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Index to Animation Scripts for Dynamic Systems Written in MATLAB at the University of Wyoming

Question and comments should be directed to Raymond G. Jacquot at quot@uwyo.edu.

- Vibrations and Structural Dynamics-Lumped Parameter System
- Electrical Transmission Lines
- Beam Vibration
- Heat Conduction
- Beach Nourishment
- String Vibration
- Groundwater Drawdown
- Wave Propagation in Elastic Bars
- Static Beam Bending Problems
- Fluid Dynamics
- General Mathematics
- References

***Select and Open File then Save As a file with a .m extension or as noted in bold type.***

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#### Vibrations and Structural Dynamics-Lumped Parameter System:

- springmassforced.m Calculates, plots and animates the motion of a forced or unforced one degree-of-freedom system. Possible forcing functions are a step function, a rectangular pulse, one of three triangular pulses, a half sine pulse or a sine function. Inputs are mass, stiffness, viscous damping coefficient and type of forcing function and associated forcing function parameters or initial conditions for the unforced problem.
- shockspectra.m Calculates the shock spectrum which is the ratio of the maximum time response to the static deflection for a pulse input as a function of the dimensionless pulse width. Possible force inputs are a rectangular pulse, a half sine pulse, a one cycle sine pulse, a symmetric triangular pulse and two non-symmetric triangular pulses.
- singledegreeoffreedom.m Calculates and animates the motion of a forced single degree-of-freedom rotational system for fixed geometry, mass, stiffness and damping. The driving function is a step function of force.
- onedofbuildingforcedvib.m Calculates, plots and animates the motion of a forced or unforced one degree-of-freedom one-story building frame. Possible forcing functions are a step function, a rectangular pulse, one of three triangular pulses, a half sine pulse or a sine function. Inputs are mass, stiffness, viscous damping coefficient and type of forcing function and associated forcing function parameters or initial conditions for the unforced problem.
- onedefbuildinggroundmotion.m Calculates, plots and animates the displacement, velocity and relative displacement of a one story frame for arbitrary initial displacement and velocity and a sinusoidal ground motion. User inputs are mass, stiffness, damping, initial displacement and velocity and the amplitude and frequency of the ground motion.
- onedofbuildinggroundnotionquake.m Calculates, plots and animates the displacement, velocity and relative displacement of a one story frame for a ground motion in the form of the N-S acceleration record for the 1940 El Centro, CA earthquake. User inputs are mass, stiffness and damping. This script needs the ElCentroData6.mat file in the active directory.
- twomass.m Calculates the natural frequencies and mode shapes for an undamped system of two masses and three springs. The script calculates, plots and animates the response of the system subject to two arbitrary initial displacements and zero initial velocities.
- twodegreeoffreedom.m Calculates displacements and velocities and animates the forced response of an undamped two degree-of-freedom system involving two booms and two springs. The first graphics window makes clear the configuration and the values of the system variables.
- twostoryfreevibmodalresp.m Calculates and plots the mode shapes and the free vibration response of the two story building frame to arbitrary initial displacements and zero velocities. The responses are animated. Uses uncoupled equations in the normal coordinates to calculate the response.
- twostoryforcedvibmodalresp.m Calculates, plots and animates the forced vibration response of the three story building to a 3000 kip decaying blast force applied to the second floor of the structure (half that for the roof assembly)for zero initial displacements and zero initial velocities. Uses the uncoupled equations in the normal coordinates to calculate the response using Chopra's interpolation of excitation method.
- threestoryfreevibmodalresp.m Calculates and plots the mode shapes and the free vibration response of the three story building frame to arbitrary initial displacements. The responses are animated. Uses uncoupled equations in the normal coordinates to calculate the response.
- threestoryforcedvibmodalresp2.m Calculates, plots and animates the forced vibration response of the three story building to a 3000 kip decaying blast force applied to each floor of the structure (except the roof assembly) for zero initial displacements and velocities. The script uses the uncoupled equations in the normal coordinates to calculate the response.
- threestorygroundmotion3.m Calculates, plots and animates the response of a three story building to a sinusoidal ground motion of fixed amplitude and frequency. Responses are calculated in the normal coordinates. Inputs are the amplitude and frequency of the ground motion.
- threestorygroundmotionquake3.m Calculates, plots and animates the three story building response to the N-S component of the 1940 El Centro, CA earthquake motion, Responses are calculated in the normal coordinates. Needs the ElCentroData6.mat file in the active directory.
- threestoryfreqresp.m Calculates the steady-state sinusoidal response of the three story frame using the phasor method. The frame is forced at the roof level with p3(t)=3000 cos(12t) kips.
- chimneyforcedvib.m Calculates natural frequencies, mode shapes, and response of the reinforced concrete chimney in Example 15.1 in Structural Dynamics by A. K. Chopra to a suddenly applied step load of 1000 kips at the tip of the chimney. Animates the motion. Calculations done in the uncoupled equations of the normal coordinates.
- ElCentroreponsespectrum.m Calculates and plots the earthquake response spectrum for the N-S component of the 1940 El Centro, CA earthquake using the procedure outlined in Chapter 6 of Structural Dynamics by A. K. Chopra. Also plotted are the pseudo-velocity spectrum and the pseudo-acceleration spectrum for a variety of damping ratios. The independent variable in the spectrum is the undamped natural period. Needs the ElCentroData6.mat file in the active directory.
***For ElCentroData6 and GilroyData, download files and remove ".txt" extension so the filename reads "filename.mat"**- ElCentroData6.mat A MATLAB data file with 1560 entries which are samples of the N-S acceleration of the 1940 El Centro., CA earthquake. The accelerations are in g's and sampled at a rate of 50 samples per second or with a sampling period is 0.02 sec. (20 ms).
- GilroyData.mat A MATLAB data file with 7989 entries which are samples of the horizontal acceleration of the Gilroy, CA earthquake (date unknown). The accelerations are in g's and sampled at a rate of 200 samples per second or with a sampling period of 0.005 sec. (5 ms).

