Refined Dynamical Theories of Beams, Plates and Shells and Their Applications Proceedings of the Euromech-Colloquium 219

As is known, classical theories of vibration of the most fre­ quently encountered structural elements (e. g. , beams, plates and shells) disregard the effects of the shear deformation and rotary inertia. Refined theories, with these effects taken into account, have been pioneered by Bresse, Lord Rayleigh, Timoshenko, Eric Reissner, Mindlin and others. These refined theories have been fruitfully applied in recent decades in both theoretical and prac­ tical solid mechanics problems. The European Mechanics Committee approved holding EURO~illCH Colloquium 219 on "Refined Dynamical Theories of Beams, Plates and Shells and Their Applications" for reviewing the recent devel­ opments, providing guidelines for future investigations and presenting a forum for current work of younger researchers. The Colloquium was held during September 23 - 26, 1986, at the Uni­ versitat-Gesamthochschule Kassel, in the city of Kassel, Federal Republic of Germany. 45 Representatives of academia and industry, from nine European countries, as well as from Israel, USA and India participated in this Colloquium. IV 36 lectures were presented during the five sessions: Session A: Theory of Vibrations of Plates and Shells Session B: Various Approaches for Dynamical Problems of Beams Session C: Random Vibrations and Dynamic Stability Session D: Vibrations of Composite Structures Session E: Special Dynamical Problems of Beams, Plates and Shells The papers in this volums were divided into two parts: papers of invited keynote lectures and those of the invited contributed lectures.

Invited Keynote Lectures.- From Newton’s Fluid to the Theory of Plates.- On a Certain Mixed Variational Theorem and on Laminated Elastic Shell Theory.- A Note on the Derivation of Higher-Order Two-Dimensional Theories of Transverse Bending of Elastic Plates.- A General Transverse Shear Deformation Theory of Anisotropic Plates.- Component Mode Synthesis of Multi-Rotor Systems.- Dynamic Stability of Initially Curved Columns under a Time Dependent Axial Displacement of Their Support.- Theoretical and Experimental Results on the Dynamic Behaviour of Composite Beams, Plates and Shells.- Invited Contributed Lectures.- Session A Theory of Vibrations of Plates and Shells.- Study of the Dynamic Behaviour of Eccentrically Stiffened Mindlin Plates under the Influence of Plane Forces.- On the Vibration of Thick Annular Plates.- An “Exact” Solution for the Linear Small-Amplitude Vibrations of a Rectangular Plate.- Consistent and Inconsistent Higher Order Beam and Plate Theories: Some Surprising Comparisons.- Energy-Consistent Models of Plates with Moderate Thickness.- Geometrically Nonlinear Theories for Laminated Composite Plates Treated in the Framework of the Small Strain and Moderate Rotation Concept.- A Three-Dimensional Refined Theory of Elastic Plates.- Session B Various Approaches for Dynamical Problems of Beams.- Refined Effects in Beam Theories and their Influence on the Natural Frequencies of Beams.- Nonlinear Vibrations of Beams Including Shear Deformations and Rotary Inertia.- Torsion and Related Concepts: Some Steps Beyond Saint-Venant’s Principle.- Wave Propagation in Elastic Rods, With Shear and Rotary Inertia Effects.- On Nonlinear Equations of a Beam.- Riemann’s Formulae and their Application to the Timoshenko Beam Model.- Session C Random Vibrations andDynamic Stability.- Dynamic Stability of Thick, Orthotropic, Circular Cylindrical Shells.- On the Wave Solution for Beams on a Viscoelastic Foundation Subjected to a Travelling and Oscillating Force.- Influence of the Shear Deformation and Rotary Inertia on the Flutter of a Cantilever Subjected to a Follower Force — Exact and Symbolic Manipulation Solutions.- Dynamic Response and Reliability of Laminated Plates to Random Loading.- Session D Vibrations of Composite Structures.- A Mixed Variational Formulation for Laminated Plates.- Influence of the Variation of Structural Properties on the Probability of a Composite Plate to Meet a Target Eigenfrequency.- On Higher-Order Effects of Coupled Wave Motion in Layered Structures.- Free Vibration Analysis of Thickness Shear Deformable Cross-Ply Laminated Oval Cylindrical Shells.- A Dynamical Theory of Inhomogeneous Slender Structures and its Applications.- Session E Special Dynamical Problems of Beams, Plates and Shells.- Some Static and Dynamical Contact Problems Between a Mindlin Plate and an Elastic Foundation.- One-Dimensional Theories for Cracked Beams.- Refined Effects in Turbomachinery Blade Vibrations.- Self-Adjointness and Definiteness — a Necessary Condition for the Boundary Value Problem of the Free Undamped Vibrations of the Plate.- Damped Response of Orthotropic Shallow Spherical Shells on Nonlinear Elastic Foundation.- Nonlinear Dynamic Analysis of Shells of Revolution.- Various Approaches for the Modeling of Flexible Robot Arms.- On the Generality of Systems having an Infinitely Dense Discrete Spectrum of Resonant Frequencies.