MATLAB Functions in CD-ROMruk.usc.edu/Books/yang-sssd/key features/MATLAB functions in CD-… · MATLAB Functions in CD-ROM The book “Stress, Strain, and Structural Dynamics”

MATLAB Functions in CD-ROM The book “Stress, Strain, and Structural Dynamics” has an attached CD-ROM that contains 16 toolboxes of MATLAB functions for interactive computing in engineering analysis, one for each chapter of the book. These toolboxes are

• Toolbox for Chapter 2 Static Analysis of Euler-Bernoulli Beams • Toolbox for Chapter 3 Static Analysis of Bars, Shafts and Strings • Toolbox for Chapter 4 Buckling Analysis of Columns • Toolbox for Chapter 5 Stress Analysis in Two-Dimensional Problems • Toolbox for Chapter 6 Static Analysis of Constrained Multispan Beams • Toolbox for Chapter 7 Static Analysis of Plane Trusses • Toolbox for Chapter 8 Static Analysis of Plane Frames • Toolbox for Chapter 9 Dynamics of Particles and Rigid Bodies • Toolbox for Chapter 10 Vibration Analysis of One-Degree-of-Freedom Systems • Toolbox for Chapter 11 Vibration and Control of Multiple-Degree-of-Freedom Systems • Toolbox for Chapter 12 Dynamics and Control of Euler-Bernoulli Beams • Toolbox for Chapter 13 Dynamic Analysis of Bars, Shafts, and Strings • Toolbox for Chapter 14 Dynamic Analysis of Constrained, Combined, and Stepped

Beams • Toolbox for Chapter 15 Static Analysis of Linearly Elastic Bodies • Toolbox for Chapter 16 Free Vibration of Membranes and Plates • Toolbox for Appendix A.12 Inverse Laplace Transform via Partial Fraction Expansion

The main functions contained these toolboxes given in the following pages.

1

Toolbox for Chapter 2 Static Analysis of Euler-Bernoulli Beams

System Setup

setbeam Set up beam parameters and boundary conditions Window 3.1

Static Analysis of Beams

beamf Compute beam response to external loads Window 3.2 beamb Compute beam response to boundary disturbances Window 3.4 mathf Obtain exact analytical expressions of beam response subject

to an external load Window 3.5

mathb Obtain exact analytical expressions of beam response subject to boundary disturbances

Window 3.6

maxresp Determine maximum beam response and location Window 3.7 reactf Obtain reaction forces at beam boundaries Window 3.8 plotbeam Plot spatial distribution of beam response Window 3.3 minertia Compute moments of inertia of beam cross section area Window 4.1

Utilities

systinfo Display beam parameters and boundary conditions Window 3.9 setxpt setxpt1

Select or reset spatial points for computation

Window 3.10

getxpt Get access to spatial points that are set up for computation Window 3.11TBdemo Show how the Toolbox works and what it can do Section 2.1 TBinfo Display the information of the Toolbox Section 2.1 RunEx Run all the numerical examples contained in this chapter Section 2.1 The main functions contained these toolboxes given in the following pages. For demonstrative example of what these functions can do click the button Demo Examples in the home page.

2

Toolbox for Chapter 3 Static Analysis of Bars, Shafts and Strings

System Setup

setbar Set up parameters and boundary conditions for a bar Window 3.1 setshaft Set up parameters and boundary conditions for a shaft Window 3.1 setstring Set up parameters and boundary conditions for a string Window 3.1

Static Analysis

force2os Compute system response subject to external loads Window 3.2 bd2os Compute system response due to boundary disturbances Window 3.3 plot2os Plot spatial distribution of system response, and output

computed response data Window 3.4

Stepped Bars and Shafts

setbar2 Set up a stepped bar Window 4.1 setshaft2 Set up a stepped shaft Window 4.1 step2osfb Compute the response of a stepped bar or stepped shaft subject

to external loads and/or boundary disturbances Window 4.2

plot2os2 Plot spatial distribution of the response of a stepped bar or shaft, and output computed response data

Window 4.3

Utilities

TBdemo Show how the Toolbox works and what it can do Section 3.1 TBinfo Show the information of the Toolbox Section 3.1 RunEx Run all the numerical examples contained in this chapter Section 3.1 systinfo systinfo2

Display system parameters and boundary conditions Sections 3.3.1 & 3.4.2

The main functions contained these toolboxes given in the following pages. For demonstrative example of what these functions can do click the button Demo Examples in the home page.