#### Electrical Transmission Lines:

- tls.m Displays solution to lossless, sinusoidally driven transmission line, has GUI. Requires MATLAB 7.0 or newer.
- tls.png Contains a drawing used by tls.m.
***For tls.fig, download file and remove ".txt" extension so the filename reads "filename.fig"**- tls.fig Contains the graphics for the GIU used by tls.m.
- transmline2.m Displays solution to lossless, sinusoidally driven transmission
line the same as tls.m.
Does not have a GUI and user must change parameters in the script.
Specific source and line parameters are specified in the script and the
input is the load impedance Z
_{L}. - lossytransmline.m
Displays solution to a lossy, sinusoidally driven transmission line.
Specific source and line parameters are specified in the script. Input
is the load impedance Z
_{L}. - transmwave3.m
Displays the solution to lossless line driven by a d.c. source.
Specific source and line parameters are specified in the script and the
load resistance R
_{L}is an input. - transmlinepulse.m
Displays the solution to lossless line driven by a rectangular pulse.
Source and line parameters are specified in the script and the pulse
width and the load resistance R
_{L}are inputs. - TmlSqWv.m
Displays the line voltage for a lossless transmission line driven by a
square wave source. All waveforms are represented by Fourier series
truncated after the 41
^{st}term.

#### Beam Vibration:

- beamvibration.m
Displays the solution to a free vibration of a cantilever beam
from an initial displacement. Uses generalized Fourier series in the
orthogonal beam functions. The initial deflection shape is y(x,0)=y
_{0}[0.667(x/L)^{2}+0.333(x/L)^{3}]. - cantvib3.m Solves the same problem as beamvibration.m except the beam is discretized spatially using 16 nodes and finite differences in space.
- clampedclampedbeam.m Displays the free vibration solution to a clamped-clamped beam starting with an initial condition y(x,0)=2(x/L)
^{2}-(x/L)^{3}-4(x/L)^{4}+3(x/L)^{5}. Solution is in generalized Fourier series in the orthogonal beam functions. - cantbeamimpulse.m Displays the response of a cantilever beam driven by an impulse function of intensity I
_{0}at a location x=a. Input quantity is the impulse location a/L. Solution is in generalized Fourier series in the orthogonal beam functions. - forcedbeamvibration.m Displays the vibration of an undamped cantilever beam driven by a uniform distributed force f
_{0}which is constant in time and suddenly applied at t=0. Solution is in generalized Fourier series in the orthogonal beam functions. - dampedbeams.m Displays the motions of damped (or undamped) simply supported, cantilever, clamped-pinned and clamped-clamped beams to point or uniformly distributed loads or initial conditions. The temporal form of the load can be an impulse, step or sinusoid. The damping is assumed to be proportional to local velocity (viscous). Generalized Fourier series solution.
- BR.m Displays the motion of a damped beam as in dampedbeams.m except it is done with a GUI.
***For BR.fig, download file and remove ".txt" extension so the filename reads "filename.fig"**- BR.fig Contains the graphihcs for the GUI used by BR.m
- cantbeamanimation.m Displays the steady-state motion of a cantilever beam excited by a sinusoidal displacement of amplitude Y
_{0}at the fixed end. - canttipforceanimation.m Displays the steady-state sinusoidal vibration of a
cantilever beam forced at the free end with a sinusoidal force of amplitude F
_{0}. - movingload2.m Displays the motion of a simply supported beam with a moving load P starting from the left end with a user controlled velocity. The input variable is the ratio of the transit time to the first natural period of the beam.
- ssbeamdispex.m Displays the steady-state motion of a simply supported beam driven by a
sinusoidal displacement of amplitude Y
_{0}at the left end.

