Alan Whitman - Academia.edu (original) (raw)
Papers by Alan Whitman
Mechanical Engineering Series, Dec 5, 2019
Mechanical engineering series, 2023
The Mechanical Engineering Series presents advanced level treatment of topics on the cutting edge... more The Mechanical Engineering Series presents advanced level treatment of topics on the cutting edge of mechanical engineering. Designed for use by students, researchers and practicing engineers, the series presents modern developments in mechanical engineering and its innovative applications in applied mechanics, bioengineering, dynamic systems and control, energy, energy conversion and energy systems, fluid mechanics and fluid machinery, heat and mass transfer, manufacturing science and technology, mechanical design, mechanics of materials, micro-and nano-science technology, thermal physics, tribology, and vibration and acoustics. The series features graduate-level texts, professional books, and research monographs in key engineering science concentrations.
Mechanical engineering series, 2023
Journal of Applied Physics, 1976
The stability of electric arc discharges has been explored through the use of an energy balance c... more The stability of electric arc discharges has been explored through the use of an energy balance coupled with charge conservation. In order to facilitate this analysis, a new model for the electrical conductivity function has been proposed. Asymptotic solutions for the arc governing equations have been obtained. Stability criteria have been developed from both the linear theory (infinitesimal size disturbance) and from a minimizing solution point of view for finite size disturbances. The results delineate an open region in the stability diagram where arc instabilities may be possible.
Journal of Ship Research, 1973
A correlation is presented of the maximum pressure that obtains in the flat-plate hydrodynamic im... more A correlation is presented of the maximum pressure that obtains in the flat-plate hydrodynamic impact problem due to "trapped air." For large plates this becomes a similarity relation so that it is possible to scale impacts.
Optical, Infrared, Millimeter Wave Propagation Engineering, 1988
We discuss the importance of the isoplanatic assumption in conventional imaging and in imaging us... more We discuss the importance of the isoplanatic assumption in conventional imaging and in imaging using intensity interferometry. For conventional imaging, we treat both short- and long-time exposures. In imaging using intensity interferometry, we present a general result, in which isoplanicity is not assumed, and then study the first order non-isoplanatic correction. Explicit calculations are given for the correction under typical atmospheric conditions.
Journal of the Franklin Institute, 1975
Journal of Dynamic Systems, Measurement, and Control, 1983
Analytic formulae for the critical speed and frequency of an interconnected pair of wheelsets bas... more Analytic formulae for the critical speed and frequency of an interconnected pair of wheelsets based on an asymptotic expansion in a truck geometric parameter are derived. No restriction is placed on the values of either the shear or bending stiffness; consequently, the entire structure of the stability surface is obtained. The surface is a symmetric function of the two dimensionless stiffnesses and it depends predominantly on their series combination. Expressions are obtained for the local and global extrema and their locations. The frequency varies monotonically from the wheelset kinematic frequency to the rigid truck frequency as a function of stiffness. The results are compared with numerical solutions and found to be accurate in the region of physically obtainable values of the expansion parameter.
Journal of Applied Mechanics, 1987
We calculate the variation in critical speed of a flexible truck as a function of limit cycle amp... more We calculate the variation in critical speed of a flexible truck as a function of limit cycle amplitude and truck parameters (i.e., shear and bending stiffnesses, and truck geometry), by means of a perturbation procedure. We find that the creep force nonlinearity is dominant, and that it can cause the nonlinear critical speed to be either lower or higher than the linear critical speed, depending on the values of the two stiffnesses.
Journal of Applied Mechanics, 1972
We derive, by means of an asymptotic analysis, a simple expression for the added mass per unit le... more We derive, by means of an asymptotic analysis, a simple expression for the added mass per unit length of a finite length, slender, cylinder vibrating in the breathing mode. We find, to dominant order in the expansion, that when the wavelength of the vibration is smaller than the half length, the added mass is independent of the aspect ratio while in the antithetical case it is solely dependent on that quantity.
Journal of Modern Optics, 1976
In a previous paper [1] we obtained an asymptotic expression for the irradiance fluctuations of a... more In a previous paper [1] we obtained an asymptotic expression for the irradiance fluctuations of a finite beam propagating in a random medium in the strong-scattering case (i.e. the characteristic diffraction length is large compared to the characteristic scattering length). The solution was given as the product of a plane wave portion and a finite beam correction. We show here that if the statistics of the fluctuations of the infinite and finite beams are assumed to be gaussian (in which case the fourth-order coherence function may be expressed in terms of second-order coherence functions), then the finite beam result obtained is in disagreement with our previous result. Consequently, we conclude that the statistics of a finite beam cannot be gaussian. However, assuming that the statistics of the infinite beam are gaussian leads to no contradiction. This result is an indication of the importance of finite beam size effects in irradiance fluctuation studies.
