The MATLAB codes for the rod, beam, unimorph, plate
and AFM models developed in Chapter7 and approximated
in Chapter 8 are respectively compiled in the subdirectories

  Rod_Code
  Beam_Code
  Unimorph_Code
  Plate_Code
  AFM_Code

The files and datafiles required for each of the models are
described below.


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(1) Rod Model

The primary file for the rod code is

  afm_disp_model_demo.m

This provides the option of characterizing the rod using a lumped
model (spring model) or the PDE model developed in Section 7.3
using the finite element techniques in Section 8.2.  The input
is taken to be a prespecified polarization which, for example,
could be computed using the models detailed in Chapter 2.  The
displacement is plotted as function of the input polarization.

Note that this code can be directly used to characterize the
rod employed in a Terfenol-D transducer once units are changed
and an appropriate input is provided.

Required Data Files:
  params_disp_ode_demo.dat
  params_disp_pde_demo.dat

Required Functions:
  setup_pde.m

Relevant Sections
  Section 7.3 (Model Development)
  Section 8.2 (Numerical Approximation)


(2) Beam Model

The main file for the beam model developed in 
Section 7.4 is

  beam_model_demo.m

which approximates the displacements of a cantilever
beam with fixed end conditions at x=0 and free end
conditions at x = L.  A cubic spline basis is used
to discretize in space and the resulting semidiscrete
system is integrated in time using the stiff solver
ode15s.m.  The forcing function consists of a 5 Hz
signal, that is uniform in space, applied for T=.74
seconds.  After that, the beam vibrations are allowed
to decay.  The model includes the input term B used
in subsequent control design.  The solution is plotted
as a function of time at the spatial point x = 3*ell/5.

Required Functions:
  bevaluate_beam.m
  control_input_beam.m
  force_beam.m
  gauss_points.m
  gauss_weights.m 
  matrix_construct_beam.m
  parameters_beam.m
  solution_beam.m
  yprime_beam.m

Relevant Sections
  Section 7.4.2 (Model Development)
  Section 8.3.1 (Numerical Approximation}


(3) Unimorph Model

The main file for the unimorph model discussed in Section 7.4.1 is

  unimorph_model_demo.m

Required Data Files:
  25volt.dat
  50volt.dat
  75volt.dat
  100volt.dat

Required Functions:
  b_input_unimorph.m
  bevaluate_unimorph.m
  force_unimorph.m
  gauss_points.m
  gauss_weights.m
  matrix_construct_unimorph.m
  parameters_unimorph.m
  solution_unimorph.m
  yprime_unimorph.m

Relevant Sections
  Section 7.4.1 (Model Development)
  Section 8.3.1 (Numerical Approximation)


(4) Plate Model

The main file for the plate model developed in Section 7.5 is

  plate_model_demo.m

which approximates the displacements of a thin plate with
clamped edges at x = 0, 0 < y < a and y = 0, 0 < x < ell 
and free end conditions at the remaining edges.  A tensored
cubic spline basis is employed in the Galerkin discretization
detailed in Section 8.4.  The applied force is uniform in
space and harmonic in time with frequencies of 10 Hz, 12 Hz,
19 Hz, 26 Hz and 37 Hz.  The solution at the opint (ell,a) is
plotted as a function of time. 

Required Functions:
  bevaluate_plate.m
  force_plate.m
  gauss_points.m
  gauss_weights.m
  matrix_construct_plate.m
  parameters_plate.m
  solution_plate.m
  yprime_plate.m 

Relevant Sections
  Section 7.5 (Model Development)
  Section 8.4 (Numerical Approximation)


(5) AFM Model

The primary file for the AFM model is

  afm_model_demo

This employs a spring model calibrated to produce a response
that is equivalent to the rod model developed in Section 7.3
with the nonlinear constitutive relation (7.3).  It yields
plots analogous to those in Section 7.3.3.  The code which
incorporates thermal relaxation is slow compared with that
which neglects relaxation.  Additional code for the polarization
model can be found in Chapter 2.

Required Data files:
  params_afm_gen_freq_demo.dat
  params_afm_nor_demo.dat
  params_afm_nor_freq_demo.dat
  params_afm_gen_demo.dat

Required Functions:
  polar_func.m
  gauss_weights.m
  gauss_points.m