, the equations of motion are transformed using the Lyapunov-Floquet (LF) transformation, which makes the linear part of new set of equations time invariant. At this point, either linear or nonlinear order reduction methodologies can be applied. The linear order reduction technique is based on classical technique of aggregation and nonlinear technique is based on 'Time periodic invariant manifold theory'. These methods do not assume the parametric excitation term to be small. The nonlinear order reduction technique yields superior results. An example of two degrees of freedom system representing a magnetic bearing is included to show the practical implementation of these methods. The conditions when order reduction is not possible are also discussed.

Research paper thumbnail of Order Reduction of Nonlinear Systems Subjected to an External Periodic Excitation

Design Engineering, Parts A and B, 2005

Research paper thumbnail of Guided Navigation Control of an Unmanned Ground Vehicle using Global Positioning Systems and Inertial Navigation Systems

International Journal of Electrical and Computer Engineering (IJECE), 2014

Research paper thumbnail of Dynamics and Control of a Stop Rotor Unmanned Aerial Vehicle

International Journal of Electrical and Computer Engineering (IJECE), 2012

Research paper thumbnail of Sensor Fusion via Brain Emotional Learning for Ground Vehicle

TELKOMNIKA Indonesian Journal of Electrical Engineering, 2014

Research paper thumbnail of Fuzzy Logic Based Sensor Fusion for Accurate Tracking

Lecture Notes in Computer Science, 2011

ABSTRACT Accuracy and tracking update rates play a vital role in determining the quality of Augme... more ABSTRACT Accuracy and tracking update rates play a vital role in determining the quality of Augmented Reality(AR) and Virtual Reality(VR) applications. Applications like soldier training, gaming, simulations & virtual conferencing need a high accuracy tracking with update frequency above 20Hz for an immersible experience of reality. Current research techniques combine more than one sensor like camera, infrared, magnetometers and Inertial Measurement Units (IMU) to achieve this goal. In this paper, we develop and validate a novel algorithm for accurate positioning and tracking using inertial and vision-based sensing techniques. The inertial sensing utilizes accelerometers and gyroscopes to measure rates and accelerations in the body fixed frame and computes orientations and positions via integration. The vision-based sensing uses camera and image processing techniques to compute the position and orientation. The sensor fusion algorithm proposed in this work uses the complementary characteristics of these two independent systems to compute an accurate tracking solution and minimizes the error due to sensor noise, drift and different update rates of camera and IMU. The algorithm is computationally efficient, implemented on a low cost hardware and is capable of an update rate up to 100 Hz. The position and orientation accuracy of the sensor fusion is within 6mm & 1.5°. By using the fuzzy rule sets and adaptive filtering of data, we reduce the computational requirement less than the conventional methods (such as Kalman filtering). We have compared the accuracy of this sensor fusion algorithm with a commercial infrared tracking system. It can be noted that outcome accuracy of this COTS IMU and camera sensor fusion approach is as good as the commercial tracking system at a fraction of the cost.

Research paper thumbnail of Order Reduction of Parametrically Excited Nonlinear Systems: Techniques and Applications

Nonlinear Dynamics, 2005

The basic problem of order reduction of nonlinear systems with time periodic coefficients is cons... more The basic problem of order reduction of nonlinear systems with time periodic coefficients is considered in state space and in direct second order (structural) form. In state space order reduction methods, the equations of motion are expressed as a set of first order equations and transformed using the Lyapunov-Floquet (L-F) transformation such that the linear parts of new set of equations are time invariant. At this stage, four order reduction methodologies, namely linear, nonlinear projection via singular perturbation, post-processing approach and invariant manifold technique, are suggested. The invariant manifold technique yields a unique 'reducibility condition' that provides the conditions under which an accurate nonlinear order reduction is possible. Unlike perturbation or averaging type approaches, the parametric excitation term is not assumed to be small. An alternate approach of deriving reduced order models in direct second order form is also presented. Here the system is converted into an equivalent second order nonlinear system with time invariant linear system matrices and periodically modulated nonlinearities via the L-F and other canonical transformations. Then a master-slave separation of degrees of freedom is used and a nonlinear relation between the slave coordinates and the master coordinates is constructed. This method yields the same 'reducibility conditions' obtained by invariant manifold approach in state space. Some examples are given to show potential applications to real problems using above mentioned methodologies. Order reduction possibilities and results for various cases including 'parametric', 'internal', 'true internal' and 'true combination resonances' are discussed. A generalization of these ideas to periodic-quasiperiodic systems is included and demonstrated by means of an example.

