Comments on the Bernoulli-Euler Beam Theory Derivation of the Beam Theory Including Rotary Inertia Effect Incorporation of the Effect of Shear Deformation in Addition to That of Rotary Inertia Topic of Priority: The So-Called Timoshenko Beam Theory Developed by S.P. Timoshenko and P. Ehrenfest Alternative Accounting of the Rotary Inertia and Shear E f fe c t s Controversy Associated with Two Frequency Branches Review of Some Recent Definitive Works Controversy about Shear Coefficient . Exact Solution of Timoshenko-Ehrenfest Equations 107 Exact Solution for Vibration of a Shear-Deformable Beam Without Transverse Vibration Free Vibration Analysis for Arbitrary Set of B C s Determination of the Whole Spectrum of the Timoshenko-Ehrenfest Beam Intermediate Theory Between the Bernoulli-Euler and the Timoshenko- Ehrenfest Beam Theories: Truncated Timoshenko-Ehrenfest Equations Contributions of Various Terms in Timoshenko- Ehrenfest Equation for Simply Supported Beam Physical Reasoning for Truncating Timoshenko- Ehrenfest Equations More Consistent Derivation of Refining T e rm s Physical Significance of Truncation Differential Equations and Boundary Conditions Simmonds’ Comments Asymptotic Approach in Case of Plane S t r e s s Boundary and Initial Conditions Application of the Krein’s Method for Determination of Natural Frequencies of Periodically Supported Beam Based on Truncated Timoshenko-Ehrenfest Equations Vibration Analysis of Multi-Span Beam Simply Supported of Both E n d s Chapter 4. Refined Theories May Be Needed for Buckling or Vibration Analyses of Structures with Overhang 185 A n a ly s is Boundary Conditions S o lu t io n Results and Discussion Effect of Shear Deformation on Buckling of Columns with Overhang Effect of End Shortening in Columns with Overhang A Controversy Between Two Buckling Formulas Stability of an Overhanging Pipe Conveying Fluid Intermediate Theory Between Kirchhoff- Love and Uflyand-Mindlin Plate Theories: Truncated Uflyand-Mindlin Equations Effect of Rotary Inertia on Vibrations of Uniform and Homogeneous Plates Uflyand’s Plate Theory Mindlin’s Plate Theory Derivation of Exact Vibration Formula for the Simply Supported Uflyand-Mindlin P la t e s Vibrations of the Rectangular Uflyand-Mindlin Plates Simply Supported at Two Opposite E d g e s Extended Bolotin’s Dynamic Edge Effect Method for General Boundary Conditions Some Misconceptions on the Timoshenko-Ehrenfest Beams and the Uflyand-Mindlin Plates Chapter 6. Non-local Theory of Nanobeams with Surface Effects Based on Truncated Timoshenko-Ehrenfest Equations Analysis without Surface Effects Analysis with Surface Effects Free Vibrations of Non-local Bernoulli-Euler Beams Free Vibration Analysis of the Timoshenko-Ehrenfest Beams without Surface Effects Free Vibrations Analysis of the Timoshenko-Ehrenfest Beams with Surface Effects Virus Sensor Based on Single-Walled Carbon Nanotube with Surface Effects Taken into A c cou n t . Finite Element Method for the Timoshenko-Ehrenfest Beams and the Uflyand-Mindlin Plates Preliminary Concepts Solution of the Timoshenko -Ehrenfest Dynamic Problem by a Single Variable Approach Interdependent Shape P o lynom ia ls Element Stiffness and Mass M a t r ic e s Numerical Example Solution of the Uflyand-Mindlin Plate Problem by a Single Variable Approach The Fictitious Deflection in the Uflyand-Mindlin Plate Dynamic P r o b lem The Interdependent Shape Polynomials for the UMPM . . . 376 The Element Stiffness and Mass Matrices Numerical Examples for FEM Analysis of the Uflyand-Mindlin Plates Chapter 8. Random Vibration of Space Shuttle Weather Protection Systems and Related . The Equivalent Timoshenko-Ehrenfest B e a m Random Vibration of a Weather-Protection System Modeled as a Timoshenko-Ehrenfest Beam Random Vibration of a Structure Subjected to a Non-White Excitation Some Closed-Form Solutions in Random Vibration of the Timoshenko-Ehrenfest Beams Subjected to Space-Time White N o i s e Transverse-Viscous Damping The Timoshenko-Ehrenfest Beam with Structural Damping The Timoshenko-Ehrenfest Beam with Voigt Damping The Timoshenko-Ehrenfest Beam with Rotary and Transverse D am p in g Elucidation of Random Vibration Results on a Simple M o d e l Conclusion and Directions for Further Biographical Notes Multi-Span Beam Clamped at Both Ends Multi-Span Beam Simply Supported at One End and Clamped at the Other Different Possible Solutions for Eqs. (5.63a)-(5.63c) (Chapter 5) On the Existence of Eigenvalues with Application o f Hamilton’s Principle to the Non-local Timoshenko-Ehrenfest Beams Expression o f Element o f Matrix C The Expression o f the Element Stiffness and Mass Matrices Some Closed-Form Solutions in Random Vibration o f Bernoulli-Euler Beams A Tribute Written by Prof. Chia-Shun Yih (Stephen P. Timoshenko Distinguished University Professor, University of Michigan) in October 1972, the Year of Prof. Timoshenko’s Death