ABSTRACT
Eigenvalue problems occur often in mechanics, especially linear system dynamics, and elastic stability. Usually nontrivial solutions are sought for homogeneous systems of differential equations. For a few simple systems like the elastic string, or a rectangular membrane, the eigenvalues and eigenfunctions can be determined exactly. More often, some discretization methods such as Þnite difference or Þnite element methods are employed to reduce the system to a linear algebraic form which is numerically solvable. Several eigenvalue problems analyzed in earlier chapters reduced easily to algebraic form where the function eig could immediately produce the desired results. The present chapter deals with several instances where reduction to eigenvalue problems is more involved. We will also make some comparisons of exact, Þnite difference, and Þnite element analyses. Among the physical systems studied are Euler beams and columns, two-dimensional trusses, and elliptical membranes.