3

Toolbox for Chapter 4 Buckling Analysis of Columns

Uniform Columns

setcolumn Compute the buckling loads and mode shapes of a uniform column

Window 2.1

eigcolumn Determine buckling loads and mode shapes Window 2.2 plotmsh Plot and output buckling mode shapes Window 2.3 eccenload Compute the response of an eccentrically loaded column at a

point versus the axial load Window 2.4

eccenload1 Compute the spatial distribution of the response of an eccentrically loaded column

Window 2.5

beamcolumn Compute the spatial distribution of the response of a beam-column subject to a transverse load

Window 2.6

beamcolumn1 Compute the response of a beam-column at a particular point versus the axial load

Window 2.7

systinfo Display the information on the column and its eigensolutions Section 4.2.2

Stepped and Nonuniform Columns

setcolumn2 Compute the buckling loads and mode shapes of a constrained stepped column

Window 3.1

plotmsh2 Plot and output buckling mode shapes Window 3.2 nonucolumn Compute the buckling loads and mode shapes of a nonuniform

column Window 3.3

systinfo2 Display the information of a stepped or nonuniform column Section 4.3

Utilities

TBdemo Show how the Toolbox works and what it can do Section 4.1 TBinfo Show the information of the functions in the Toolbox Section 4.1 RunEx Run all the numerical examples contained in this chapter Section 4.1 The main functions contained these toolboxes given in the following pages. For demonstrative example of what these functions can do click the button Demo Examples in the home page.

4

Toolbox for Chapter 5 Stress Analysis in Two-Dimensional Problems

Stress

stressTF Transform stress components from an element to another of different orientation

Window 2.1

pristress Compute principal stresses and maximum in-plane shear stress, and plot Mohr’s circle for plane stress

Window 2.2

Strain

strainTF Transform strain components from an element to another of different orientation

Window 2.3

pristrain Compute principal strains and maximum in-plane shear strain, and plot Mohr’s circle for plane strain

Window 2.4

strgauges Determine strain components based on the readings from a set of three strain gauges

Window 2.5

Material Properties

hooks2e Compute strain components based on Hooke’s law Window 2.6 hooke2s Compute stress components based on Hooke’s law Window 2.6 failure2D Tell if a material under a given state of in-plane stress will fail,

based on one of three commonly used criteria of failure Window 2.7

Utilities

TBdemo Show how the Toolbox works and what it can do Section 5.1 TBinfo Show the information of the Toolbox Section 5.1 RunEx Run all the numerical examples contained in this chapter Section 5.1 The main functions contained these toolboxes given in the following pages. For demonstrative example of what these functions can do click the button Demo Examples in the home page.

5

Toolbox for Chapter 6 Static Analysis of Constrained Multispan Beams

System Setup

setbeam2 Set up beam parameters, boundary conditions and constraints Window 3.1

Static Analysis of Beams

Compute beam response subject to external loads Window 3.2

Compute beam response due to boundary disturbances Window 3.3

Compute beam response due to support settlements Window 3.4

beam2fbs

Compute total response due external and boundary disturbances and support settlement

Window 3.5

plotbeam2 Plot spatial distribution of beam response Window 3.6

infline Plot influence lines for response at a specific point Window 3.7

inflreact Plot influence lines for reactions at a support or node Window 3.8

Utilities

systinfo Display the information of a multispan beam Section 6.3.1

TBdemo Show how the Toolbox works and what it can do Section 6.1

TBinfo Show the information of the Toolbox Section 6.1

RunEx Run all the numerical examples contained in this chapter Section 6.1 The main functions contained these toolboxes given in the following pages. For demonstrative example of what these functions can do click the button Demo Examples in the home page.

6

Toolbox for Chapter 7 Static Analysis of Plane Trusses

Static Analysis of Trusses

settruss Set up parameters and boundary conditions of a truss Window 3.1

Compute truss response subject to external loads Window 3.2

Compute truss response due to support settlement Window 3.3

Compute truss response due to fabrication errors Window 3.4

Compute truss response due to thermal effects Window 3.5

trussresp

Compute the total response of a truss Window 3.6

plottruss Display the undeformed and deformed configurations of a truss Window 3.7

