The Energy-Rate method is an applied method to determine the transient curves and stability chart... more The Energy-Rate method is an applied method to determine the transient curves and stability chart for the parametric equations. This method is based on the first integral of the energy of the systems. Energy-Rate method finds the values of parameters of the system equations in such a way that a periodic response can be produced. In this study, the Energy-Rate method is applied to the following forced Mathieu equation: ( ) ( ) ( ) 2 y hy 1 2 2 cos 2rt y 2 sin rt + + − β+ β = β && & This equation governs the lateral vibration of a microcanilever resonator in linear domain. Its stability chart in the β-r plane shows a complicated map, which cannot be detected by perturbation methods.
The Energy-Rate method is an applied method to determine the transient curves and stability chart... more The Energy-Rate method is an applied method to determine the transient curves and stability chart for the parametric equations. This method is based on the first integral of the energy of the systems. Energy-Rate method finds the values of parameters of the system equations in such a way that a periodic response can be produced. In this study, the Energy-Rate method is applied to the following forced Mathieu equation: ( ) ( ) ( ) 2 y hy 1 2 2 cos 2rt y 2 sin rt + + − β+ β = β && & This equation governs the lateral vibration of a microcanilever resonator in linear domain. Its stability chart in the β-r plane shows a complicated map, which cannot be detected by perturbation methods.
2004 International Conference on MEMS, NANO and Smart Systems (ICMENS'04), 2004
Micro-electro-mechanical systems (MEMS) are microscopic mechanical systems coupled with electric ... more Micro-electro-mechanical systems (MEMS) are microscopic mechanical systems coupled with electric or electronic circuits. MEMS have been extensively used as micro-scale high-quality oscillators, communication resonators, microphones, amplifiers and other micro-oscillators. In this investigation, mathematical model of a micro-mechanical resonator is developed subject to a full nonlinear model. The governing equation is a nonlinear parametric and hence, the stability of the system depends on the value of its parameters. The output signal of MEMS is not reliable when it is operating in a saturated or in an instable region. From a design viewpoint, a stability chart is needed to indicate the relationship between the parameters to determine when the system is stable, periodic, or unstable. Nondimensional and linearized model of the MEMS is studied and a stability diagram is developed for the system.
This paper describes analysis of steady motions for underwater gliders, a type of highly efficien... more This paper describes analysis of steady motions for underwater gliders, a type of highly efficient underwater vehicle which uses gravity for propulsion. Underwater gliders are winged underwater vehicles which locomote by modulating their buoyancy and their attitude. Several such vehicles have been developed and have proven their worth as efficient long-distance, long-duration ocean sampling platforms. To date, the primary emphasis in underwater glider development has been on locomotive efficiency; maneuverability has been a secondary concern. The ultimate aim of our research is to develop optimal motion control strategies which enhance the natural locomotive efficiency of underwater gliders by minimizing the energy expended by the control system. Ambitious applications such as persistent undersea surveillance require not only efficient vehicles, but efficient guidance and control schemes. This technical report aims to develop a better understanding of glider maneuverability, particularly with regard to turning motions. As a preliminary step, we develop an approximate analytical expression for steady turning motion for a realistic glider model. The problem is formulated in terms of regular perturbation theory, with the vehicle turn rate as the perturbation parameter. The resulting solution exhibits a special structure that allows one to apply existing optimal path planning results for planar mobile robots. The ultimate result is a simple, energy-efficient motion control method for underwater gliders.
ABSTRACT This paper presents the dynamic behavior of microcantilever-based microresonators and co... more ABSTRACT This paper presents the dynamic behavior of microcantilever-based microresonators and compares their steady state behavior for polarized and nonpolarized systems at different levels of nonlinearities. A microcantilever, equipped with a time-varying capacitor, makes the microresonator system. The capacitor is activated by a constant polarization voltage, and an alternative actuating voltage. The partial differential equation of motion of the vibrating electrode can be reduced to a highly nonlinear parametric second order ordinary differential equation. The steady state behavior of the microresonator has been analyzed with and without polarization voltage. The main characteristic of the non-polarized model is explained by the stability of the system in parameter plane. A set of stability chart is provided to predict the boundary between the stable and unstable domains. Furthermore, the main characteristic of the polarized model is determination by the period-amplitude relationship of the system. Applying perturbation methods, analytical equations are derived to describe the frequency response of the system, which are suitable to be utilized in parameter study and design.
—This letter presents the design and potential impact of the developed Research Oriented Underwat... more —This letter presents the design and potential impact of the developed Research Oriented Underwater Glider for Hands-on Investigative Engineering (ROUGHIE). The ROUGHIE is an open-source, highly-maneuverable, and low-cost vehicle that enables rapid development and testing of new hardware and software. ROUGHIE is an internally actuated glider capable of performing steady sawtooth glides in shallow water down to 3 meters, tight turns with a minimum radius of 3 meters, and a minimum endurance of 60 hours. The novelty of the work is twofold: 1) a rail-based design to facilitate modularity and ease of assembly and 2) an effective internal rotary mass mechanism to increase maneuverability and perform tight turns. The ROUGHIE design strategically uses 3D printed plastic parts in low stress situations which allows extreme design flexibility and enables tightly packed modules that can be easily customized.
