Related papers: On the Eigenvalue Distribution for a Beam with Att…
The paper is devoted to the observability study of a dynamic system, which describes the vibrations of an elastic beam with an attached rigid body and distributed control actions. The mathematical model is derived using Hamilton's principle…
The mathematical model of a real flexible elastic system with distributed and discrete parameters is considered. It is a partial differential equation with non-classical boundary conditions. Complexity of the boundary conditions results in…
This paper addresses the dynamics of locally-resonant sandwich beams, where multi-degree-of-freedom viscously-damped resonators are periodically distributed within the core matrix. Using an equivalent single-layer Timoshenko beam model…
We consider the eigenvalue problem for the Reissner-Mindlin system arising in the study of the free vibration modes of an elastic clamped plate. We provide quantitative estimates for the variation of the eigenvalues upon variation of the…
The eigenvalues of a new microbeam-rigid-body gyroscope are computed and studied to show the variation of frequencies versus the input spin rate. To this end, assuming the harmonic solution of the dynamic equation of motion the…
The present work attempts to present a consistent and efficient approach to piezoelectric laminated beams. The influence of hypotheses on three-dimensional sectional deformations and stress distributions on the estimate of the beam…
A mechanical system consisting of an elastic beam under harmonic excitation and an attached sliding body is investigated. Recent experimental observations suggest that the system passively (self-)adapts the axial location of the slider to…
Vibrations of structures subjected to concentrated point loads have many applications in mechanical engineering. Experiments are expensive and numerical methods are often used for simulations. In this paper, we consider the plate vibration…
A system consisting of a doubly clamped beam with an attached body (slider) free to move along the beam has been studied recently by multiple research groups. Under harmonic base excitation, the system has the capacity to passively adapt…
In this paper, we consider the problem of mechanical wave scattering from a spatially finite system into an infinite surrounding environment. The goal is to illuminate why the scattering spectrum undergoes peaks and dips (resonances) at…
One of the most used approaches in simulating materials is the tight-binding approximation. When using this method in a material simulation, it is necessary to compute the eigenvalues and eigenvectors of the Hamiltonian describing the…
Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…
The purpose of this paper is to analyze a mixed method for linear elasticity eigenvalue problem, which approximates numerically the stress, displacement, and rotation, by piecewise $(k+1)$, $k$ and $(k+1)$-th degree polynomial functions…
The present paper introduces the analysis of the eigenvalue problem for the elasticity equations when the so called Navier-Lam\'e system is considered. Such a system introduces the displacement, rotation and pressure of some linear and…
The eigenvalue distribution is investigated for matrix models related via the localization to Chern-Simons-matter theories. An integral representation of the planar resolvent is used to derive the positions of the branch points of the…
In the present work, eigenvalue distributions defined by a random rectangular matrix whose components are neither independently nor identically distributed are analyzed using replica analysis and belief propagation. In particular, we…
In this paper, we investigate a transmission eigenvalue problem that couples the principles of acoustics and elasticity. This problem naturally arises when studying fluid-solid interactions and constructing bubbly-elastic structures to…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
The direct calculation of magnetoelastic wave dispersion in layered media is presented using an efficient, accurate computational technique. The governing, coupled equations for elasticity and magnetism, the Navier and Landau-Lifshitz…
The eigenvalue problem for the p-wave bound states formed by two unequal-mass scalar particles through the massive scalar particle exchange is analyzed numerically in the framework of the Bethe-Salpeter ladder model. As in the s-wave case,…