Research paper thumbnail of Order reduction of nonlinear systems with time periodic coefficients using invariant manifolds

Journal of Sound and Vibration, 2005

The basic problem of order reduction of nonlinear systems with time periodic coefficients is cons... more The basic problem of order reduction of nonlinear systems with time periodic coefficients is considered. First, the equations of motion are transformed using the Lyapunov-Floquet transformation such that the linear parts of new set of equations are time invariant. At this stage, the linear order reduction technique can be applied in a straightforward manner. A nonlinear order reduction methodology is also suggested through a generalization of the invariant manifold technique via 'Time Periodic Center Manifold Theory'. A 'reducibility condition' is derived to provide conditions under which a nonlinear order reduction is possible. Unlike perturbation or averaging type approaches, the parametric excitation term is not assumed to be small. An example consisting of two parametrically excited coupled pendulums is given to show potential applications to real problems. Order reduction possibilities and results for various cases including 'parametric', 'internal', 'true internal' and 'combination' resonances are discussed. r

Research paper thumbnail of Stability and robustness analysis of a linear time-periodic system subjected to random perturbations

Communications in Nonlinear Science and Numerical Simulation, 2012

Research paper thumbnail of Reducibility of Periodic Quasi-Periodic Systems

International Journal of Modern Nonlinear Theory and Application, 2014

Research paper thumbnail of Failure Analysis and Reliability Study of NAND Flash- Based Solid State Drives

This research focuses on conducting failure analysis and reliability study to understand and anal... more This research focuses on conducting failure analysis and reliability study to understand and analyze the root cause of Quality, Endurance component Reliability Demonstration Test (RDT) failures and determine SSD performance capability. It addresses essential challenges in developing techniques that utilize solid-state memory technologies (with emphasis on NAND flash memory) from device, circuit, architecture, and system perspectives. These challenges include not only the performance degradation arising from the physical nature of NAND flash memory, e.g., the inability to modify data in-place read/write performance asymmetry, and slow and constrained erase functionality, but also the reliability drawbacks that limits Solid State Drives (SSDs) performance. In order to understand the nature of failures, a Fault Tree Analysis (FTA) was performed that identified the potential causes of component failures. In the course of this research, significant data gathering and analysis effort was carried out that led to a systematic evaluation of the components under consideration. The approach used here to estimate reliability utilized a sample of drives to reflect the reliability parameters (RBER, AFR, and MRR) over 1 year. It is anticipated that this study can provide a methodology for future reliability studies leading to systematic testing and evaluation procedure for SSD RDT's and critical components.

Research paper thumbnail of Unmanned Ground Vehicle Navigation Using Brain Emotional Learning Based Intelligent Controller (BELBIC)

Research paper thumbnail of Failure Analysis and Reliability Study of NAND Flash-Based Solid State Drives

Indonesian Journal of Electrical Engineering and Computer Science, 2016

Research paper thumbnail of Fuzzy logic based sensor fusion for accurate tracking

Proceedings of the 7th International Conference on Advances in Visual Computing Volume Part Ii, 2011

ABSTRACT Accuracy and tracking update rates play a vital role in determining the quality of Augme... more ABSTRACT Accuracy and tracking update rates play a vital role in determining the quality of Augmented Reality(AR) and Virtual Reality(VR) applications. Applications like soldier training, gaming, simulations & virtual conferencing need a high accuracy tracking with update frequency above 20Hz for an immersible experience of reality. Current research techniques combine more than one sensor like camera, infrared, magnetometers and Inertial Measurement Units (IMU) to achieve this goal. In this paper, we develop and validate a novel algorithm for accurate positioning and tracking using inertial and vision-based sensing techniques. The inertial sensing utilizes accelerometers and gyroscopes to measure rates and accelerations in the body fixed frame and computes orientations and positions via integration. The vision-based sensing uses camera and image processing techniques to compute the position and orientation. The sensor fusion algorithm proposed in this work uses the complementary characteristics of these two independent systems to compute an accurate tracking solution and minimizes the error due to sensor noise, drift and different update rates of camera and IMU. The algorithm is computationally efficient, implemented on a low cost hardware and is capable of an update rate up to 100 Hz. The position and orientation accuracy of the sensor fusion is within 6mm & 1.5°. By using the fuzzy rule sets and adaptive filtering of data, we reduce the computational requirement less than the conventional methods (such as Kalman filtering). We have compared the accuracy of this sensor fusion algorithm with a commercial infrared tracking system. It can be noted that outcome accuracy of this COTS IMU and camera sensor fusion approach is as good as the commercial tracking system at a fraction of the cost.

