"Vibration simulation using MATLAB" chapter I "Fundamentals of Matlab"

MATLAB is an interactive language which can be used for numerical analysis and data visualization, and it is widely used in the analysis and design of vibration control engineering. A variety of toolboxes allow MATLAB to be extended to different areas.

1.1 Matrix Generation

　　A matrix is a collection of values organized by rows and columns (column).

　　A=[1 2 3 4;5 6 7 8;9 10 11 12]

The matrix can be transpose (transpose) with an apostrophe (apostrophe)

　　B=a '

Use a colon (colon) between two integers to generate all integers between two integers

　　A=1:8 generates line vectors (row vector) a=[1 2 3 4 5 6 7 8]

Use a colon between three numbers to generate all numbers in the middle number of steps between two numbers

　　b=0.0:. 2:1 generates a row vector (row vector) b=[0.0 0.2 0.4 0.6 0.8 1.0]

Other ways to build it are as follows:

　　C=linspace (0,10,21)//Generate linear space line vector (21 generated between 0~10)

　　D=logspace ( -1,1,10)//Generate logarithmic space row vectors (10 generated between -1~1)

　　Eye (3)//Generate 3*3 unit matrix (identity matrix)

　　Zeros (3,2)//Generate 3*2 full 0 matrix

1.2 Matrix Processing

　　Number of matrix cells

Suppose there is a matrix A (2,3)

Size (A) returns the number of rows and columns

　　D=size (A)//d=[2 3]

Length (A) returns the maximum value in all dimensions

　　E=length (rand (2,3,5))//e=5

Transpose (Transpose)

　　A

Get a column or a row in a matrix

　　A (:, 3)//Get the 3rd column of data in a

　　A (2,:)//Get the 2nd row of data in a

Matrix point multiplication, two matrix dimensions must be exactly the same

　　A (2,3); B (2,3); C=a.*b;

If it is a square matrix, similar to E, multiple multiplication can be abbreviated as

　　E.^4

Matrix multiplication

　　A (2,3); B (3,2); C=a*b//c should be C (2,2)

If it is a square matrix, similar to E, multiple multiplication can be abbreviated as

　　E^4

1.3 Functions

MATLAB contains many standard functions, such as sin and cos

　　i=0+1.0i;

　　j=0+1.0i;

　　cos (pi) =-1;

　　EXP (1) = 2.7183;

　　LOG (exp (1)) = 1;

　　LOG10 (10) = 1;

INV () returns the inverse matrix of the matrix (inverse matrix)

　　b=Inv (A);

Det () Returns the value of the determinant of the matrix (determinant of a matrix)

　　Det (A);

Trace () returns the sum of the main diagonal values of the matrix

　　Trace (A);

You can use the Help function name to get a description of the function

1.4 Drawing

MATLAB can be convenient for drawing rich numerical graphics.

e.g in [pi/100, 10pi] The figure of sin (x) x/

　　X=pi/100:pi/100:10*pi;

　　Y=sin (x)/x;

　　Plot (x, y);

　　grid;

Common drawing functions:

Plot (x, y)//Paint function

Subplot ()//a sheet of paper to draw multiple graphs, to determine the position of the diagram

　　Figure

　　Subplot (2,1,1);

　　Plot (x,y1);

　　Subplot (2,1,2);

　　Plot (x,y2);

　　Title ()

Xlabel ();

Ylabel ();

Grid

1.5 Programming

1.5.1 M-File

Files that contain many MATLAB statements are called M files.

1.5.2 Cycle

For loop

　　　　　　For N=0:10

　　　　　　　　X (n+1) =sin (PI*N/10);

　　　　　　End

Loops can be nested

　　　　　　H=zeors (5)

　　　　　　For K=1:5

　　　　　　　　For L=1:5

　　　　　　　　　　H (k,l) =1/(K+L-1)

　　　　　　　　End

　　　　　　End

1.5.3 If statement

　　　　　　If condition

　　　　　　　　Statement

　　　　　　End

　　　　　　If condition

　　　　　　　　Statement

　　　　　　else condition

　　　　　　　　Statement

　　　　　　End

1.5.4 Sub-function

functions [return value] = function name (parameter)

　　　　function [mean] = stat (x)

　　　　n = length (x);

　　　　mean = SUM (x)/n;

"Vibration simulation using MATLAB" chapter I "Fundamentals of Matlab"