Python Plate Vibration

Utility

The scripts on this page require the utility module tompy.py

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Rectangular Plates

A script for calculating the natural frequency of a rectangular plate supported at each corner is given at plate_corners.py

The natural frequency is calculated via the Rayleigh method. The resulting fundamental mode shape is displayed using a Matplotlib surface plot.

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Circular Plates

A script for calculating the natural frequencies of the bending modes of a circular plate, with options for both homogenous and honeycomb-sandwich designs is given at circular_plate.py. This script demonstrates a 3D surface plot for a polar base.

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– Tom Irvine

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Python Generalized Eigenvalue Problem

Utilities

The Python scripts on this page require the utility modules

tompy.py

transfer_modes.py

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Primary Method

A script for calculating the eigenvalues and vectors for a mass and stiffness matrix system is given at: gen_eig.py

The script uses the following functions:

from scipy.linalg import eig, eigh

The references for these functions are:
eig
eigh

They provide an interface to the LAPACK routines dgeev and zgeev. These routines implement the QR method with Householder reflectors.

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Sparse Matrices

Here is a script for find a subset of the lowest eigenvalues and vectors for a sparse system: gen_eig_sparse.py

The scripts uses the functions:

from scipy.sparse.linalg import eigsh

from scipy.sparse.linalg import eigs

It also uses these functions in shift-inverted mode to find the lowest eigenvalues with speed and accuracy.

Reference: Sparse Eigenvalue Problems with ARPACK

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Alternate Method

Another method is to use the Locally Optimal Block Preconditioned Conjugate Gradient Method (LOBPCG).

from scipy.sparse.linalg import lobpcg

But there are anecdotal reports that this method is inaccurate in some cases.

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Fortran

Here is a pure Fortran program for the generalized eigenvalue problem: geigen.f.

The program can be compiled via:

$ gfortran -o geigen geigen.f -lblas -llapack

The program uses LAPACK routines DSYGV and DSYEV.

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C/C++

Here is C/C++ program for the generalized eigenvalue problem: gen_eig.cpp.

The program can be compiled via:

gcc -o gen_eig gen_eig.cpp -lblas -llapack -lstdc++

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Scilab

A Scilab program is given at: generalized_eigen_read.sci

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Related Posts

Mixed Fortran & Python – Gives an example using the generalized eigenvalue problem

Vibrationdata Blog Entry – Instructions for the generalized eigenvalue problem including Lapack installation.

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– Tom Irvine