About

James M. Sloss is an Emeritus Faculty member in the Department of Mathematics at the University of California, Santa Barbara. His specialization is in Partial Differential Equations. He is associated with the department located in South Hall, Room 6607, and can be contacted via phone at (805) 893-5808 or through the department's email. His office hours are Monday to Friday from 9 am to 12 pm and 1 pm to 4 pm. His research focus is on Partial Differential Equations, contributing to the mathematical understanding and development within this field.

Research topics

• Mathematics
• Mathematical analysis
• Computer science
• Applied mathematics
• Physics

Selected publications

• Effect of vibration control on the frequencies of a cantilever beam with non-collocated piezo sensor and actuator

  IET Control Theory and Applications · 2011-10-05 · 8 citations

  article

  Displacement feedback control of a cantilever beam is studied using non-collocated piezoelectric patch sensors and actuators. The solution to the problem is obtained using two different methods, one analytical and another numerical. The analytical method involves an integral equation formulation of the problem where the eigensolutions of the integral equation are shown to be the eigensolutions of the governing differential equation of motion of the smart beam. This approach eliminates the difficulties associated with discontinuities caused by patch sensors and actuators which introduce Heaviside functions and derivatives of the Heaviside functions into the differential equation formulation. The numerical method of solution uses a finite-element model of the controlled beam with modified beam element mass and stiffness matrices to account for the piezo patches and the control effect. The control circuit consists of a piezoceramic and polyvinylidene fluoride sensor patch and a lead zirconium titanate actuator patch. The mass and stiffness of the piezoceramic actuator patch are taken into account in the mass and stiffness calculations. Numerical examples with non-collocated sensor and actuator patches are presented and the first three natural frequencies are given using the integral equation and the finite-element methods. The results of these methods match very closely which provides a verification of the results.

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• Velocity feedback control of piezo-beams: integral equation and finite element approaches

  2010-04-11

  article

  The phosphorylation and dephosphorylation of the dihydropyridine-sensitive Ca2+ channel was studied in transverse-tubule membranes isolated from rabbit skeletal muscle. Exposure of these membranes to either the cAMP-dependent protein kinase or a Ca2+/calmodulin-dependent protein kinase resulted in a rapid phosphorylation of a protein with properties similar to the major component of the skeletal muscle Ca2+ channel. The molecular mass of the phosphoprotein was 140 or 160 kDa, depending on the electrophoretic conditions. The stoichiometry of the phosphorylation was calculated to be 0.4-1.0 mol of phosphate per mol of protein. Neither the rate nor the extent of phosphorylation was affected by dihydropyridines. Limited proteolytic digestion of the protein that had been phosphorylated by either or both protein kinases yielded a single phosphopeptide of approximately equal to 5.4 kDa. The Ca2+-dependent phosphatase calcineurin dephosphorylated the membrane-bound Ca2+ channel that had been previously phosphorylated by either protein kinase. The results suggest that the major component of the dihydropyridine-sensitive Ca2+ channel from skeletal muscle can be effectively phosphorylated and dephosphorylated in its native state by cAMP- and Ca2+-dependent processes.

  PublisherDOI

• Active Displacement Feedback Control of a Smart Beam: Analytic and Numerical Solutions

  2009-03-01 · 1 citations

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  Abstract: Active vibration control of a smart beam with integrated piezoceramic actuator and sensor patches is considered. An analytical solution of this problem is worked out for the case of the controlled beam including the mass and stiffness of the piezoceramic patches. The equation of motion for the controlled beam includes Heaviside functions and derivatives of the Heaviside function due to finite patch lengths. This makes the problem difficult to solve using conventional methods. An integral equation is introduced, where the eigensolutions of the integral equation are eigensolutions of the differential equation of motion for the controlled beam. A finite element model of a controlled beam is also formulated. The model contains modified beam element mass and stiffness matrices to account for the piezo patches and control effect. Two case studies are presented and the first three natural frequencies and mode shapes are found using the finite element and integral equation solutions. The results from the integral equation solution match very closely the results from the finite element solution.

  Publisher

• Piezo Control of Free Vibrations of Damped Beams with Time Delay in the Sensor Feedback

  Mechanics of Advanced Materials and Structures · 2009-06-19 · 6 citations

  article

  The effect of the time delay between the sensor output and actuation is studied on the displacement and velocity feedback control of a cantilever beam. The system consists of a piezoelectric sensor and actuator pair bonded to an Euler-Bernoulli beam to form an actively controlled laminated structure. The effects of Kelvin-Voigt damping are also included in the problem. The piezoelectric actuators and sensors are taken as patches of partial length which leads to a differential equation formulation with discontinuities. The numerical solution is obtained by replacing the original formulation with an integral equation which is solved by expanding the state function in terms of the eigenfunctions of the freely vibrating beam. This approach leads to an infinite set of linear equations which can be solved with a high degree of accuracy by computing the characteristic equation using a small number of terms. Numerical results are given to analyze the control effectiveness in terms of changes in the natural frequencies for various gains, damping coefficients and time delays.