Utilities

systinfo Display truss parameters and boundary conditions Section 7.3.1




7

Toolbox for Chapter 8 Static Analysis of Plane Frames

Static Analysis of Frames

setframe Set up parameters and boundary conditions of a frame Window 3.1

frameresp Compute frame response subject to external loads Window 3.2

Compute frame response due to support settlement Window 3.3

Compute the total response of a frame Window 3.4

maxresp Obtain maximum response of a frame and locations Window 3.5

reactf Obtain reactions at supports Window 3.6

plotframe Plot undeformed and deformed configurations of a frame Window 3.7

membresp Compute response of frame members Window 3.8

plotmember Plot response along a frame member, and show response at the two ends of the member

Window 3.9

Utilities

systinfo Display frame parameters and boundary conditions Window 3.1




8

Toolbox for Chapter 9 Dynamics of Particles and Rigid Bodies

Dynamics of Particles

resultant Compute resultant force and moment of a system of forces Window 2.1 part2d Simulate the motion for a particle in two dimensions Window 2.2 part3d Simulate the motion for a particle in three dimensions Window 2.2

partmotion Animate the motion of a particle in two or three dimensions Window 2.3 mscenter Compute total mass and mass center of a particle system Window 2.4

Rigid Body Dynamics in Two Dimensions

massmin Compute mass moments of inertia of a rigid body Window 3.1 rigid2d Plot dynamic response of a rigid body in plane motion Window 3.2 animotion2d Animate the two-dimensional motion of a rigid body Window 3.3

Rigid Body Dynamics in Three Dimensions

inertiaTF Transform the moments and products of inertia from one coordinate system to another

Window 4.1

prinertia Determine the principal axes and principal moments of inertia of a rigid body

Window 4.2

axisym3d Plot Euler angles and angular velocities of an axisymmetric rigid body

Window 4.3

eulermotion Animate the motion of an axisymmetric rigid body by using Euler angles

Window 4.4

Utilities

TBdemo Show how the Toolbox works Section 9.1 TBinfo List MATLAB functions contained in this Toolbox Section 9.1 RunEx Run all the numerical examples contained in this chapter Section 9.1 The main functions contained these toolboxes given in the following pages. For demonstrative example of what these functions can do click the button Demo Examples in the home page.

9

Toolbox for Chapter 10 Vibration Analysis of One-Degree-of-Freedom Systems

System Setup set1dof Input system parameters (m, c, k) Window 2.1 set1dof2 Input system parameters ( , ,nω ξ m) Window 2.1

Time Response freevib Compute and display free response Window 3.1 forcedvib Compute and display forced response Window 3.2 stepchract Compute maximum overshoot, rise time and settling time of

step response of an underdamped system Section 10.3.3

compltvib Plot total response due to both initial and external disturbances Window 3.9 energy Compute and display mechanical energy function Window 3.11 stepcharact Compute characteristic parameters of step response Section 10.3.3plotvib Plot time response Window 3.12 getpts Get times of simulation Window 3.13

Analytical Vibration Solutions forcedANL Obtain analytical expressions of forced response Window 4.1 plotANL Plot forced response by exact analytical solutions Window 4.2

Frequency Response harmonic Plot frequency response to a harmonic excitation Window 5.1 plotfr Plot frequency response from computed data Window 5.2 normhar Plot normalized frequency response Window 5.3 transm Plot force or displacement transmissibility due to harmonic

excitation Window 5.4

basevib Plot frequency response to a harmonic base excitation Window 5.5 unbalance Plot the frequency response of a rotating machine with an

unbalanced mass Window 5.6

isolator Design the parameters of a vibration isolator Window 5.7 Response to Periodic Excitations

periodic Plot steady-state response to a periodic excitation Window 6.1 fseries Obtain the Fourier series for a periodic forcing function Window 6.2

Nonlinear Vibration setNL Specify a 1-DOF nonlinear vibration system Window 7.1 NLvib Obtain numerical solution of nonlinear vibration Window 7.2

Utilities TBdemo Show how the Toolbox works and what it can do Section 10.1 TBinfo Show the information of the Toolbox Section 10.1 RunEx Run all the numerical examples contained in this chapter Section 10.1 systinfo Display system information and step response specifications Window 2.1

10

Toolbox for Chapter 11 Vibration and Control of Multiple-Degree-of-Freedom Systems

System Setup

setmdof Input matrices [M], [C] and [K], and compute eigensolutions Window 2.1

Modes of Vibration animode Animate vibration in a particular mode Window 2.3 chareq Obtain characteristic equation ( )2[ ] [ ] [ ] 0s M s C Kdet + + = Section

