Written by the world’s leading researchers on various topics of linear, nonlinear, and stochastic mechanical vibrations, this work gives an authoritative overview of the classic yet still very modern subject of mechanical vibrations. It poses the question: What are the most important contributions made in the past decade? The reader will be able to gain a critical and authoritative overview of the subject from various complementary perspectives.

Basic Equations of the Linearized Theory of Elasticity: A Brief Review (E. Viola).- Dynamical Analysis of Spherical Structural Elements and Using the First-Order Shear Deformation Theory (E. Viola, F. Tornabene).- A Comparison of Two Dimensional Structural Theories for Isotropic Plates (E. Viola, F. Daghia).- Thickness Effect on the Dynamic Behavior of Three Dimensional Plates by Using the Ritz Method (E. Viola, C. Gentilini).- Exact Analysis of Wave Motions in Rods and Hollow Cylinders (E. Viola, A. Marzani).- Semi-Analytical Formulation for Guided Wave Propagation (E. Viola, A. Marzani, I. Bartoli).- Numerical Evaluation of Semi-Analytical Finite Element (SAFE) Method for Plates, Rods and Hollow Cylinders (E. Viola, A. Marzani, I. Bartoli).- Smart Materials and Structures (D. Inman).- Applications of Smart Materials for Vibration Suppression (D. Inman).- Basics of Control for Vibration Suppression (D. Inman).- Smart Materials in Structural Health Monitoring (D. Inman, B. L. Grisso, H. A. Sodano).- Vibration Mechanics: A General Approach to Solving Nonlinear Problems (I. I. Blekhman).- Linearization Techniques in Stochastic Dynamic Systems (L. Socha).- Models, Verification, Validation, Identification and Stochastic Eigenvalue Problems (S. Adhikari).- Vibration of Beams and Plates: Review of First Closed-Form Solutions in the Past 250 Years (I. Elishakoff).- Closed-Form Trigonometric Solution of Inhomogeneous Beam-Columns 1: Buckling Problem (I. Caliò, I. Elishakoff).- Closed-Form Trigonometric Solution of Inhomogeneous Beam-Columns 2: Vibration Problem (I. Elishakoff, I. Caliò).

''There is always a delightful sense of movement, vibration and life"". Theodore Robinson (1852-1896) "/ have never solved a major mechanical or interpretive problem at the keyboard. I have always solved it in my mind". Jorge Bolet (1914-1990) The idea of this book stems from the realization that scientists, not unlike laymen, should occasionally interrupt their regular work and reflect on the past, to see both the accomplishments and the drawbacks, so as to be able to plan for future research in the "proper" perspective. But an inquisitive reader may ask: Can one really document in any field, let alone mechanical vibrations (whose very name signifies change), ''where do we stand"? Did not a Greek philosopher famously claim that one cannot enter a river twice? Another, on an even more sophisticated note, added that actually it is impossible to enter a river even once! For in the process of entering, both entrant and river change. Likewise, one can argue that it is nearly impossible to answer the question posed in the title of this volume. But experience shows, despite the sage observations of the philosophers, that one does enter a river, lake, sea, or ocean. Likewise, scientists do stop (if not for a minute, for a conference) to reflect on the past, and if not in its detail, then at least in big strokes on various topics presented by the participants; questions by the listeners often change the research direction of the presenter.