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Many analysis and design problems in engineering and science involve uncertainty to varying degrees. This paper is concerned with the structural vibration problem involving uncertain material or geometric parameters, specified as fuzzy parameters. The requirement is to propagate the parameter uncertainty to the eigenvalues of the structure, specified as fuzzy eigenvalues. However, the usual approach is to transform the fuzzy problem into several interval eigenvalue problems by using the α-cuts method. Solving the interval problem as a generalized interval eigenvalue problem in interval mathematics will produce conservative bounds on the eigenvalues. The purpose of this paper is to investigate strategies to efficiently solve the fuzzy eigenvalue problem.

Based on the fundamental perturbation principle and vertex theory, an efficient perturbation method is proposed, that gives the exact extrema of the first-order deviation of the structural eigenvalue. The fuzzy eigenvalue approach has also been improved by reusing the interval analysis results from previous α-cuts.

The proposed method was demonstrated on a simple cantilever beam with a pinned support, and produced very accurate fuzzy eigenvalues. The approach was also demonstrated on the model of a highway bridge with a large number of degrees of freedom.

This proposed Vertex-Perturbation method is more efficient than the standard perturbation method, and more general than interval arithmetic methods requiring the non-negative decomposition of the mass and stiffness matrices. The new increment method produces highly accurate solutions, even when the membership function for the fuzzy eigenvalues is complex.

The dynamics of coupling between spectrum and resolvent under ε‐perturbations of operator and matrix spectra are studied both theoretically and numerically. The phenomenon of non‐trivial pseudospectra encountered in these dynamics is treated by relating information in the complex plane to the behaviour of operators and matrices. On a number of numerical results we show how an intrinsic blend of theory with symbolic and numerical computations can be used effectively for the analysis of spectral problems arising from engineering applications.

The computer implementation of a method for calculating coupled vibration eigenmodes and eigenfrequencies and the transient response of an elastic enclosure filled with a compressible fluid is described. The formalism is based on a simultaneous discretization of the fluid pressure and the fluid displacement potential. Attention is focused on the resulting form of the dynamic equilibrium equations and on their solution both in free vibration and transient analyses. In the eigenvalue analysis, an adapted Lanczos iteration scheme is proposed which takes account of the specific form of the equations. Applications are presented which demonstrate the effectiveness of the method.

The purpose of the paper is to introduce the dynamic phasor modelling (DPM) approach for stability investigation and control design of single-phase phase-locked loops (PLLs). The aim is to identify the system instabilities not predicted using the existent analysis and design methods based on the simplified average model approach.

This paper starts by investigating the performance of three commonly used PLL schemes: the inverse park-PLL, the second-order generalised integrators (SOGI)-frequency-locked loop and the enhanced-PLL, designed using the simplified average model and will show that following this approach, there is a mismatch between their actual and desired transient performance. A new PLL design method is then proposed based on the DPM approach that allows the development of fourth-order DPM models. The small-signal eigenvalues analysis of the fourth-order DPM models is used to determine the control gains and the stability limits.

The DPM approach is proven to be useful for single-phase PLLs stability analysis and control parameters design. It has been successfully used to design the control parameters and to predict the PLL stability limits, which have been validated via simulation and experimental tests consisting of grid voltage sag, phase jump and frequency step change.

This paper has introduced the use of DPM approach for the purpose of single-phase PLL stability analysis and control design. The approach has enabled accurate control gains design and stability limits identification of single-phase PLLs.

The purpose of this paper is to examine the numerical stability of a space-time finite integration (FI) method. A symmetric correction is proposed to give an accurate constitutive relation at the subgrid connections.

A scheme for the numerical stability analysis of the space-time FI method is presented, where the growth rate of instability is evaluated by a numerical eigenvalue analysis formulated from an explicit time-marching scheme.

The 3D and 4D subgrid schemes using the space-time FI method are conditionally stable, where a symmetric correction does not induce numerical instability. The staircase-type 4D space-time subgrid allows a larger time-step than the straight-type subgrid.

