The eigenvalue problem for networks of beams

DOI10.1016/S0024-3795(00)00118-XzbMath0979.74026MaRDI QIDQ1580533

Bertrand Dekoninck, Serge Nicaise

Publication date: 14 September 2000

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

graphspectrumcharacteristic equationWeyl's formulaasymptotic behaviour of eigenvaluesnetworks of Euler-Bernoulli beams

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics (74H10) Vibrations in dynamical problems in solid mechanics (74H45)

Related Items (36)

Poincaré--Perron's method for the Dirichlet problem on stratified sets ⋮ Higher-order operators on networks: hyperbolic and parabolic theory ⋮ On vertex conditions for elastic systems ⋮ Spectrum of a network of Euler-Bernoulli beams ⋮ Null-Controllability of the Linear Kuramoto--Sivashinsky Equation on Star-Shaped Trees ⋮ Asymptotic convergence of solutions of Keller-Segel equations in network shaped domains ⋮ Exact controllability to eigensolutions of the bilinear heat equation on compact networks ⋮ A pinned network of Euler-Bernoulli beams under feedback controls ⋮ Inverse nodal problem for Sturm-Liouville operator on a star graph with nonequal edges ⋮ Stability and Riesz basis property for general network of strings ⋮ Stabilization and Riesz basis of a star-shaped network of Timoshenko beams ⋮ Three‐dimensional elastic beam frames: Rigid joint conditions in variational and differential formulation ⋮ Asymptotic behavior of some elastic planar networks of Bernoulli–Euler beams ⋮ Surgery transformations and spectral estimates of \(\delta\) beam operators ⋮ Spectral properties of a fourth‐order differential operator on a network ⋮ On the existence of a solution of a boundary value problem on a graph for a nonlinear equation of the fourth order ⋮ Exponential stabilization of variable coefficient wave equations in a generic tree with small time-delays in the nodal feedbacks ⋮ Modeling and discretization methods for the numerical simulation of elastic frame structures ⋮ \(n\)-Laplacians on metric graphs and almost periodic functions. I ⋮ The structural property of a class of vector-valued hyperbolic equations and applications ⋮ Recovering differential pencils on compact graphs ⋮ Bi-Laplacians on graphs and networks ⋮ Optimal Control Problems Driven by Time-Fractional Diffusion Equations on Metric Graphs: Optimality System and Finite Difference Approximation ⋮ Control of a network of Euler-Bernoulli beams ⋮ Inverse problems for differential operators on trees with general matching conditions ⋮ Unitary dimension reduction for a class of self-adjoint extensions with applications to graph-like structures ⋮ Weyl formula with optimal remainder estimate of some elastic networks and applications ⋮ Boundary controllability of a chain of serially connected Euler-Bernoulli beams with interior masses ⋮ Inverse spectral problems for differential pencils on a graph with a rooted cycle ⋮ Exponential stability of a network of serially connected Euler–Bernoulli beams ⋮ Elastodynamics on graphs—wave propagation on networks of plates ⋮ Uniform exponential stabilisation of serially connected inhomogeneous Euler-Bernoulli beams ⋮ On the Spectral Gap for Networks of Beams ⋮ Exponential stability of a network of beams ⋮ Control of networks of Euler-Bernoulli beams ⋮ Initial state estimation from limited observations of the heat equation in metric graphs

Cites Work

• Classical solvability of linear parabolic equations on networks
• Modeling, analysis and control of dynamic elastic multi-link structures
• A class of fourth-order differential equations on a spatial net
• A characteristic equation associated to an eigenvalue problem on \(c^ 2\)-networks
• A characterization of a generalized \(C^{\infty}\)-notion on nets
• Regular solutions of transmission and interaction problems for wave equations
• Modeling, Stabilization and Control of Serially Connected Beams
• Sturm-Liouville eigenvalue problems on networks
• Analysis, Designs, and Behavior of Dissipative Joints for Coupled Beams
• Explicit Heat Kernel on Generalized Cones
• Control of Planar Networks of Timoshenko Beams
• Dynamical interface transition in ramified media with diffusion
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