For the past four years, Profs. Banks, Fitzpatrick and Tran have developed modeling courses (MA573-574) based on fundamental physical processes: heat flow, wave propagation, fluid, population and structural dynamics, electromagnetic dispersion, and optics. A major innovative component of the course has been the exposure of students to specific laboratory experiments, data collection and analysis. As usual in such modeling courses, the pedagogy involves beginning with first principles in a physical, chemical or biological process and deriving quantitative models (partial differential equations with boundary conditions, initial conditions, etc.) in the context of a specific application such as thermal nondestructive damage detection in structures, active noise suppression in acoustic chambers, smart material (piezoceramic sensing and actuation) structures vibration suppression, and fluid transport in thin film vapor deposition reactors. The students then use the models (with appropriate computational software - some from MATLAB, some from routines the instructors have developed specifically for the course) to carry out simulations and analyze experimental data. The students are exposed to experimental design and data collection through laboratory demos in certain experiments and through actual hands-on experience in other experiments.
Our experience with this approach
to teaching advanced mathematics with a strong laboratory experience has
been, not surprisingly, overwhelmingly positive. Indeed, with support from
NSF grant DUE 9751284, and Center for Research in Scientific Computation
and Department of Mathematics thu cost sharing, we have developed our own
teaching experimental laboratory. This laboratory provides capabilities
for three distinct physical experiments: heat conduction, beam vibration,
and acoustic wave propagation.
This experiment is designed for
heat transport studies in a rod. The surface temperature distribution of
the rod which is heated at one end by a soldering iron is measured by fast
response thermocouples. These thermocouples are inserted at multiple locations
(15) on the rod. The temperature measurements are recorded in real time
on a PC computer using a front-end analog multiplexer that quadruples the
number of analog input signals. The analog signals are digitized by the
MIO series multifunction DAQ boards. Copper and aluminum bars are available
in the lab to study the properties of different metals and how do they
affect the heat conduction.
A PVC pipe is used to study the
acoustic response of an enclosed sound field. A sound wave source is induced
at one end of the PVC pipe through excitation of a commercial acoustic
loudspeaker. The other end of the PVC pipe is used to study the effects
of different types of boundary conditions (reflective, absorptive, semi-infinite
axis, etc.) on the enclosed sound field. The acoustic response of the system
is measured at various locations throughout the pipe by electnet condenser
microphones. These sound level measurements are monitored in real time
by an HP oscilloscope. In addition, a HP dynamic signal analyzer is used
to record and analyze the measurement data. The dynamic analyzer is capable
of providing both real time and frequency measurement.
In this experiment, modal analysis
is performed on a cantilever beam in a "smart material" paradigm. One end
of the beam is clamped while the other end is free and the beam is mounted
with two self-sensing, self-actuating piezoceramic patches. The beam can
be excited by two sources: (a) an impulse excitation and (b) a periodic
excitation (through piezoceramic actuators). The beam transverse acceleration
is measured by accelerometers. In addition, the beam transverse displacement
can also be measured by a proximity sensor (non-contacting) and by the
piezoceramic sensors. Data are again recorded and analyzed with the HP
dynamic signal analyzer.