Refined dynamical theories of beams, plates and shells and their applications : proceedings of the Euromech-Colloquium 219, [held during September 23-26, 1986, in Kassel, Federal Republic of Germany

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. Front Matter....Pages I-IX From Newton’s Fluid to the Theory of Plates....Pages 1-16 On a Certain Mixed Variational Theorem and on Laminated Elastic Shell Theory....Pages 17-27 A Note on the Derivation of Higher-Order Two-Dimensional Theories of Transverse Bending of Elastic Plates....Pages 28-31 A General Transverse Shear Deformation Theory of Anisotropic Plates....Pages 32-43 Component Mode Synthesis of Multi-Rotor Systems....Pages 44-55 Dynamic Stability of Initially Curved Columns under a Time Dependent Axial Displacement of their Support....Pages 56-71 Theoretical and Experimental Results on the Dynamic Behaviour of Composite Beams, Plates and Shells....Pages 72-88 Study of the Dynamic Behaviour of Eccentrically Stiffened Mindlin Plates under the Influence of Plane Forces....Pages 91-101 On the Vibration of Thick Annular Plates....Pages 102-111 An “Exact” Solution for the Linear Small-Amplitude Vibrations of a Rectangular Plate....Pages 112-121 Consistent and Inconsistent Higher Order Beam and Plate Theories: Some Surprising Comparisons....Pages 122-130 Energy-Consistent Models of Plates with Moderate Thickness....Pages 131-139 Geometrically Nonlinear Theories for Laminated Composite Plates Treated in the Framework of the Small Strain and Moderate Rotation Concept....Pages 140-150 A Three-Dimensional Refined Theory of Elastic Plates....Pages 151-159 Refined Effects in Beam Theories and Their Influence on the Natural Frequencies of Beams....Pages 163-179 Nonlinear Vibrations of Beams Including Shear Deformations and Rotatory Inertia....Pages 180-191 Torsion and Related Concepts: Some Steps Beyond Saint-Venant’s Principle....Pages 192-201 Wave Propagation in Elastic Rods, with Shear and Rotary Inertia Effects....Pages 202-212 On Nonlinear Equations of a Beam....Pages 213-222 Riemann’s Formulae and Their Application to the Timoshenko Beam Model....Pages 223-232 Dynamic Stability of Thick, Orthotropic, Circular Cylindrical Shells....Pages 235-244 On the Wave Solution for Beams on a Viscoelastic Foundation Subjected to a Travelling and Oscillating Force....Pages 245-260 Influence of the Shear Deformation and Rotary Inertia on the Flutter of a Cantilever Subjected to a Follower Force — Exact and Symbolic Manipulation Solutions....Pages 261-273 Dynamic Response and Reliability of Laminated Plates to Random Loading....Pages 274-285 A Mixed Variational Formulation for Laminated Plates....Pages 289-303 Influence of the Variation of Structural Properties on the Probability of a Composite Plate to Meet a Target Eigenfrequency....Pages 304-314 On Higher-Order Effects of Coupled Wave Motion in Layered Structures....Pages 315-323 Free Vibration Analysis of Thickness Shear Deformable Cross-Ply Laminated Oval Cylindrical Shells....Pages 324-332 A Dynamical Theory of Inhomogeneous Slender Structures and its Applications....Pages 333-347 Some Static and Dynamical Contact Problems between a Mindlin Plate and an Elastic Foundation....Pages 351-361 One-Dimensional Theories for Cracked Beams....Pages 362-372 Refined Effects in Turbomachinery Blade Vibrations....Pages 373-382 Self-Adjointness and Definiteness —A Necessary Condition for the Boundary Value Problem of the Free Undamped Vibrations of the Plate....Pages 383-392 Damped Response of Orthotropic Shallow Spherical Shells on Nonlinear Elastic Foundation....Pages 393-401 Nonlinear Dynamic Analysis of Shells of Revolution....Pages 402-419 Various Approaches for the Modeling of Flexible Robot Arms....Pages 420-429 On the Generality of Systems Having an Infinitely Dense Discrete Spectrum of Resonant Frequencies....Pages 430-436 Back Matter....Pages 438-438 As is known, classical theories of vibration of the most freƯ 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 pracƯ 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 develƯ 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 UniƯ 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