Vibrations of Beams and Plates: Review of First Closed-Form Solutions in the Past 250 Years
From MaRDI portal
Publication:2928211
DOI10.1007/978-3-211-70963-4_15zbMath1298.74102OpenAlexW974757208MaRDI QIDQ2928211
Publication date: 7 November 2014
Published in: Mechanical Vibration: Where do we Stand? (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-3-211-70963-4_15
Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Vibrations in dynamical problems in solid mechanics (74H45) Plates (74K20) Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids (74-02) Explicit solutions of dynamical problems in solid mechanics (74H05)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Some exact solutions for the bending of beams with spatially stochastic stiffness
- Perturbation method in the problem of large deflections of circular plates with nonuniform thickness
- Transverse vibration of circular and elliptic plates with variable thickness
- Transverse vibration of circular and elliptic plates with quadratically varying thickness
- A remarkable nature of the effect of boundary conditions on closed-form solutions for vibrating inhomogeneous Bernoulli-Euler beams
- Transverse vibration of a circular plate with arbitrary thickness variation
- Three-dimensional elasticity solutions for free vibrations of circular plates: A polynomials-Ritz analysis
- A novel formulation leading to closed-form solutions for buckling of circular plates
- Axisymmetric vibrations of circular plates of linearly varying thickness
- Closed-form solutions for axially graded beam-columns
- CLOSED-FORM TRIGONOMETRIC SOLUTIONS FOR INHOMOGENEOUS BEAM-COLUMNS ON ELASTIC FOUNDATION
- An Analogy Between the Flexural Vibrations of a Cone and a Disc of Linearly Varying Thickness
- Some special solutions for the flexural vibration of discs of varying thickness
- An exact, closed form, solution for the flexural vibration of a thin annular plate having a parabolic thickness variation
- The Vibration of a Circular Plate With Varying Thickness
- Analysis of High-Speed Rotating Disks With Variable Thickness and Inhomogeneity
- Eigenvalues of Inhomogeneous Structures
- Vibration Frequencies of Tapered Bars and Circular Plates
- FREE VIBRATION OF POLAR ORTHOTROPIC CIRCULAR PLATES OF VARIABLE THICKNESS WITH ELASTICALLY RESTRAINED EDGE
- New Closed-Form Solutions for Buckling of a Variable Stiffness Column by Mathematica®
- THE NORMAL MODES OF A CIRCULAR PLATE OF VARIABLE THICKNESS
- Random Eigenvalue Problems in Structural Analysis
- Vibrations of circular plates of variable thickness under an inplane force
- Apparently first closed-form solution for vibrating inhomogeneous beams