11.2.3 geteig Output eigensolutions computed by function setmdof Window 2.2

Time Response freeMD Obtain free response by modal analysis Window 3.1 forcedMD Obtain forced response by modal analysis Window 3.2 freeLT Obtain free response by inverse Laplace transform Window 3.3 forcedLT Obtain forced response by inverse Laplace transform Window 3.4 freeRK Compute free response by Runge-Kutta algorithm Window 3.6 forcedRK Compute forced response by Runge-Kutta algorithm Window 3.7 respCV Compute system response based on analytical expressions

obtained by freeMD, forcedMD, freeLT, and forcedLT Window 3.5

plotvib Plot time response obtained by functions freeRK, forcedRK, respCV, ctrmdof1 and ctrmdof2

Window 3.8

Frequency Response frfun Obtain frequency response (magnitude and phase) Window 3.9 plotfr Plot frequency response Window 3.10

Dynamic Vibration Absorption

absorb Characterize the dynamic behaviors of a vibrating system combined with an undamped vibration absorber

Window 4.1

absorbdmp Plot the steady-state response of a vibrating system combined with a damped vibration absorber

Window 4.2

absorbmsratio Obtain a range of mass ratio for vibration absorber design Window 4.3 absorbopt Optimally tune a damped absorber Window 4.4

Transfer Function and Green’s Function

getTF Obtain transfer function ( ) 12( ) [ ] [ ] [ ] [ ]fH s s M s C K B−

= + + Window 5.1

getGF Obtain Green’s function [ ]1( ) ( ) [ ]fG t H s B−=L Window 5.2

pzTF Compute transfer function poles and zeros Window 5.3

Vibration Control System ssmdof1 Obtain a state representation for vibration control of a

mechanical system Window 6.1

11

clpmdof1 Obtain the closed-loop state equation for vibration control Window 6.2 ctrmdof1 Plot the response of a vibration control system Window 6.4

Position Control System ssmdof2 Obtain a state representation for position control of a

mechanical system Window 6.1

clpmdof2 Obtain the closed-loop state equation for position control Window 6.3 ctrmdof2 Plot the response of a position control system Window 6.5

Utilities

systinfo Display information on system parameters and eigensolutions Section 11.2.3

TBdemo Demonstrate how the Toolbox works and what it can do Section 11.1 TBinfo Show the solution procedure of the Toolbox Section 11.1 RunEx Run all the numerical examples contained in this chapter Section 11.1


12

Toolbox for Chapter 12 Dynamics and Control of Euler-Bernoulli Beams

System Setup

setbeam Set up a uniform beam and compute its natural frequencies and mode shapes

Window 2.1

setdamp Specify or reset damping in a beam Window 3.2 systinfo Display the parameters, boundary conditions, damping status,

natural frequencies and mode shapes of a beam Section 12.2.3

Eigensolutions

eigenbeam Determine eigenvalues and normalized eigenfunctions of a beam

Window 2.2

plotmsh Plot mode shape of a beam Window 2.3 nodalpts Determine the nodal points of an eigenfunction (mode shape) Window 2.4 animode Animate a mode of vibration of a beam Window 2.5

Dynamic Response

freebeam freebeam1

Compute and display free response of a beam

Window 3.3

forcedbeam forcedbeam1

Compute and display forced response of a beam

Window 3.4

plotbeam Plot time response of a beam at a spatial point Window 3.6 plotbeam1 Plot spatial distribution of beam response at a specific time Window 3.6 beammovie Animate time response of a beam Window 3.7 frfbeam Plot the magnitude and phase of steady-state response of a

beam subject to a pointwise sinusoidal force

Window 3.8

Feedback Control

tfbeam Obtain the open-loop transfer function of a beam with a pair of sensor and actuator

Window 4.1

ssbeam Obtain a state representation for a beam Window 4.2 clpbeam Obtain the closed-loop state equation for a beam under

feedback control Window 4.3

contrbeam Compute the response of a beam with or without feedback control by a Runge-Kutta algorithm

Window 4.4

Nonuniform Beams

nonubeam Set up a nonuniform beam and compute its natural frequencies and mode shapes

Window 5.1

systinfo2 Display the parameters, boundary conditions, damping status, natural frequencies and mode shapes of a nonuniform beam

Section 12.5

plotmsh2 Plot mode shape of a beam Window 5.2 animode2 Animate a mode of vibration Window 5.3 getmkb0 Create a discretized model for a beam Window 5.4 respnubeam Plot time response of a nonuniform beam Window 5.5 nubmovie Play animated vibration of a beam Window 5.6