#### Heat Conduction:

- conduction.m Displays solution to the diffusion equation for T=T
_{0}at left boundary and T=0 at right boundary, zero initial temperature, Fourier series solution. - conduction2.m Displays solution to the diffusion equation for T=T
_{0}at left boundary and T=T_{0}at right boundary, zero initial temperature, Fourier series solution. - conduction3.m Displays solution to the diffusion equation for T=T
_{0}at left boundary and T=0 at right boundary, zero initial temperature. This is a finite difference solution in space. - conduction4.m Displays solution to the diffusion equation with convective
boundaries for T=T
_{0}at left boundary and T=0 at right boundary, zero initial temperature. This is a finite difference solution in space. - conduction5.m Displays solution to the diffusion equation for T=0 at left
boundary and T=0 at right boundary, T
_{0}initial temperature. Fourier series solution. - conduction6.m Displays temperature distribution in a slab with both faces
insulated and initially the left half at T
_{0}and the right half at zero temperature. Fourier series solution. - infiniteslab.m Displays the temperature in an infinite slab with initial temperature
T
_{0}between -L and L at t=0 and zero elsewhere. Fourier series solution. - convboundaries.m Displays temperatures in a finite slab with convective heat
transfer coefficients h
_{1}and h_{2}on the left and right boundaries respectively. The film coefficients are assumed to be the same on both the left and right. Fourier series solution. - conductioncyl.m
Displays radial temperatures in an infinite cylinder with zero initial
temperature and temperature at r = R suddenly elevated to T
_{0}at t = 0. Generalized Fourier series solution in Bessel functions. - heatedcyl.m Displays radial temperature distribution in an infinite cylinder of radius R that is heated by a uniform volumetric generation of heat q as in ohmic heating of an electrical conductor. The initial temperature is zero and the boundary temperature is zero. Generalized Fourier series solution in Bessel functions.
- semiinfiniteslabstep.m Displays temperatures in semiinfinite medium (halfspace) when the temperature at x = 0 suddenly changes from 0 to T
_{0}at t = 0 with the halfspace initially at zero temperature. Fourier transform solution. - semiinfiniteslab.m Displays steady-state sinusoidal temperatures in a semi-infinite slab when the surface at x=0 temperature varies sinusoidally. Phasor Solution.
- conductionsphere.m Displays the thermal response of a homogeneous sphere driven from zero initial temperature T
_{0}by a sudden temperature change T_{H}at the surface r=R. Fourier series solution. - conductionspheresinusoid.m Displays the steady-state thermal response of a sphere to a sinusoidal temperature variation of amplitude T
_{0}at the surface r=R. The input is dimensionless sinusoid frequency ωR^{2}/κ where κ is the diffusivity of the material of the sphere. Phasor solution. - conductionspherecooling.m Displays the thermal response of a homogeneous sphere driven from initial temperature T
_{0}by a sudden temperature change to zero at the surface at r=R. Fourier series solution. - conductionspheresource.m Displays the temperature in a sphere of radius R with a point source of heat Q
_{0}and the origin and a temperature of zero at r=R and zero initial temperature everywhere. Fourier series solution. - insulatedslab.m Displays the temperature in a slab of thickness L and insulated
on the x = L face with a suddenly imposed temperature T
_{H}on the x = 0 boundary. Initial temperature is T_{0}. Fourier series solution. - conductionslabsinusoid.m Displays the steady-state thermal response of a
slab to a sinusoidal temperature variation of amplitude T
_{0}at the surface x = 0. Tha slab is insulated at x=L. The input is dimensionless sinusoid frequency ωL^{2}/κ where κ is the diffusivity of the material of the sphere. Phasor solution.

