Does eigenvalue analysis=modal analysis? Does eigenfrequency=natural frequency?

Question

Does eigenvalue analysis=modal analysis? Does eigenfrequency=natural frequency?
Please explain what is the definition or what you understand by each term? List out their differences and similarities. Please bring in relevant concepts if needed!

Answer 1

The goal of modal analysis in structural mechanics is to determine the natural shapes and frequencies of an object or structure during free vibration. The types of equations which arise from modal analysis are those seen in eigensystems. The physical interpretation of the eigenvalues and eigenvectors resulting from solving equations of these types of system are that they represent the natural or eigen frequencies and their corresponding mode shapes.



PS - in quantum mechanics, the eigenvalues corresponds to the natural energy states of the quantum system. The mathematics involved in eigenvalue analysis and quantum mechanics is nearly identical, and the physical interprestation is very similar.

Answer 2

Hello



The eigen word is comun in quantum physics. I think is not possible to "mix" this word with modal analysis and natural frequency. In quantum physics people speak the eigen values refer to a solution of a Scrhodinger equation.



In that equuation we have a density of prbabilitu wave function.. thats no represent a real word.

Answer 3

The factor by which the magnitude is scaled is called the eigenvalue (help·info) of that vector. (See Fig. 1). Often, a transformation is completely described by its eigenvalues and eigenvectors. The eigenspace for a factor is the set of eigenvectors with that factor as eigenvalue. These concepts play a major role in several branches of both pure and applied mathematics — appearing prominently in linear algebra, functional analysis, and to a lesser extent in nonlinear situations. It is common to prefix any natural name for the vector with eigen instead of saying eigenvector. For example, eigenfunction if the eigenvector is a function, eigenmode if the eigenvector is a harmonic mode, eigenstate if the eigenvector is a quantum state, and so on (e.g. the eigenface example below). Similarly for the eigenvalue, e.g. eigenfrequency if the eigenvalue is (or determines) a frequency.