Modal parameters obtained from modal testing (such as modal vectors, natural frequencies, and damping ratios) have been used extensively in system identi"cation, "nite element model updating, and structural health monitoring. As an alternative to modal vectors, load-dependent Ritz vectors have been shown useful in various areas of structural dynamics such as model reduction and damage detection...

The open profile thin elastic wavy shell natural oscillations problem is considered. proposed method for determining the numerical values of lowest frequencies and corresponding forms vibrations shells with a complicated shape based on Rayleigh-Ritz energy method. results calculation rigidly pinched lower contour are presented.

We consider a model of three electrons and one hole confined in a two-dimensional (2D) plane, interacting with one another through Coulomb forces. Using a Ritz variational method we find an upper bound of ≈ −0.0112me 4 /8π 2 ǫ 2 ¯ h 2 for the ground-state energy of such a system when the particles are near one another. The possible connections of such a complex to other fields of physics are di...

Power supply is a bottle-neck problem of wireless micro-sensors, especially where the replacement of batteries is impossible or inconvenient. Now piezoelectric material is being used to harvest vibration energy for self-powered sensors. However, the geometry of a piezoelectric cantilever beam will greatly affect its vibration energy harvesting ability. This paper deduces a remarkably precise an...

Using deep neural networks to solve PDEs has attracted a lot of attentions recently. However, why the learning method works is falling far behind its empirical success. In this paper, we provide rigorous numerical analysis on Ritz (DRM) \cite{wan11} for second order elliptic equations with Neumann boundary conditions. We establish first nonasymptotic convergence rate in $H^1$ norm DRM using $\m...

In this paper a guaranteed upper bound of the global discretization error in linear elastic finite element approximations is presented, based on a generalized Trefftz functional. Therefore, the general concept of complementary energy functionals and the corresponding approximation methods of Ritz, Trefftz, the method of orthogonal projection and the hypercircle method are briefly outlined. Furt...

Abstract: Condition numbers for infinite-dimensional optimization, as defined in Zolezzi (2002, 2003), are shown to exhibit a stable behavior when employing finite-dimensional solution methods of the Ritz type, in particular finite elements. The same behavior is shown to hold in connection with the so called extended Ritz method.

In this paper, an elastic shell model is presented for postbuckling prediction of a long thinwalledcylindrical shell under axial compression. The Ritz method is applied to solve the governingequilibrium equation of a cylindrical shell model based on the von-Karman type nonlinear differentialequations. The postbuckling equilibrium path is obtained using the energy method for a long thin-walledcy...

In this paper at first introduced constituent equations for piezoelectric and then by the help of this equations, internal energy of hinged-hinged piezoelectric multilayer beam was computed. Then by the principle of minimum potential energy and Rayleigh -Ritz method the bending curvature equation of hinged-hinged piezoelectric multilayer beam under concentrated moment, concentrated force, unifo...

Eigenvalue estimates that are optimal in some sense have selfevident appeal and leave estimators with a sense of virtue and economy. So, it is natural that ongoing searches for effective strategies for difficult tasks such as estimating matrix eigenvalues that are situated well into the interior of the spectrum revisit from time to time methods that are known to yield optimal bounds. This artic...