Mechanical Vibration: Where Do We Stand?

1. Front Matter

   Pages i-x

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2. Basic Equations of the Linearized Theory of Elasticity: a Brief Review

   • Erasmo Viola

   Pages 1-15

3. Dynamical Analysis of Spherical Structural Elements Using the First-order Shear Deformation Theory

   • Erasmo Viola, Francesco Tornabene

   Pages 17-41

4. A Comparison of Two Dimensional Structural Theories for Isotropic Plates

   • Erasmo Viola, Federica Daghia

   Pages 43-55

5. Thickness Effect on the Dynamic Behavior of Three-Dimensional Plates by using the Ritz Method

   • Erasmo Viola, Cristina Gentilini

   Pages 57-81

6. Exact Analysis of Wave Motions in Rods and Hollow Cylinders

   • Erasmo Viola, Alessandro Marzani

   Pages 83-104

7. Semi-analytical Formulation for Guided Wave Propagation

   • Erasmo Viola, Alessandro Marzani, Ivan Bartoli

   Pages 105-121

8. Numerical Evaluation of Semi-analytical Finite Element (SAFE) Method for Plates, Rods and Hollow Cylinders

   • Erasmo Viola, Alessandro Marzani, Ivan Bartoli

   Pages 123-138

9. Smart Materials and Structures

   • Daniel J. Inman

   Pages 139-149

10. Applications of Smart Materials for Vibration Suppression

    • Daniel J. Inman

    Pages 151-165

11. Basics of Control for Vibration Suppression

    • Daniel J. Inman

    Pages 167-178

12. Smart Structures in Structural Health Monitoring

    • Daniel J. Inman

    Pages 179-188

13. Vibrational Mechanics - a General Approach to Solving Nonlinear Problems

    • Iliya I. Blekhman

    Pages 189-247

14. Linearization Techniques in Stochastic Dynamic Systems

    • Leslaw Socha

    Pages 249-319

15. Models, Verification, Validation, Identification and Stochastic Eigenvalue Problems

    • Sondipon Adhikari

    Pages 321-388

16. Vibrations of Beams and Plates: Review of First Closed-Form Solutions in the Past 250 Years

    • Isaac Elishakoff

    Pages 389-453

17. Closed Form Trigonometric Solution of Inhomogeneous Beam-Columns

    • Ivo Caliò, Isaac Elishakoff

    Pages 455-474

18. Closed Form Trigonometric Solution of Inhomogeneous Beam-Columns

    • Isaac Elishakoff, Ivo Caliò

    Pages 475-488

''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.

• Smart Materials
• Vibration
• beam
• calculus
• computer-aided design (CAD)
• control
• deformation
• elasticity
• finite element method
• identification
• mathematics
• mechanics
• plates
• smart material
• verification

• Florida Atlantic University, Boca Raton, USA

  Isaac Elishakoff

Isaac Elishakoff, Florida Atlantic University, Boca Raton, USA

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