Related papers: On the first frequency of reinforced partially hin…

An important class of resonance problems involves the study of perturbations of systems having embedded eigenvalues in their continuous spectrum. Problems with this mathematical structure arise in the study of many physical systems, e.g.…

A pinned or free-floating rigid plate lying on the free surface of a thin film of viscous fluid, which itself lies on top of a horizontal substrate that is moving to the right at a constant speed is considered. The focus of the present work…

The selective frequency damping method was applied to a bent flow. The method was used in an adaptive formulation. The most dangerous frequency was determined by solving an eigenvalue problem. It was found that one of the patterns,…

A piecewise-homogeneous elastic orthotropic plate, reinforced with a finite patch of the wedgeshaped, which meets the interface at a right angle and is loaded with tangential and normal forces is considered. By using methods of the theory…

In this paper, stability and sensitivity properties of a class of parametric constrained optimization problem, whose feasible region is defined by a set-valued inclusion, are investigated through the associated optimal value function.…

We determine the asymptotic behaviour of eigenvalues of clamped plates under large compression, by relating this problem to eigenvalues of the Laplacian with Robin boundary conditions. Using the method of fundamental solutions, we then…

Maximization and minimization problems of the principle eigenvalue for divergence form second order elliptic operators with the Dirichlet boundary condition are considered. The principal eigen map of such elliptic operators is introduced…

In this paper we consider the inverse problem of determining a rigid inclusion inside a thin plate by applying a couple field at the boundary and by measuring the induced transversal displacement and its normal derivative at the boundary of…

In this paper we consider some stabilization problems for the wave equation with switching. We prove exponential stability results for appropriate damping coefficients. The proof of the main results is based on D'Alembert formula and some…

A recently developed nonlinear analytical model for axially loaded thin-walled stringer-stiffened plates based on variational principles is extended to include local buckling of the main plate. Interaction between the weakly stable global…

A new $n-$ noded polygonal plate element is proposed for the analysis of plate structures comprising of thin and thick members. The formulation is based on the discrete Kirchhoff Mindlin theory. On each side of the polygonal element,…

- The purpose of this article is to study possible concentrations of eigenfunc-tions of Laplace operators (or more generally quasi-modes) on product manifolds. We show that the approach of the first author and Zworski [10, 11] applies…

We study the rate of convergence for (variational) eigenvalues of several non-linear problems involving oscillating weights and subject to different kinds of boundary conditions in bounded domains.

We consider a gyroscopic system under the action of small dissipative and non-conservative positional forces, which has its origin in the models of rotating bodies of revolution being in frictional contact. The spectrum of the unperturbed…

We propose a general framework to study the stability of the subspace spanned by $P$ consecutive eigenvectors of a generic symmetric matrix ${\bf H}_0$, when a small perturbation is added. This problem is relevant in various contexts,…

Functionally graded materials (FGMs) represent a promising class of advanced materials designed with tailored microstructures to achieve optimized mechanical, thermal, and functional properties across varying gradients. The strategic…

This paper concerns the global propagation of impact-induced tensile waves in a kind of phase-transforming materials. It is well-known that the governing system of partial differential equations is hyperbolic-elliptic and the…

We study a nonlinear, nonlocal eigenvalue problem driven by the fractional p-Laplacian with an indefinite, singular weight chosen in an optimal class. We prove the existence of an unbounded sequence of positive variational eigenvalues and…

This work investigates the multiplicity and differentiability of eigenfrequencies in structures with various symmetries. In particular, the study explores how the geometric and design variable symmetries affect the distribution of…

Hydrodynamic instability of a gravity-driven flow down an inclined plane is investigated in the presence of a floating elastic plate which rests on the top surface of the flow. Linear instability of the system with respect to infinitesimal…