Advanced Mechanical Vibrations: Physics, Mathematics and Applications provides a concise and solid exposition of the fundamental concepts and ideas that pervade many specialised disciplines where linear engineering vibrations are involved. Covering the main key aspects of the subject - from the formulation of the equations of motion by means of analytical techniques to the response of discrete and continuous systems subjected to deterministic and random excitation - the text is ideal for intermediate to advanced students of engineering, physics and mathematics. In addition, professionals working in - or simply interested in - the field of mechanical and structural vibrations will find the content helpful, with an approach to the subject matter that places emphasis on the strict, inextricable and sometimes subtle interrelations between physics and mathematics, on the one hand, and theory and applications, on the other hand. It includes a number of worked examples in each chapter, two detailed mathematical appendixes and an extensive list of references.