The Energy-Rate method is an applied method to determine the transient curves and stability chart... more The Energy-Rate method is an applied method to determine the transient curves and stability chart for the parametric equations. This method is based on the first integral of the energy of the systems. Energy-Rate method finds the values of parameters of the system equations in such a way that a periodic response can be produced. In this study, the Energy-Rate method is applied to the following forced Mathieu equation: ( ) ( ) ( ) 2 y hy 1 2 2 cos 2rt y 2 sin rt + + − β+ β = β && & This equation governs the lateral vibration of a microcanilever resonator in linear domain. Its stability chart in the β-r plane shows a complicated map, which cannot be detected by perturbation methods.
The Energy-Rate method is an applied method to determine the transient curves and stability chart... more The Energy-Rate method is an applied method to determine the transient curves and stability chart for the parametric equations. This method is based on the first integral of the energy of the systems. Energy-Rate method finds the values of parameters of the system equations in such a way that a periodic response can be produced. In this study, the Energy-Rate method is applied to the following forced Mathieu equation: ( ) ( ) ( ) 2 y hy 1 2 2 cos 2rt y 2 sin rt + + − β+ β = β && & This equation governs the lateral vibration of a microcanilever resonator in linear domain. Its stability chart in the β-r plane shows a complicated map, which cannot be detected by perturbation methods.
2004 International Conference on MEMS, NANO and Smart Systems (ICMENS'04), 2004
Micro-electro-mechanical systems (MEMS) are microscopic mechanical systems coupled with electric ... more Micro-electro-mechanical systems (MEMS) are microscopic mechanical systems coupled with electric or electronic circuits. MEMS have been extensively used as micro-scale high-quality oscillators, communication resonators, microphones, amplifiers and other micro-oscillators. In this investigation, mathematical model of a micro-mechanical resonator is developed subject to a full nonlinear model. The governing equation is a nonlinear parametric and hence, the stability of the system depends on the value of its parameters. The output signal of MEMS is not reliable when it is operating in a saturated or in an instable region. From a design viewpoint, a stability chart is needed to indicate the relationship between the parameters to determine when the system is stable, periodic, or unstable. Nondimensional and linearized model of the MEMS is studied and a stability diagram is developed for the system.
This paper describes analysis of steady motions for underwater gliders, a type of highly efficien... more This paper describes analysis of steady motions for underwater gliders, a type of highly efficient underwater vehicle which uses gravity for propulsion. Underwater gliders are winged underwater vehicles which locomote by modulating their buoyancy and their attitude. Several such vehicles have been developed and have proven their worth as efficient long-distance, long-duration ocean sampling platforms. To date, the primary emphasis in underwater glider development has been on locomotive efficiency; maneuverability has been a secondary concern. The ultimate aim of our research is to develop optimal motion control strategies which enhance the natural locomotive efficiency of underwater gliders by minimizing the energy expended by the control system. Ambitious applications such as persistent undersea surveillance require not only efficient vehicles, but efficient guidance and control schemes. This technical report aims to develop a better understanding of glider maneuverability, particularly with regard to turning motions. As a preliminary step, we develop an approximate analytical expression for steady turning motion for a realistic glider model. The problem is formulated in terms of regular perturbation theory, with the vehicle turn rate as the perturbation parameter. The resulting solution exhibits a special structure that allows one to apply existing optimal path planning results for planar mobile robots. The ultimate result is a simple, energy-efficient motion control method for underwater gliders.
ABSTRACT This paper presents the dynamic behavior of microcantilever-based microresonators and co... more ABSTRACT This paper presents the dynamic behavior of microcantilever-based microresonators and compares their steady state behavior for polarized and nonpolarized systems at different levels of nonlinearities. A microcantilever, equipped with a time-varying capacitor, makes the microresonator system. The capacitor is activated by a constant polarization voltage, and an alternative actuating voltage. The partial differential equation of motion of the vibrating electrode can be reduced to a highly nonlinear parametric second order ordinary differential equation. The steady state behavior of the microresonator has been analyzed with and without polarization voltage. The main characteristic of the non-polarized model is explained by the stability of the system in parameter plane. A set of stability chart is provided to predict the boundary between the stable and unstable domains. Furthermore, the main characteristic of the polarized model is determination by the period-amplitude relationship of the system. Applying perturbation methods, analytical equations are derived to describe the frequency response of the system, which are suitable to be utilized in parameter study and design.
—This letter presents the design and potential impact of the developed Research Oriented Underwat... more —This letter presents the design and potential impact of the developed Research Oriented Underwater Glider for Hands-on Investigative Engineering (ROUGHIE). The ROUGHIE is an open-source, highly-maneuverable, and low-cost vehicle that enables rapid development and testing of new hardware and software. ROUGHIE is an internally actuated glider capable of performing steady sawtooth glides in shallow water down to 3 meters, tight turns with a minimum radius of 3 meters, and a minimum endurance of 60 hours. The novelty of the work is twofold: 1) a rail-based design to facilitate modularity and ease of assembly and 2) an effective internal rotary mass mechanism to increase maneuverability and perform tight turns. The ROUGHIE design strategically uses 3D printed plastic parts in low stress situations which allows extreme design flexibility and enables tightly packed modules that can be easily customized.
Uploads
Papers by N. Mahmoudian