Researchers, scientists and design engineers always try to know about first few modes of vibrations before finalizing any design of machine or structure so that they can save the money & time of the nation. For these two fold requirements i.e. money and time, they can get a lot of help from the contents of this book. Actually, deeply analysis of the graphs in each chapter or model can provide them the required or desired values of frequency parameters & surely, they can get the same with the proper choice of varying parameters i.e. thermal gradient, taper parameters, non-homogeneity constant,...