This article presents an analysis of free vibration of elastically supported Timoshenko beams by using the spectral element method. The governing partial differential equation is elaborated to formulate the spectral stiffness matrix. Effectively, the non classical end boundary conditions of the beam are the primordial task to calibrate the phenomenon of the Timoshenko beam-soil foundation inter...

A two-grid discretization scheme is proposed for solving eigenvalue problems, including both partial differential equations and integral equations. With this new scheme, the solution of an eigenvalue problem on a fine grid is reduced to the solution of an eigenvalue problem on a much coarser grid, and the solution of a linear algebraic system on the fine grid and the resulting solution still ma...

The partial quadratic eigenvalue assignment problem (PQEAP) is to compute a pair of feedback matrices such that a small number of unwanted eigenvalues in a structure are reassigned to suitable locations while keeping the remaining large number of eigenvalues and the associated eigenvectors unchanged. The problem arises in active vibration control of structures. For real-life applications, it is...

Для случайных $(n\times n)$-матриц $X_n$ с независимыми элементами и собственными значениями $\lambda_1,\ldots,\lambda_n$ в основополагающей работе Б. Райдера Дж. Сильверстейна 2006 г. утверждается, что флуктуации линейных статистик собственных значений $\sum_{i=1}^n f(\lambda_i)$ для достаточно "хороших" тестовых функций $f$ сходятся к гауссовскому распределению. Мы изучаем сумм $\sum_{i=1}^{n...

Wind power is seen as the most cost effective way to generate electricity from renewable sources. The wind turbine prime mover, wind, is uncontrollable as compared to the conventional power plant prime mover. Therefore, it becomes very important to carry out investigations on the dynamic behavior of wind power generating systems. In this paper, the dynamic model of 1 MVA unit is extrapolated fr...

3 Why Use SDP? 5 3.1 Tractable Relaxations of Max-Cut . . . . . . . . . . . . . . . . . . . . . . . . 5 3.1.1 Simple Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.2 Trust Region Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.3 Box Constraint Relaxation . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.4 Eigenvalue Bound . . . . . . . . . . . . ...

An approach for eigenvalue assignment in linear descriptor systems via output feedback is proposed. Sufficient conditions in order that a given set of eigenvalues is assignable are established. Parametric form of the desired output feedback gain matrix is also given. The approach assigns the full number of generalised eigenvalues, guarantees the closed-loop regularity and overcomes the defects ...