arXiv subjects

Josip Tambača

Publications and source records attributed to Josip Tambača.

5 recordsLinked to original sources

arXiv2026

Optimal placement and tuning of pointwise dampers for vibrating strings via a Lyapunov framework

We study the optimal placement and tuning of a small number of pointwise viscous dampers for a vibrating string. Starting from a finite element discretization of the damped wave equation, the system is transformed into a first-order phase-space formulation, which enables a unified Lyapunov trace framework. Three optimization criteria are considered: average total energy, average total displacement, and energy for a fixed initial state. For all criteria, explicit gradient formulas with respect to damper positions and viscosities are derived, requiring only one primal and one dual Lyapunov solve. Due to the strong non-convexity of the problem, a simple heuristic based on an explicit single-damper formula is proposed to generate effective initial guesses. Numerical examples illustrate the influence of spectral selection and discretization on the optimal damping configuration.

math.NA↗

arXiv2026

A fully averaged poroelastic Kirchhoff plate interacting with an incompressible, viscous fluid: analysis and numerical simulation

We study a new fully averaged poroelastic Kirchhoff plate model coupled with the flow of an incompressible, viscous fluid governed by the time-dependent Stokes equations. The fully averaged formulation offers several advantages over the classical Biot poroelastic plate model: both elastodynamic and pressure equations are posed on a codimension-one interface, the resulting numerical schemes are simpler to implement and computationally more efficient, and the fluid-structure coupling is more natural. We analyze a linearly coupled fluid-structure interaction problem with kinematic and dynamic interface conditions enforcing continuity of normal velocities, the Beavers-Joseph-Saffman slip in the tangential velocities, and balance of forces between the fluid and the poroelastic structure. We establish the existence of weak solutions using energy methods, and then prove global-in-time existence of a unique strong solution to a regularized version of the problem using sectoriality of the associated spatial operator and maximal $\mathrm{L}^p$-regularity of the resulting Cauchy problem. For data with exponential decay, we prove exponential decay of solutions. Finally, we develop a finite element method for the numerical approximation of the coupled system and show that it provides an excellent approximation of the full Biot-Stokes system in the thin-structure regime. The main advantage of this model lies in the remarkably simple implementation, as the poroelastic plate equations constitute a surface model bounding a bulk fluid domain. These results provide a rigorous analytical and computational framework for the study of coupled fluid-poroelastic structure interactions involving thin poroelastic interfaces modeled by the fully averaged Kirchhoff poroelastic plate equations.

math.AP↗

arXiv2019

Homogenization of the time-dependent heat equation on planar one-dimensional periodic structures

In this paper we consider the homogenization of a time-dependent heat conduction problem on a planar one-dimensional periodic structure. On the edges of a graph the one-dimensional heat equation is posed, while the Kirchhoff junction condition is applied at all (inner) vertices. Using the two-scale convergence adapted to homogenization of lower-dimensional problems we obtain the limit homogenized problem defined on a two-dimensional domain that is occupied by the mesh when the mesh period $δ$ tends to $0$. The homogenized model is given by the classical heat equation with the conductivity tensor depending on the unit cell graph only through the topology of the graph and lengthes of its edges. We show the well-posedness of the limit problem and give a purely algebraic formula for the computation of the homogenized conductivity tensor. The analysis is completed by numerical experiments showing a convergence to the limit problem where the convergence order in $δ$.

math.AP↗

arXiv2017

Mixed formulation of the one-dimensional equilibrium model for elastic stents

In this paper we formulate and analyze the mixed formulation of the one-dimensional equilibrium model of elastic stents. The model is based on the curved rod model for the inextensible and ushearable struts and is formulated in the weak form in Čanić and Tambača, 2012. It is given by a system of ordinary differential equations at the graph structure. In order to numerically treat the model using finite element method the mixed formulation is plead for. We obtain equivalence of the weak and the mixed formulation by proving the Babuska--Brezzi condition for the stent structure.

math-ph↗

arXiv2011

Derivation of the nonlinear bending-torsion model for a junction of elastic rods

In this paper we derive the one-dimensional bending-torsion equilibrium model modeling the junction of straight rods. The starting point is a three-dimensional nonlinear elasticity equilibrium problem written as a minimization problem for a union of thin rod-like bodies. By taking the limit as the thickness of the 3D rods goes to zero, and by using ideas from the theory of $Γ$-convergence, we obtain that the resulting model consists of the union of the usual one-dimensional nonlinear bending-torsion rod models which satisfy the following transmission conditions at the junction point: continuity of displacement and rotation of the cross-sections and balance of contact forces and contact couples.

math.AP↗