Three‐dimensional elastic beam frames: Rigid joint conditions in variational and differential formulation
From MaRDI portal
Publication:6064094
DOI10.1111/sapm.12485zbMath1528.74072arXiv2104.01275MaRDI QIDQ6064094
Mahmood Ettehad, Gregory Berkolaiko
Publication date: 12 December 2023
Published in: Studies in Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2104.01275
irreducible representationsymmetry groupEuler-Bernoulli beamself-adjoint differential operatoroscillation mode
Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Vibrations in dynamical problems in solid mechanics (74H45) Junctions (74K30)
Related Items
Computing nodal deficiency with a refined Dirichlet-to-Neumann map ⋮ Impediments to diffusion in quantum graphs: Geometry-based upper bounds on the spectral gap ⋮ Surgery transformations and spectral estimates of \(\delta\) beam operators
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On vertex conditions for elastic systems
- Bloch principle for elliptic differential operators with periodic coefficients
- Spectral analysis on graph-like spaces
- Periodic orbit theory and spectral statistics for quantum graphs
- Modeling, analysis and control of dynamic elastic multi-link structures
- The eigenvalue problem for networks of beams
- Exact boundary controllability of two Euler-Bernoulli beams connected by a point mass
- Fourth-order differential equations on geometric graphs
- Perturbation theory for linear operators.
- Modeling of the junction between two rods
- A characteristic equation associated to an eigenvalue problem on \(c^ 2\)-networks
- Bi-Laplacians on graphs and networks
- Closed-form solution for the free axial-bending vibration problem of structures composed of rigid bodies and elastic beam segments
- On the ground state for quantum graphs
- \(n\)-Laplacians on metric graphs and almost periodic functions. I
- Limits of quantum graph operators with shrinking edges
- Exact boundary controllability on a tree-like network of nonlinear planar Timoshenko beams
- Spectrum of a network of Euler-Bernoulli beams
- An overview of periodic elliptic operators
- Norm convergence of sectorial operators on varying Hilbert spaces
- Thin tubes in mathematical physics, global analysis and spectral geometry
- Modelling of dynamic networks of thin thermoelastic beams
- Boundary Controllability of a Hybrid System Consisting in Two Flexible Beams Connected by a Point Mass
- Stabilization of Berger–Timoshenko's equation as limit of the uniform stabilization of the von Kármán system of beams and plates
- A finite element method for quantum graphs
- Homogenization of elasticity problems on singular structures
- Surgery principles for the spectral analysis of quantum graphs
- A GENERAL ALGORITHM FOR COMPUTING NATURAL FREQUENCIES OF ELASTIC STRUCTURES
- Convergence of spectra of mesoscopic systems collapsing onto a graph