Mechanical Engineering Series, 2019
The quantityẆ F is a derived dimension [E/t] = [FL/t] = [ML 2 /t 3 ] (the dot over the symbol is ... more The quantityẆ F is a derived dimension [E/t] = [FL/t] = [ML 2 /t 3 ] (the dot over the symbol is meant to indicate a rate, and W F is a derived dimension [E]), we call it the power developed by the force. When the power developed is positive, we say that the force generates power, and when it is negative, we say that it absorbs power. The natural units for power are kg m 2 /s 3 in the SI, and lbm ft 2 /s 3 in the English System.
Dynamics, as you have learned in previous courses, is the study of how particles and rigid bodies... more Dynamics, as you have learned in previous courses, is the study of how particles and rigid bodies move under the action of the forces and moments that are exerted on them. Thermodynamics is the theory that integrates dynamics with the concept of temperature. Dynamics is a fundamental part of physics because of Newton’s second law, which describes how the momentum of a fixed quantity of matter evolves in time.
In the last chapter, you learned how to calculate the work done by and the heat transfer to a sys... more In the last chapter, you learned how to calculate the work done by and the heat transfer to a system that undergoes a specified change of state. On the other hand, you could not calculate the change of state caused by given values for the work and heat interactions. Furthermore, although you learned how to calculate the work done and heat transfer independent of one another, experience tells us that they are intimately related. Indeed there is a fundamental relation between the work done by a system, the heat transfer to the system, and its change of state. Exploring and exploiting this relation is one of the basic concerns of thermodynamics.
Mechanical Engineering Series, 2019
In our study till now, we established the first law of thermodynamics, in which we saw that heat ... more In our study till now, we established the first law of thermodynamics, in which we saw that heat and work are equivalent insofar as they are different manifestations of the energy exchange between a system and its surroundings (or between various parts of a system). However, in this development, an asymmetry between heat and work has remained.
An approximate inverse dynamic solution for differential drive mobile robots is presented where t... more An approximate inverse dynamic solution for differential drive mobile robots is presented where the wheel speeds are analytically calculated for a specified desired trajectory. The differential equations of motion of the mobile robot are nondimen-sionalized and a small parameter is defined based on the ratio of wheel slip and wheel speed variation time scales. Approximate dominant and first order inverse solutions are derived for general trajectories. Next, a trajectory planning strategy is devised to ensure continuous wheel speed profiles in achieving any desired target trajectory. The case of target circular trajectories is specifically considered and with inverse solutions which are verified both through simulations and experiments.Copyright © 2015 by ASME
It is impossible to overestimate the impact that the development of steam- and gasoline-powered e... more It is impossible to overestimate the impact that the development of steam- and gasoline-powered engines have had on the history of Western civilization. Indeed, the availability of large sources of power fueled the Industrial Revolution, while sources of increasingly higher power density extended the range of travel to the global scale. Today we are so dependent on easy access to power that it is difficult to imagine life without it. In this part of the current chapter, we will study the technical aspects of this development.
Mechanical Engineering Series, 2020
The Mechanical Engineering Series presents advanced level treatment of topics on the cutting edge... more The Mechanical Engineering Series presents advanced level treatment of topics on the cutting edge of mechanical engineering. Designed for use by students, researchers and practicing engineers, the series presents modern developments in mechanical engineering and its innovative applications in applied mechanics, bioengineering, dynamic systems and control, energy, energy conversion and energy systems, fluid mechanics and fluid machinery, heat and mass transfer, manufacturing science and technology, mechanical design, mechanics of materials, micro-and nano-science technology, thermal physics, tribology, and vibration and acoustics. The series features graduate-level texts, professional books, and research monographs in key engineering science concentrations.
Volume 1C: 16th Biennial Conference on Mechanical Vibration and Noise, 1997
A pair of spur gears with involute teeth is considered. Nondimensional expressions are derived fo... more A pair of spur gears with involute teeth is considered. Nondimensional expressions are derived for the dynamic tooth loading. The resulting parametrically excited equations are analyzed by the procedures of asymptotic analysis. The results show that instability regions can occur leading to large vibrations and failure. These instability regimes are presented as a function of speed and other parameters. Minimum damping values to prevent the instabilities are derived as a function of the gear ratio and number of pinion teeth. In addition, given some inherent damping, response amplitudes of the transmission error are presented as a function of nondimensional parameters.
