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theone
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why are diagonal matrices and eigen vectors useful in vibrations analysis?
Because resonance is an eigenstate.theone said:why are diagonal matrices and eigen vectors useful in vibrations analysis?
fresh_42 said:Because resonance is an eigenstate.
Thank you! And 'classroom' was exactly where I got it from ...DrClaude said:Be careful about that example: https://www.physicsforums.com/threads/expunging-myths-from-the-classrooom.849853
DrClaude said:Because the eigenvalues and eigenvectors correspond to normal modes.
A diagonal matrix is a type of square matrix in which all the non-diagonal elements are zero. This means that the entries of the matrix are only present on the main diagonal, going from the top left to the bottom right.
Diagonal matrices are used in vibration analysis to simplify and speed up calculations. They are particularly useful in solving systems of linear equations, which are commonly used in vibration analysis to model and analyze the behavior of structures under different types of loads and excitations.
There are several benefits to using diagonal matrices in vibration analysis. Firstly, they can reduce the amount of computation required, as many operations on diagonal matrices are simpler and faster compared to general matrices. Additionally, diagonal matrices can help to identify patterns and relationships in the data, making it easier to interpret and analyze the results.
Diagonal matrices can be used for many types of vibration analysis, particularly in linear systems. However, they may not be suitable for certain types of nonlinear or complex systems, where other types of matrices may be more appropriate. It is important to consider the specific characteristics of the system being analyzed when determining whether diagonal matrices are suitable for the analysis.
Diagonal matrices can be constructed in a variety of ways for vibration analysis, depending on the specific application. In some cases, the matrix may be given directly based on physical properties of the system, while in other cases it may be constructed using data from measurements or simulations. Additionally, diagonal matrices can also be created through transformation of other types of matrices, such as symmetric or triangular matrices.