# Modal Ritz analysis and Modal Eigen analysis are two different methods used in structural dynamics

Modal Ritz analysis and Modal Eigen analysis are two different methods used in structural dynamics to determine the natural frequencies, mode shapes, and dynamic response of structures.

Modal Ritz analysis is a numerical method used to determine the natural frequencies and mode shapes of structures by approximating the mode shapes using a trial function. The trial function is chosen based on the physical characteristics of the structure, and the natural frequencies and mode shapes are obtained by solving a generalized eigenvalue problem. Modal Ritz analysis is commonly used when analytical solutions are not available or when the structure has complex geometries.

Modal Eigen analysis, on the other hand, is a numerical method that directly solves the eigenvalue problem to obtain the natural frequencies and mode shapes of a structure. The method involves solving the matrix equation of motion and the corresponding boundary conditions to determine the eigenvalues (natural frequencies) and eigenvectors (mode shapes) of the structure. Modal Eigen analysis is commonly used in linear structural analysis and is a widely accepted method for determining the dynamic response of structures.

In summary, Modal Ritz analysis is an approximate method that uses a trial function to determine natural frequencies and mode shapes, while Modal Eigen analysis is a direct method that solves the eigenvalue problem to determine the natural frequencies and mode shapes of a structure.