Mechanical Vibrations: Theory and Application to Structural Dynamics, Third Edition is a comprehensively updated and reorganized new edition of the popular textbook. It presents the theory of vibrations in the context of structural analysis and covers applications in mechanical and aerospace engineering, This new edition now includes the fundamentals of signal processing and identification technique, and develops the concepts of dynamic reduction and substructuring. A more detailed discussion of the concept of eigensolution sensitivity to physical parameters is included and the fundamental cases of wave propagation in solids are considered. It also includes a chapter on the finite element method for one-dimensional structures. This new edition contains coherent and uniform notation and now includes solved exercises at the end of each chapter.