Analytical and Numerical Methods for Vibration Analyses

Illustrates theories and associated mathematical expressions with numerical examples using various methods, leading to exact solutions, more accurate results, and more computationally efficient techniques

This book presents the derivations of the equations of motion for all structure foundations using either the continuous model or the discrete model. This mathematical display is a strong feature of the book as it helps to explain in full detail how calculations are reached and interpreted. In addition to the simple ‘uniform’ and ‘straight’ beams, the book introduces solution techniques for the complicated ‘non uniform’ beams (including linear or non-linear tapered beams), and curved beams. Most of the beams are analyzed by taking account of the effects of shear deformation and rotary inertia of the beams themselves as well as the eccentricities and mass moments of inertia of the attachments.

   Demonstrates approaches which dramatically cut CPU times to a fraction of conventional FEM
   Presents "mode shapes" in addition to natural frequencies, which are critical for designers
   Gives detailed derivations for continuous and discrete model equations of motions
   Summarizes the analytical and numerical methods for the natural frequencies, mode shapes, and time histories of
   straight structures
   rods
   shafts
   Euler beams
   strings
   Timoshenko beams
   membranes/thin plates
   Conical rods and shafts
   Tapered beams
   Curved beams
   Has applications for students taking courses including vibration mechanics, dynamics of structures, and finite element analyses of structures, the transfer matrix method, and Jacobi method

This book is ideal for graduate students in mechanical, civil, marine, aeronautical engineering courses as well as advanced undergraduates with a background in General Physics, Calculus, and Mechanics of Material. The book is also a handy reference for researchers and professional engineers.

Product Details

   Hardcover: 672 pages
   Publisher: Wiley; 1 edition (October 7, 2013)
   Language: English
   ISBN-10: 111863215X
   ISBN-13: 978-1118632154