The numerical stability of space-time FI method is proven by an eigenvalue analysis, which provides 3D and 4D stable subgrid schemes.

This paper presents a new framework to predict a structure’s effective properties and sensitivities to multiple simultaneous uncertain endogenous parameters. The methodology is based on the use of fuzzy sets and this paper extends the fuzzy set theory to a dynamic finite element analysis of engineering systems containing uncertainty on material properties. A general algorithm, which can resolve the uncertain eigenvalue problem by using a Neumann expansion, is studied. This algorithm is applied to the study of the modal behavior of structures presenting uncertain material properties. Finally, the entropy and the specificity of fuzzy responses lead to the identification of a plate structure’s most sensitive eigenvalue to uncertain sources.

The free vibration analysis of cyclic symmetric structures is considered as a Hermitian eigenvalue problem in semi‐complex domain using subspace iteration method is presented. The trial vectors are selected using a modified Ritz vector scheme. A modified convergence criterion which gives true error estimates which is suited for clustered eigenvalue problems is presented. Also the effect of purification of trial vectors on convergence is considered.

It is generally known that the perforated section such as the castellated section is good to sustain distributed loads but inadequate to sustain highly concentrated loads. Therefore, it is possible to design the opening in a different arrangement of web opening to achieve section efficiency, thus improving the strength and torsional behaviour of the section with web opening. This study aims to focus on the finite element analysis of I-beam with and without openings in steel section dominated to lateral-torsional buckling behaviour.

In this work, the analysis of different sizes, shapes and arrangements of web opening is performed by using LUSAS application to conduct numerical analysis on lateral-torsional buckling behaviour. This involves three diameter sizes of web opening, five types of opening shapes and two criteria of the model.

The section with c-hexagon web opening was placed about 200-mm centre to centre and 100-mm edge distance, contribute to 7.26% increase of buckling capacity. For the section with 150-mm centre to centre and 50-mm edge distance, the occurrence of local buckling contributes to decrease of lateral buckling section capacity to 19.943 kNm, where pure lateral-torsional buckling mostly occurred because of prevented section. Besides that, the web opening diameter was also analysed. The web crippling was observed because of the increase of opening diameter from 0.67 to 0.80 D.

This contributes to a decrease in buckling capacity as figured in the contour of the deformed shape. For Model 1, an increase of buckling capacity (31.46%) is observed when the opening diameter are changed from 0.67 to 0.80 D.

This work compares the performance of the three boundary element techniques for solving Helmholtz problems: dual reciprocity, multiple reciprocity and direct interpolation. All techniques transform domain integrals into boundary integrals, despite using different principles to reach this purpose.

Comparisons here performed include the solution of eigenvalue and response by frequency scanning, analyzing many features that are not comprehensively discussed in the literature, as follows: the type of boundary conditions, suitable number of degrees of freedom, modal content, number of primitives in the multiple reciprocity method (MRM) and the requirement of internal interpolation points in techniques that use radial basis functions as dual reciprocity and direct interpolation.

Among the other aspects, this work can conclude that the solution of the eigenvalue and response problems confirmed the reasonable accuracy of the dual reciprocity boundary element method (DRBEM) only for the calculation of the first natural frequencies. Concerning the direct interpolation boundary element method (DIBEM), its interpolation characteristic allows more accessibility for solving more elaborate problems. Despite requiring a greater number of interpolating internal points, the DIBEM has presented higher-quality results for the eigenvalue and response problems. The MRM results were satisfactory in terms of accuracy just for the low range of frequencies; however, the neglected higher-order primitives impact the accuracy of the dynamic response as a whole.

There are safe alternatives for solving engineering stationary dynamic problems using the boundary element method (BEM), but there are no suitable comparisons between these different techniques. This paper presents the particularities and detailed comparisons approaching the accuracy of the three important BEM techniques, aiming at response and frequency evaluation, which are not found in the specialized literature.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.