13

tfbeam2 Create the transfer function of a nonuniform beam under a pair of sensor and actuator

Window 5.7

ssbeam2 Create a state-space representation of a nonuniform beam under multiple sensors and actuators

Window 5.8

Utilities

TBdemo Show how the Toolbox works and what it can do Section 12.1 TBinfo Display the information about this Toolbox Section 12.1 RunEx Run all the numerical examples contained in this chapter Section 12.1


14

Toolbox for Chapter 13 Dynamic Analysis of Bars, Shafts, and Strings

System Setup

setbar Set up a bar and compute its eigensolutions Window 2.1 setshaft Set up a shaft and compute its eigensolutions Window 2.1 setstring Set up a string and compute its eigensolutions Window 2.1 systinfo Display the information on system parameters, boundary

conditions, and eigensolutions Section 13.2.3

Eigensolutions

eigen2os Determine eigenvalues and normalized eigenfunctions Window 2.2 nodalpts Determine the nodal points of eigenfunctions Window 2.3 plotmsh Plot spatial distribution of eigenfunctions Window 2.4 animode Animate modes of vibration Window 2.5

Dynamic Response

free2os free2os1

Plot the free vibration of a second-order system Window 3.1

forced2os forced2os1

Plot the forced vibration of a second-order system Window 3.2

frf2os Plot the frequency response of a second-order system Window 3.5 movie2os Animate time response due to external and initial disturbances Window 3.4

Free Vibration of Stepped Systems

setbar2 Set up a stepped bar and compute its eigensolutions Window 4.1 setshaft2 Set up a stepped shaft and compute its eigensolutions Window 4.1 setstring2 Set up a stepped string and compute its eigensolutions Window 4.1 systinfo2 Display the information on system parameters, boundary

conditions, and eigensolutions Section 13.4.3

plotmsh2 Plot spatial distribution of eigenfunctions of a stepped system Window 4.2 eigenstep2 Obtain eigenfunctions of a stepped system Window 4.3 animode2 Animate modes of vibration for a stepped system Window 4.4

Utilities

TBdemo Show how the Toolbox works and what it can do Section 13.1 TBinfo Show the information of the functions in the Toolbox Section 13.1 RunEx Run all numerical examples in this chapter Section 13.1 The main functions contained these toolboxes given in the following pages. For demonstrative example of what these functions can do click the button Demo Examples in the home page.

15

Toolbox for Chapter 14 Dynamic Analysis of Constrained, Combined, and Stepped Beams

Constrained Beams

setbeam Set up a constrained beam and compute its eigensolutions Window 2.1 systinfo Display system information and eigensolutions Section

14.2.2 plotmsh Plot mode shape distribution along beam length Window 2.2 animode Play animated beam response in a mode of vibration Window 2.3 eiglocus Plot eigenvalue loci of a beam versus a constraint parameter Window 2.4 frfbeam Plot the steady-state displacement of a constrained beam

subject to a pointwise sinusoidal force Window 2.5

Combined Beams

setbeam2 Set up a combined beam and compute its eigensolutions Window 3.1 systinfo Display system information and eigensolutions Section

14.3.2 plotmsh Plot mode shape distribution along beam length Window 2.2 animode Play beam response in a mode of vibration Window 2.3 trbeam2 Plot the time history of the transient displacement of a

combined beam subject to external and initial disturbances Window 3.2

trbeam2s Plot the spatial distribution of the transient displacement of a combined beam at a specific time

Window 3.3

beammovie2 Animate transient vibration of combined beam Window 3.4 frfbeam2 Plot the steady-state response of a combined beam subject to a

pointwise sinusoidal force Window 3.5

Stepped Beams

setbeam3 Set up a stepped beam and compute its eigensolutions Window 4.1 systinfo3 Display system information and eigensolutions Section

14.4.2 plotmsh3 Plot mode shape distribution along beam length Window 4.2 animode3 Play animated beam response in a mode of vibration Window 4.3

Utilities

TBdemo To show how The toolbox works and what it can do Section 14.1 TBinfo To show the information of the Toolbox Section 14.1 RunEx Run all the numerical examples contained in this chapter Section 14.1 The main functions contained these toolboxes given in the following pages. For demonstrative example of what these functions can do click the button Demo Examples in the home page.

