# Three‐dimensional elastic beam frames: Rigid joint conditions in variational and differential formulation

@article{Berkolaiko2022ThreedimensionalEB, title={Three‐dimensional elastic beam frames: Rigid joint conditions in variational and differential formulation}, author={Gregory Berkolaiko and Mahmood Ettehad}, journal={Studies in Applied Mathematics}, year={2022}, volume={148}, pages={1586 - 1623} }

We consider three‐dimensional elastic frames constructed out of Euler–Bernoulli beams and describe a simple process of generating joint conditions out of the geometric description of the frame. The corresponding differential operator is shown to be self‐adjoint. In the special case of planar frames, the operator decomposes into a direct sum of two operators, one coupling out‐of‐plane displacement to angular (torsional) displacement and the other coupling in‐plane displacement with axial…

## 2 Citations

On Vertex Conditions In Elastic Beam Frames: Analysis on Compact Graphs

- Mathematics
- 2021

We consider three-dimensional elastic frames constructed out of Euler-Bernoulli beams and describe extension of matching conditions by relaxing the vertex-rigidity assumption and the case in which…

On the Spectra of Periodic Elastic Beam Lattices: Single-Layer Graph

- Physics, Mathematics
- 2021

We present full description of spectra for a Hamiltonian defined on periodic hexagonal elastic lattices. These continua are constructed out of Euler-Bernoulli beams, each governed by a scalar-valued…

## References

SHOWING 1-10 OF 60 REFERENCES

Wave Analysis of In-Plane Vibrations of L-Shaped and Portal Planar Frame Structures

- Engineering
- 2012

This paper concerns in-plane vibration analysis of coupled bending and longitudinal vibrations in L-shaped and portal planar frame structures. An exact analytical solution is obtained using wave…

Exact boundary controllability of two Euler-Bernoulli beams connected by a point mass

- Mathematics
- 2000

Boundary Controllability of a Hybrid System Consisting in Two Flexible Beams Connected by a Point Mass

- Mathematics
- 1998

We consider a hybrid system consisting of two flexible beams connected by a point mass. The constant of rotational inertia is assumed to be nonzero. In a previous paper we have proved that, in the…

Modelling of dynamic networks of thin thermoelastic beams

- Mathematics
- 1993

We derive a distributed-parameter model of a thin non-linear thermoelastic beam in three dimensions. The beam can also be initially curved and twisted. Our main task is to formulate the…

A GENERAL ALGORITHM FOR COMPUTING NATURAL FREQUENCIES OF ELASTIC STRUCTURES

- Computer Science
- 1971

On the Spectra of Periodic Elastic Beam Lattices: Single-Layer Graph

- Physics, Mathematics
- 2021

We present full description of spectra for a Hamiltonian defined on periodic hexagonal elastic lattices. These continua are constructed out of Euler-Bernoulli beams, each governed by a scalar-valued…