  PublisherDOI

• Analytic and Finite Element Solutions for Active Displacement Feedback Control using PZT Patches

  Journal of Vibration and Control · 2009-10-28 · 6 citations

  article

  An analytical solution to the equation of motion of a beam controlled with piezoceramic (PZT — lead zirconate titanate) sensor and actuator patches is proposed. The contribution of the mass and stiffness of the piezoceramic patches to the piezo structure are taken into account. The equation of motion for the controlled structure includes Heaviside functions and derivatives of the Heaviside function due to finite patch lengths making the equation of motion difficult to solve using conventional methods. In the present study, an integral equation is introduced where the eigensolutions of the integral equation are eigensolutions of the differential equation of motion for the controlled beam. A finite element model of the controlled beam is also formulated. The model contains modified beam element mass and stiffness matrices to account for the piezo patches and control effect. Two case studies are presented and the first three natural frequencies and mode shapes are found using the integral equation and finite element solutions. The results from the integral equation solution match very closely the results from the finite element solution.

  PublisherDOI

• Placement of Multiple Piezo Patch Sensors and Actuators for a Cantilever Beam to Maximize Frequencies and Frequency Gaps

  Journal of Vibration and Control · 2009-02-04 · 17 citations

  article

  Active vibration control is implemented using multiple piezoelectric actuators and sensors bonded to the top and bottom surfaces of a cantilever beam. The control is exercised using closed-loop displacement feedback. The objective of the study is to determine the optimal locations of patch actuators and sensors such that the fundamental frequency or the frequency gap between higher frequencies of the beam is maximized. Maximizing the fundamental frequency is useful to avoid resonance when the excitation frequency is less than the fundamental frequency. Alternatively, the excitation frequency can also be placed in between two higher order frequencies and the difference between the two higher order frequencies can be maximized. In the present study the fundamental frequency and the frequency gaps between the higher order frequencies are investigated with respect to actuator and sensor locations with a view towards determining their optimal locations for largest frequency gaps. The locations of the piezo patches to maximize first, second and third frequencies are also given. The differential equation governing the vibrations of a feedback controlled beam/piezo patch system is solved using an integral equation approach. The numerical results are given for various patch combinations and the optimal locations of the actuators and the sensors are determined. It is observed that the optimal locations of the piezo patches depend on the specific frequency gap as well as the patch configurations.

  PublisherDOI

• Optimal multi‐interval control of a cantilever beam by a recursive control algorithm

  Optimal Control Applications and Methods · 2008-08-22 · 3 citations

  article

  Abstract The optimal‐distributed control of a transversely vibrating cantilever beam is studied with the objective of minimizing the deflection and velocity in a given period of time with the minimum possible expenditure of force. The beam undergoes transient vibrations and is subject to given displacement and velocity initial conditions. The control is exercised by means of a transversely distributed force referred to as the control force. In the present study, a multi‐interval optimal control method is developed with the application of a maximum principle. The method consists of dividing the control duration into several intervals and using the maximum principle to obtain the optimality conditions at each interval. The explicit solutions for a cantilever beam are obtained by a recursive algorithm that takes the final conditions of the last interval as the initial conditions of the next interval. The formulation and the method of solution are suitable and convenient for digital computation. Numerical results are given, which compare the deflections, velocities and the control force under the optimal multi‐interval control with those under the optimal single‐interval control. Copyright © 2008 John Wiley & Sons, Ltd.

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• Integral equation approach for piezo patch vibration control of beams with various types of damping

  Computers & Structures · 2007-03-28 · 25 citations

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• Deflection control of elastically restrained laminated frames under deterministic and uncertain loads using induced strain actuators

  Composite Structures · 2006-08-25 · 4 citations

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• A maximum principle approach to optimal control for one-dimensional hyperbolic systems with several state variables

  Journal of the Franklin Institute · 2006-03-30 · 5 citations

  articleSenior author
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Frequent coauthors

• John C. Bruch

  University of California, Santa Barbara

  109 shared

• Ibrahim Sadek

  Helwan University

  81 shared

• Sarp Adali

  University of KwaZulu-Natal

  69 shared

• Ramin S. Esfandiari

  12 shared

• J. Remar

  9 shared

• C. Spier

  University of California, Santa Barbara

  6 shared

• M. Dormiani

  Stanford Synchrotron Radiation Lightsource

  3 shared

• Özcan Kayacık

  University of California, Santa Barbara

  3 shared