#### Beach Nourishment:

- beachnourishment.m Displays the solution to the diffusion equation for an infinite domain with an initial rectangular beach projection planform. Fourier transform solution.

#### String Vibration:

- stringanimation.m Displays the d’Alembert solution to the plucked string problem. Input is the nondimensional location of the pluck, a/L.
- stringvibration.m Displays the Fourier series solution to the plucked string problem. Input is the nondimensional location of the pluck, a/L
- displacementexcitedstring.m Displays standing waves in a taut string fixed at the right end and with sinusoidal motion of amplitude Y
_{0}at the left end. Input is the ratio of the frequency of excitation to the first natural frequency of the string. Phasor solution. - forcedstring.m Displays the motion of a taut string forced at x=a by a sinusoidal force with amplitude P
_{0}. Inputs are the ratio of the forcing frequency to the first natural frequency of the string and the nondimensional location of the force a/L. Phasor solution. - stringspring.m Displays the motion of a taut string, fixed at x = 0 and terminated at x = L with a transverse spring. Input is the stiffness parameter related to the stiffness of the spring. Generalized Fourier series solution.

#### Groundwater Drawdown:

***For the framedata.mat, download file and remove ".txt" extension so the filename reads "filename.mat"**- gndw1.m Solves two layer aquifer problem and stores the solution in a data file framedata.mat to be played back by gndw2.m (Jacob model).
- framedata.mat Contains data file generated by the gndw1.m script to be played back in gndw2.m.
- gndw2.m Displays data generated in gndw1.m which is loaded as an array saved in framedata.mat.
- gndw3.m Solves and displays the solution to the one layer aquifer (Theis model).

#### Wave Propagation in Elastic Bars

- elasticbar.m Displays the solution to an elastic bar fixed on the left end and free on the right end with zero initial velocity and an initial linear displacement field (constant strain) at t = 0. Fourier series solution.
- elasticbar2.m Displays the solution to an elastic bar fixed on the left end with a suddenly applied constant force F on the right end and no initial velocity or displacement. Fourier series solution.
- elasticbar4.m
Displays the solution to an elastic bar fixed at the left end, free at
the right end, driven by a compressive impulse of intensity I
_{0}at the free end. The bar has no initial deformation or velocity. - torsionbar.m Displays torsional wave propagation in a round bar with an initial twist proportional to the distance from the fixed end and no initial velocity. Fourier series solution.
- torsionbar2.m Displays torsional wave propagation in a round bar fixed at the left end with a suddenly applied constant torque T to the right end and no initial angular twist or velocity. Fourier series solution.

#### Static Beam Bending Problems

- ssbeamoneload.m Displays the static shear, bending moment and deflection for a simply-supported beam as a load P traverses from left to right.
- ssbeamtwoloads.m Displays the static shear, bending moment and deflection as two loads of value P traverse a simply-supported beam. The loads are 30% of the span length apart in spacing.
- cantileverbeamoneload.m Displays the shear, bending moment and deflection as a load P traverses a cantilever beam from the fixed end to the free end.

#### Fluid Dynamics

- Blasius.m Displays the flowfield for the viscous, incompressible flow over a flat plate by first solving the Blasius equation. The solutions for the velocity field come from the solution to the Blasius equation and the derivatives thereof.

#### General Mathematics

- centrallimit.m Displays the probability density functions (from a histogram) for the sum of n random uniformly distributed variables where n varies from zero to 20. At each step the sum is scaled so as to have zero mean and unity variance.
- GibbsPhenom.m Animates the evolution of the Gibbs phenomenon for a Fourier series representation of a square wave by continusously summing the terms and displaying the resulting waveform for 61 terms.
- steppedshaft.m Displays the load, shear, moment and deflection diagrams for a shaft with two arbitrarily located simple supports, up to 4 step changes in cross section and an arbitrary number of loads, all arbitrarily located.
- criticalspeed.m Calculates the critical speed of a shaft of length L with two simple supports located at arbitrary locations. The shaft can have step changes in cross-section and can have discrete masses at arbitrary locations. Uses Rayleigh's method. Displays the shaft and the fundamental mode shape.

References