Mechanical Engineering Series, Dec 5, 2019
Mechanical engineering series, 2023
The Mechanical Engineering Series presents advanced level treatment of topics on the cutting edge... more The Mechanical Engineering Series presents advanced level treatment of topics on the cutting edge of mechanical engineering. Designed for use by students, researchers and practicing engineers, the series presents modern developments in mechanical engineering and its innovative applications in applied mechanics, bioengineering, dynamic systems and control, energy, energy conversion and energy systems, fluid mechanics and fluid machinery, heat and mass transfer, manufacturing science and technology, mechanical design, mechanics of materials, micro-and nano-science technology, thermal physics, tribology, and vibration and acoustics. The series features graduate-level texts, professional books, and research monographs in key engineering science concentrations.
Mechanical engineering series, 2023
Journal of Applied Physics, 1976
The stability of electric arc discharges has been explored through the use of an energy balance c... more The stability of electric arc discharges has been explored through the use of an energy balance coupled with charge conservation. In order to facilitate this analysis, a new model for the electrical conductivity function has been proposed. Asymptotic solutions for the arc governing equations have been obtained. Stability criteria have been developed from both the linear theory (infinitesimal size disturbance) and from a minimizing solution point of view for finite size disturbances. The results delineate an open region in the stability diagram where arc instabilities may be possible.
Journal of Ship Research, 1973
A correlation is presented of the maximum pressure that obtains in the flat-plate hydrodynamic im... more A correlation is presented of the maximum pressure that obtains in the flat-plate hydrodynamic impact problem due to "trapped air." For large plates this becomes a similarity relation so that it is possible to scale impacts.
Optical, Infrared, Millimeter Wave Propagation Engineering, 1988
We discuss the importance of the isoplanatic assumption in conventional imaging and in imaging us... more We discuss the importance of the isoplanatic assumption in conventional imaging and in imaging using intensity interferometry. For conventional imaging, we treat both short- and long-time exposures. In imaging using intensity interferometry, we present a general result, in which isoplanicity is not assumed, and then study the first order non-isoplanatic correction. Explicit calculations are given for the correction under typical atmospheric conditions.
Journal of the Franklin Institute, 1975
Journal of Dynamic Systems, Measurement, and Control, 1983
Analytic formulae for the critical speed and frequency of an interconnected pair of wheelsets bas... more Analytic formulae for the critical speed and frequency of an interconnected pair of wheelsets based on an asymptotic expansion in a truck geometric parameter are derived. No restriction is placed on the values of either the shear or bending stiffness; consequently, the entire structure of the stability surface is obtained. The surface is a symmetric function of the two dimensionless stiffnesses and it depends predominantly on their series combination. Expressions are obtained for the local and global extrema and their locations. The frequency varies monotonically from the wheelset kinematic frequency to the rigid truck frequency as a function of stiffness. The results are compared with numerical solutions and found to be accurate in the region of physically obtainable values of the expansion parameter.
Journal of Applied Mechanics, 1987
We calculate the variation in critical speed of a flexible truck as a function of limit cycle amp... more We calculate the variation in critical speed of a flexible truck as a function of limit cycle amplitude and truck parameters (i.e., shear and bending stiffnesses, and truck geometry), by means of a perturbation procedure. We find that the creep force nonlinearity is dominant, and that it can cause the nonlinear critical speed to be either lower or higher than the linear critical speed, depending on the values of the two stiffnesses.
Journal of Applied Mechanics, 1972
We derive, by means of an asymptotic analysis, a simple expression for the added mass per unit le... more We derive, by means of an asymptotic analysis, a simple expression for the added mass per unit length of a finite length, slender, cylinder vibrating in the breathing mode. We find, to dominant order in the expansion, that when the wavelength of the vibration is smaller than the half length, the added mass is independent of the aspect ratio while in the antithetical case it is solely dependent on that quantity.
Journal of Modern Optics, 1976
In a previous paper [1] we obtained an asymptotic expression for the irradiance fluctuations of a... more In a previous paper [1] we obtained an asymptotic expression for the irradiance fluctuations of a finite beam propagating in a random medium in the strong-scattering case (i.e. the characteristic diffraction length is large compared to the characteristic scattering length). The solution was given as the product of a plane wave portion and a finite beam correction. We show here that if the statistics of the fluctuations of the infinite and finite beams are assumed to be gaussian (in which case the fourth-order coherence function may be expressed in terms of second-order coherence functions), then the finite beam result obtained is in disagreement with our previous result. Consequently, we conclude that the statistics of a finite beam cannot be gaussian. However, assuming that the statistics of the infinite beam are gaussian leads to no contradiction. This result is an indication of the importance of finite beam size effects in irradiance fluctuation studies.