Research paper thumbnail of Order reduction of nonlinear systems with time periodic coefficients using invariant manifolds

Journal of Sound and Vibration, Jun 1, 2005

The basic problem of order reduction of nonlinear systems with time periodic coefficients is cons... more The basic problem of order reduction of nonlinear systems with time periodic coefficients is considered. First, the equations of motion are transformed using the Lyapunov-Floquet transformation such that the linear parts of new set of equations are time invariant. At this stage, the linear order reduction technique can be applied in a straightforward manner. A nonlinear order reduction methodology is also suggested through a generalization of the invariant manifold technique via ' Time Periodic Center Manifold Theory'. A ' reducibility condition' is derived to provide conditions under which a nonlinear order reduction is possible. Unlike perturbation or averaging type approaches, the parametric excitation term is not assumed to be small. An example consisting of two parametrically excited coupled pendulums is given to show potential applications to real problems. Order reduction possibilities and results for various cases including 'parametric', 'internal', 'true internal' and 'combination' resonances are discussed.

Research paper thumbnail of Order Reduction of Parametrically Excited Nonlinear Systems Subjected to External Periodic Excitations

Volume 4: 7th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B and C, 2009

The basic problem of order reduction of nonlinear systems with time periodic coefficients is cons... more The basic problem of order reduction of nonlinear systems with time periodic coefficients is considered in state space and in direct second order (structural) form. In state space order reduction methods, the equations of motion are expressed as a set of first order equations and transformed using the Lyapunov-Floquet (L-F) transformation such that the linear parts of new set of equations are time invariant. At this stage, four order reduction methodologies, namely linear, nonlinear projection via singular perturbation, post-processing approach and invariant manifold technique, are suggested. The invariant manifold technique yields a unique 'reducibility condition' that provides the conditions under which an accurate nonlinear order reduction is possible. Unlike perturbation or averaging type approaches, the parametric excitation term is not assumed to be small. An alternate approach of deriving reduced order models in direct second order form is also presented. Here the system is converted into an equivalent second order nonlinear system with time invariant linear system matrices and periodically modulated nonlinearities via the L-F and other canonical transformations. Then a master-slave separation of degrees of freedom is used and a nonlinear relation between the slave coordinates and the master coordinates is constructed. This method yields the same 'reducibility conditions' obtained by invariant manifold approach in state space. Some examples are given to show potential applications to real problems using above mentioned methodologies. Order reduction possibilities and results for various cases including 'parametric', 'internal', 'true internal' and 'true combination resonances' are discussed. A generalization of these ideas to periodic-quasiperiodic systems is included and demonstrated by means of an example.

Research paper thumbnail of A Direct Approach to Order Reduction of Nonlinear Systems Subjected to External Periodic Excitations

Journal of Computational and Nonlinear Dynamics, 2008

Research paper thumbnail of Order Reduction of Nonlinear Systems With Periodic-Quasiperiodic Coefficients

Volume 1: 20th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C, 2005

Research paper thumbnail of Analysis and simulation of Wiseman hypocycloid engine

Research paper thumbnail of Order Reduction of Nonlinear Time Periodic Systems Using Invariant Manifolds

Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C, 2003

The basic problem of order reduction of nonlinear systems with time periodic coefficients is cons... more The basic problem of order reduction of nonlinear systems with time periodic coefficients is considered. First, the equations of motion are transformed using the Lyapunov-Floquet transformation such that the linear parts of new set of equations are time invariant. At this stage, the linear order reduction technique can be applied in a straightforward manner. A nonlinear order reduction methodology is also suggested through a generalization of the invariant manifold technique via 'Time Periodic Center Manifold Theory'. A 'reducibility condition' is derived to provide conditions under which a nonlinear order reduction is possible. Unlike perturbation or averaging type approaches, the parametric excitation term is not assumed to be small. An example consisting of two parametrically excited coupled pendulums is given to show potential applications to real problems. Order reduction possibilities and results for various cases including 'parametric', 'internal', 'true internal' and 'combination' resonances are discussed. r

Research paper thumbnail of Some Techniques for Order Reduction of Nonlinear Time Periodic Systems

Design Engineering, Volumes 1 and 2, 2003

This work reports new approaches for order reduction of nonlinear systems with time periodic coef... more This work reports new approaches for order reduction of nonlinear systems with time periodic coefficients. First, the equations of motion are transformed using the Lyapunov-Floquet (LF) transformation, which makes the linear part of new set of equations time invariant. At this point, either linear or nonlinear order reduction methodologies can be applied. The linear order reduction technique is based on classical technique of aggregation and nonlinear technique is based on 'Time periodic invariant manifold theory'. These methods do not assume the parametric excitation term to be small. The nonlinear order reduction technique yields superior results. An example of two degrees of freedom system representing a magnetic bearing is included to show the practical implementation of these methods. The conditions when order reduction is not possible are also discussed.

