ABSTRACT
Eigenfunction expansion is a classical and a very powerful mathematical technique in solving certain types of boundary value problems of finite domain. When we talk about eigenvalues, we normally refer to the eigenvalue of a square matrix. In matrix analysis the number of eigenvalues depends on the rank of the matrix. Unlike the matrix analysis, the number of eigenvalues in homogeneous boundary value problems is typically infinite. In the case of beam vibrations, each eigenvalue is a natural vibration frequency of the beam and each vibration mode is an eigenfunction. In the case of the dynamics of beam vibrations, a beam starts to vibrate when it is subject to continuous time-dependent forces. It turns out that the time-dependent vibrations can always be expressed in terms of a summation of the fundamental vibration modes, independent of the nature of the forcing terms. T.