Mechanical Engineering Series, 2019
The quantityẆ F is a derived dimension [E/t] = [FL/t] = [ML 2 /t 3 ] (the dot over the symbol is ... more The quantityẆ F is a derived dimension [E/t] = [FL/t] = [ML 2 /t 3 ] (the dot over the symbol is meant to indicate a rate, and W F is a derived dimension [E]), we call it the power developed by the force. When the power developed is positive, we say that the force generates power, and when it is negative, we say that it absorbs power. The natural units for power are kg m 2 /s 3 in the SI, and lbm ft 2 /s 3 in the English System.
Dynamics, as you have learned in previous courses, is the study of how particles and rigid bodies... more Dynamics, as you have learned in previous courses, is the study of how particles and rigid bodies move under the action of the forces and moments that are exerted on them. Thermodynamics is the theory that integrates dynamics with the concept of temperature. Dynamics is a fundamental part of physics because of Newton’s second law, which describes how the momentum of a fixed quantity of matter evolves in time.
In the last chapter, you learned how to calculate the work done by and the heat transfer to a sys... more In the last chapter, you learned how to calculate the work done by and the heat transfer to a system that undergoes a specified change of state. On the other hand, you could not calculate the change of state caused by given values for the work and heat interactions. Furthermore, although you learned how to calculate the work done and heat transfer independent of one another, experience tells us that they are intimately related. Indeed there is a fundamental relation between the work done by a system, the heat transfer to the system, and its change of state. Exploring and exploiting this relation is one of the basic concerns of thermodynamics.
Mechanical Engineering Series, 2019
In our study till now, we established the first law of thermodynamics, in which we saw that heat ... more In our study till now, we established the first law of thermodynamics, in which we saw that heat and work are equivalent insofar as they are different manifestations of the energy exchange between a system and its surroundings (or between various parts of a system). However, in this development, an asymmetry between heat and work has remained.
An approximate inverse dynamic solution for differential drive mobile robots is presented where t... more An approximate inverse dynamic solution for differential drive mobile robots is presented where the wheel speeds are analytically calculated for a specified desired trajectory. The differential equations of motion of the mobile robot are nondimen-sionalized and a small parameter is defined based on the ratio of wheel slip and wheel speed variation time scales. Approximate dominant and first order inverse solutions are derived for general trajectories. Next, a trajectory planning strategy is devised to ensure continuous wheel speed profiles in achieving any desired target trajectory. The case of target circular trajectories is specifically considered and with inverse solutions which are verified both through simulations and experiments.Copyright © 2015 by ASME
It is impossible to overestimate the impact that the development of steam- and gasoline-powered e... more It is impossible to overestimate the impact that the development of steam- and gasoline-powered engines have had on the history of Western civilization. Indeed, the availability of large sources of power fueled the Industrial Revolution, while sources of increasingly higher power density extended the range of travel to the global scale. Today we are so dependent on easy access to power that it is difficult to imagine life without it. In this part of the current chapter, we will study the technical aspects of this development.
Mechanical Engineering Series, 2020
The Mechanical Engineering Series presents advanced level treatment of topics on the cutting edge... more The Mechanical Engineering Series presents advanced level treatment of topics on the cutting edge of mechanical engineering. Designed for use by students, researchers and practicing engineers, the series presents modern developments in mechanical engineering and its innovative applications in applied mechanics, bioengineering, dynamic systems and control, energy, energy conversion and energy systems, fluid mechanics and fluid machinery, heat and mass transfer, manufacturing science and technology, mechanical design, mechanics of materials, micro-and nano-science technology, thermal physics, tribology, and vibration and acoustics. The series features graduate-level texts, professional books, and research monographs in key engineering science concentrations.
Volume 1C: 16th Biennial Conference on Mechanical Vibration and Noise, 1997
A pair of spur gears with involute teeth is considered. Nondimensional expressions are derived fo... more A pair of spur gears with involute teeth is considered. Nondimensional expressions are derived for the dynamic tooth loading. The resulting parametrically excited equations are analyzed by the procedures of asymptotic analysis. The results show that instability regions can occur leading to large vibrations and failure. These instability regimes are presented as a function of speed and other parameters. Minimum damping values to prevent the instabilities are derived as a function of the gear ratio and number of pinion teeth. In addition, given some inherent damping, response amplitudes of the transmission error are presented as a function of nondimensional parameters.