Fundamental frequency of vibration of thin elastic plates elastically supported along internal segments

The title problem is approximately solved in a unified manner in the case of rectangular and circular plates elastically restrained against rotation along the boundary.Polynomial coordinate functions and a variational approach are used in order to obtain an approximate frequency equation. Judging from the excellent accuracy attained using the present methodology in the case where no internal supports are present, it is reasonable to expect that the results presented in this study will be sufficiently accurate for engineering purposes in the situations considered.