Purpose: – The purpose of this paper is to present an application of the Generalized Finite Element Method (GFEM) for modal analysis of 2D wave equation. Design/methodology/approach: – The GFEM can be viewed as an extension of the standard Finite Element Method (FEM) that allows non-polynomial enrichment of the approximation space. In this paper the authors enrich the approximation space with sine e cosine functions, since these functions frequently appear in the analytical solution of the problem under study. The results are compared with the ones obtained with the polynomial FEM using higher order elements. Findings: – The results indicate that the proposed approach is able to obtain more accurate results for higher vibration modes than standard polynomial FEM. Originality/value: – The examples studied in this paper indicate a strong potential of the GFEM for the approximation of higher vibration modes of structures, analysis of structures subject to high frequency excitations and other problems that concern high frequency oscillatory phenomena.

Purpose: The purpose of this paper is to check the efficiency of isogeometric analysis (IGA) by comparing its results with classical finite element method (FEM), generalized finite element method (GFEM) and other enriched versions of FEM through numerical examples of free vibration problems. Design/methodology/approach: Since its conception, IGA was widely applied in several problems. In this paper, IGA is applied for free vibration of elastic rods, beams and trusses. The results are compared with FEM, GFEM and the enriched methods, concerning frequency spectra and convergence rates. Findings: The results show advantages of IGA over FEM and GFEM in the frequency error spectra, mostly in the higher frequencies. Originality/value: Isogeometric analysis shows a feasible tool in structural analysis, with emphasis for problems that requires a high amount of vibration modes.

Based on experimental pieces of evidence collected in a set of twenty healthy large hydrogenerators, this article shows that the operating conditions of the tilting pad journal bearings of these machines may have unpredictable and significant changes. This behavior prevents the theoretical determination of bearing stiffness and damping coefficients with an adequate accuracy and makes damage detection difficult. Considering that dynamic coefficients have similar sensitivity to damage and considering that it is easier to monitor bearing stiffness than bearing damping, this article discusses a method to estimate experimentally the effective stiffness coefficients of hydrogenerators journal bearings, using only the usually monitored vibrations, with damage detection purposes. Validated using vibration signals synthesized by a simplified mathematical model that simulates the dynamic behavior of large hydrogenerators, the method was applied to a journal bearing of a 700 MW hydrogenerator, using two different excitations, the generator rotor unbalance and the vortices formed in the turbine rotor when this machine operates at partial loads. The experimental bearing stiffnesses obtained using both excitations were similar, but they were also much lower than the theoretical predictions. The article briefly discusses the causes of these discrepancies, the method’s uncertainties, and the possible improvements in its application.

The Finite Element Method (FEM), although widely used as an approximate solution method, has some limitations when applied in dynamic analysis. As the loads excite the high frequency and modes, the method may lose precision and accuracy. To improve the representation of these high-frequency modes, we can use the Generalized Finite Element Method (GFEM) to enrich the approach space with appropriate functions according to the problem under study. However, there are still some aspects that limit the GFEM applicability in problems of dynamics of structures, as numerical instability associated with the process of enrichment. Due to numerical instability, the GFEM may lose precision and even result in numerically singular matrices. In this context, this paper presents the application of two proposals to minimize the problem of sensitivity of the GFEM: an adaptation of the Stable Generalized Finite Element Method for dynamic analysis and a stabilization strategy based on preconditioning of enrichment. Examples of one-dimensional modal and transient analysis are presented as bars with cross section area variation. Numerical results obtained are discussed analyzing the effects of the adoption of preconditioning techniques on the approximation and the stability of GFEM in dynamic analysis.