![]() ![]() Plots(,Pyy],i=1.512)],style=line) Īlternatively, the same calculations can be done by using MATLAB® syntax almost entirely.ĮvalM("x=sin(2*pi*50*t) + sin(2*pi*120*t)") Plots(,data],i=1.nops(t))],symbol=DIAMOND,symbolsize=7) Plots(,x],i=1.Dimensions(t))], symbol=DIAMOND, symbolsize=8) ĭata Analysis: Fast Fourier Transform (FFT)Ī set of experimental numerical data can be analyzed with MATLAB® as a numerical engine. We must enforce the above variables as global in the MATLAB® environment so that the function mass_eqn can use them. ![]() The oscillator parameters of Mass M, Damping C, and Stiffness K are: Writeline(file, "function xdot=mass_eqn(t,x)"): Here, we create the file in the current directory. The MATLAB® function stored in the file mass_eqn.m can be created within Maple as follows, or it can be created by using any text editor. The simulation equations are coded as MATLAB® function files and are called from the Maple environment by using the ode45 command. Plots(P,heights=histogram,axes=boxed,labels=,title="temperature distribution") Ī simple spring-mass-dashpot is modeled as a second-order linear oscillator. Now, let us take the Maple solution vector and re-arrange its values in a 3 x 7 matrix that corresponds to the actual rectangular plate: Or, we can solve the system entirely within Maple: Now, we solve the system in the MATLAB® environment: , U edge at 100 units, and the other three edges at 0 temperature units. ![]() We have fixed the temperature along the U. You can do fplot (real (X), -0.002 0.002) instead to plot just the real part of the eigenvalues (assuming that's what you want). When using plot (), it plots the real part of complex numbers by default, but apparently fplot () doesn't. , U ] ,we have the system AU=B, where the matrix A and column vector B encode the interconnectivity of the nodes and the profile of the boundary temperature:Ī := BandMatrix(,7,21,21,outputoptions=]):ī := Vector( 21,, datatype=float ) 1 Answer Sorted by: 0 The second plot looks like that because the eigenvalues of B are imaginary. Representing the internal nodal temperatures U by the column vector. With our 21 plate-internal nodes and 20 boundary conditions ( = 7+3+7+3 ), the finite-difference 2-dimensional Laplace equation gives us an inhomogeneous linear system in 21 unknowns (the internal nodal temperatures). We model the plate as a 3 x 7 grid of nodes, where the nodes may be thought of as being interconnected with a square mesh of heat conductors. ![]() Heat Transfer: Finite Difference SolutionĪ difference equation method is used to find the static temperature distribution in a flat rectangular plate, given its boundary is held at a fixed temperature profile. The Eigenvectors are (in no particular order): The equivalent computations in the Maple environment: The Eigenvalues and Eigenvectors computed with MATLAB® are found: With complex inputs, plot (z) is equivalent to plot (real (z),imag (z)), where real (z) is the real part of z and imag (z) is the imaginary part of z. The Stiffness matrix K is tridiagonal with 2k on the center diagonal, and -k on the adjacent diagonals: Trial Software Product Updates Plot Imaginary and Complex Data Copy Command Plot One Complex Input This example shows how to plot the imaginary part versus the real part of a complex vector, z. To examine any of these Matrices, the Structured Data Browser can be used, by right-clicking the output Matrix and selecting Browse. M := DiagonalMatrix(, outputoptions=,storage=rectangular]) The mass matrix M is a matrix with m on the diagonal: The model equations may be formulated with the following matrix assignments. This formulation is used to compute the lowest natural frequencies and modes of a highly idealized 22-story building. Structural Analysis: A First Approximation Use the with command to access the functions in some useful packages by their short names:įor more information on the Maple-MATLAB® link, see Matlab. All that is needed then is calculating the radii of the ellipse.Initiate the MATLAB® link. \Īfter normalizing the column vectors in V, we choose the eigenvector with the larger eigenvalue and calculate its angle to the global x-axis. Geometrically, a not rotated ellipse at point \((0, 0)\) and radii \(r_x\) and \(r_y\) for the x- and y-direction is described by The radii of the ellipse in both directions are then the variances. You can confirm this by noting that A5, which is computed without any roundoff error. If the data is uncorrelated and therefore has zero covariance, the ellipse is not rotated and axis aligned. ![]()
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