16

Toolbox for Chapter 15 Static Analysis of Linearly Elastic Bodies

Stress and Strain

pristress3 Compute principal stresses and principal axes in three dimensions

Window 2.1

pristrain3 Compute principal strains and principal axes in three dimensions

Window 2.2

Generalized Hooke’s Law

hks2e Compute strain components based on Hooke’s law Window 2.3 hke2s Compute stress components based on Hooke’s law Window 2.3 elaconst Compute the values of elastic constants Window 2.4

Finite Element Analysis of Two-Dimensional Bodies

Rectangular Regions setrectan Set up a finite element mesh for a rectangular elastic body Window 4.1 setconstr Change or remove pointwise constraints Window 4.2 resprectan Compute the static response of a rectangular elastic body Window 4.3 eleminfo Display the information of a selected element Window 4.4 nodeinfo Display the information at a selected node Window 4.5 plotmesh Plot the mesh of undeformed or deformed configuration Window 4.6 plotgln Plot static response of the body along a grid line Window 4.7 getKg Obtain global stiffness matrix Window 4.8 dispFE Display the information of a rectangular elastic body Section 15.4.2

Regions of Arbitrary Shapes setabody Set up a finite element mesh for an arbitrary-shaped body Window 4.9 setbnd Set up boundary conditions Window 4.10 respabody Compute the static response of a body Window 4.11 getmesh Obtain a finite element mesh for certain regions Window 4.12 eleminfo Display the information on a selected element Window 4.4 nodeinfo Display the information at a selected node Window 4.5 plotmesh2 Plot the mesh for undeformed or deformed configuration Window 4.6 getKg Obtain global stiffness matrix Window 4.8 dispFE2 Display the information of a body of arbitrary shape Section 15.4.3

Utilities

TBdemo Show how the Toolbox works and what it can do Section 15.1 TBinfo Show the information of the Toolbox Section 15.1 RunEx Run all the numerical examples contained in this chapter Section 15.1 The main functions contained these toolboxes given in the following pages. For demonstrative example of what these functions can do click the button Demo Examples in the home page.

17

Toolbox for Chapter 16 Free Vibration of Membranes and Plates

Free Vibration of Membranes

recmemb Compute eigensolutions of a rectangular membrane Window 2.1 plotmsh1 Plot mode shapes of a rectangular membrane Window 2.2 animode1 Animate modes of vibration of a rectangular membrane Window 2.3 cirmemb Compute eigensolutions of a circular membrane Window 2.4 plotmsh2 Plot mode shapes of a circular membrane Window 2.5 animode2 Animate modes of vibration of a circular membrane Window 2.6

Free Vibration of Rectangular Plates --- Navier and Lévy Solutions

recplateLV Compute Navier- or Lévy-type eigensolutions of a rectangular plate with at least two opposite edges simply supported

Window 3.1

plotmsh3 Plot mode shapes of a rectangular plate Window 2.2 animode3 Animate modes of vibration of a rectangular plate Window 2.3

Free Vibration of Rectangular Plates --- Finite Element Solutions

recplateFE Compute eigensolutions of a rectangular plate with general boundary conditions

Window 3.2

plotmsh3f Plot mode shapes of a rectangular plate Window 3.3 animode3f Animate modes of vibration of a rectangular plate Window 3.4

Free Vibration of Circular Plates

cirplate Compute eigensolutions of a circular plate Window 4.1 plotmsh4 Plot mode shapes of a circular plate Window 2.5 animode4 Animate modes of vibration of a circular plate Window 2.6

Utilities

systinfo Display the information and eigensolutions of a membrane or plate

Sections 16.2.1, 16.2.2, 16.3.3, 16.4.2

TBdemo Show how the Toolbox works and what it can do Section 16.1 TBinfo Show the information of the functions in the Toolbox Section 16.1 RunEx Run all the numerical examples contained in this chapter Section 16.1 The main functions contained these toolboxes given in the following pages. For demonstrative example of what these functions can do click the button Demo Examples in the home page.

18

Toolbox for Appendix A.12 Inverse Laplace Transform via Partial Fraction Expansion

Free Vibration of Membranes

pfe Obtain the partial fraction expansion of a rational function Window A.1 invLT Obtain the inverse Laplace transform of a rational function Window A.2 plotLT Plot inverse-Laplace-transformed function versus time Window A.3 The main functions contained these toolboxes given in the following pages. For demonstrative example of what these functions can do click the button Demo Examples in the home page.

19

Documents

MATLAB Functions in CD-ROMruk.usc.edu/Books/yang-sssd/key features/MATLAB functions in CD-… · MATLAB Functions in CD-ROM The book “Stress, Strain, and Structural Dynamics”