Forced Vibrations of Shells by Modal Expansion

So far we have been concerned with the natural frequencies of shells and plates. For the engineer, the ultimate reason for this preoccupation is found in the study of the forced response of shells. For instance, knowing the eigenvalues makes it possible to obtain the forced solution in terms of these eigenvalues. This approach is called spectral representation or modal expansion and dates back to Bernoulli’s work (Bernoulli, 1755). It will be the major point of discussion in this chapter.