Research paper thumbnail of Order Reduction of Nonlinear Systems Subjected to an External Periodic Excitation

Design Engineering, Parts A and B, 2005

Research paper thumbnail of Guided Navigation Control of an Unmanned Ground Vehicle using Global Positioning Systems and Inertial Navigation Systems

International Journal of Electrical and Computer Engineering (IJECE), 2014

Research paper thumbnail of Dynamics and Control of a Stop Rotor Unmanned Aerial Vehicle

International Journal of Electrical and Computer Engineering (IJECE), 2012

Research paper thumbnail of Sensor Fusion via Brain Emotional Learning for Ground Vehicle

TELKOMNIKA Indonesian Journal of Electrical Engineering, 2014

Research paper thumbnail of Fuzzy Logic Based Sensor Fusion for Accurate Tracking

Lecture Notes in Computer Science, 2011

ABSTRACT Accuracy and tracking update rates play a vital role in determining the quality of Augme... more ABSTRACT Accuracy and tracking update rates play a vital role in determining the quality of Augmented Reality(AR) and Virtual Reality(VR) applications. Applications like soldier training, gaming, simulations & virtual conferencing need a high accuracy tracking with update frequency above 20Hz for an immersible experience of reality. Current research techniques combine more than one sensor like camera, infrared, magnetometers and Inertial Measurement Units (IMU) to achieve this goal. In this paper, we develop and validate a novel algorithm for accurate positioning and tracking using inertial and vision-based sensing techniques. The inertial sensing utilizes accelerometers and gyroscopes to measure rates and accelerations in the body fixed frame and computes orientations and positions via integration. The vision-based sensing uses camera and image processing techniques to compute the position and orientation. The sensor fusion algorithm proposed in this work uses the complementary characteristics of these two independent systems to compute an accurate tracking solution and minimizes the error due to sensor noise, drift and different update rates of camera and IMU. The algorithm is computationally efficient, implemented on a low cost hardware and is capable of an update rate up to 100 Hz. The position and orientation accuracy of the sensor fusion is within 6mm & 1.5°. By using the fuzzy rule sets and adaptive filtering of data, we reduce the computational requirement less than the conventional methods (such as Kalman filtering). We have compared the accuracy of this sensor fusion algorithm with a commercial infrared tracking system. It can be noted that outcome accuracy of this COTS IMU and camera sensor fusion approach is as good as the commercial tracking system at a fraction of the cost.

Research paper thumbnail of Order Reduction of Parametrically Excited Nonlinear Systems: Techniques and Applications

Nonlinear Dynamics, 2005

The basic problem of order reduction of nonlinear systems with time periodic coefficients is cons... more The basic problem of order reduction of nonlinear systems with time periodic coefficients is considered in state space and in direct second order (structural) form. In state space order reduction methods, the equations of motion are expressed as a set of first order equations and transformed using the Lyapunov-Floquet (L-F) transformation such that the linear parts of new set of equations are time invariant. At this stage, four order reduction methodologies, namely linear, nonlinear projection via singular perturbation, post-processing approach and invariant manifold technique, are suggested. The invariant manifold technique yields a unique 'reducibility condition' that provides the conditions under which an accurate nonlinear order reduction is possible. Unlike perturbation or averaging type approaches, the parametric excitation term is not assumed to be small. An alternate approach of deriving reduced order models in direct second order form is also presented. Here the system is converted into an equivalent second order nonlinear system with time invariant linear system matrices and periodically modulated nonlinearities via the L-F and other canonical transformations. Then a master-slave separation of degrees of freedom is used and a nonlinear relation between the slave coordinates and the master coordinates is constructed. This method yields the same 'reducibility conditions' obtained by invariant manifold approach in state space. Some examples are given to show potential applications to real problems using above mentioned methodologies. Order reduction possibilities and results for various cases including 'parametric', 'internal', 'true internal' and 'true combination resonances' are discussed. A generalization of these ideas to periodic-quasiperiodic systems is included and demonstrated by means of an example.

Research paper thumbnail of Order reduction of nonlinear systems with time periodic coefficients using invariant manifolds

Journal of Sound and Vibration, 2005

The basic problem of order reduction of nonlinear systems with time periodic coefficients is cons... more The basic problem of order reduction of nonlinear systems with time periodic coefficients is considered. First, the equations of motion are transformed using the Lyapunov-Floquet transformation such that the linear parts of new set of equations are time invariant. At this stage, the linear order reduction technique can be applied in a straightforward manner. A nonlinear order reduction methodology is also suggested through a generalization of the invariant manifold technique via 'Time Periodic Center Manifold Theory'. A 'reducibility condition' is derived to provide conditions under which a nonlinear order reduction is possible. Unlike perturbation or averaging type approaches, the parametric excitation term is not assumed to be small. An example consisting of two parametrically excited coupled pendulums is given to show potential applications to real problems. Order reduction possibilities and results for various cases including 'parametric', 'internal', 'true internal' and 'combination' resonances are discussed. r

Research paper thumbnail of Stability and robustness analysis of a linear time-periodic system subjected to random perturbations

Communications in Nonlinear Science and Numerical Simulation, 2012