Modal analysis of magnetic vibration of induction motor used in household appliances

The paper deals with analysis of vibrational behavior of induction motor using the combined approach linking the finite elements method (FEM) applied to modelling of magnetic and mechanical phenomena in the motor with its modal description in spectral domain. Results of investigations presented in this paper proved that relatively small rotor axis misalignment against stator leads to visible vibration if forces resulted from this effect have frequency close to rotor bending resonance. Paper contains a rigorous description of all steps in analysis with a special attention paid to details of numerical approach both in FEM and in spectral consideration. Results of theoretical investigations were confirmed by measurements.

A Modal Rendition of ENSO Diversity

The El Nino and Southern Oscillation (ENSO) ‘diversity’ has been considered as a major factor limiting its predictability, a critical need for disaster mitigation associated with the trademark climatic swings of the ENSO. Improving climate models for ENSO forecasts relies on deeper understanding of the ENSO diversity but currently at a nascent stage. Here, we show that the ENSO diversity thought previously as ‘complex,’ arises largely as varied contributions from three leading modes of the ENSO to a given event. The ENSO ‘slow manifold’ can be fully described by three leading predictable modes, a quasi-quadrennial mode (QQD), a quasi-biennial (QB) mode and a decadal modulation of the quasi-biennial (DQB). The modal description of ENSO provides a framework for understanding the predictability of and global teleconnections with the ENSO. We further demonstrate it to be a useful framework for understanding biases of climate models in simulating and predicting the ENSO. Therefore, skillful prediction of all shades of ENSO depends critically on the coupled models’ ability to simulate the three modes with fidelity, providing basis for optimism for future of ENSO forecasts.

A Characterization Theorem for a Modal Description Logic

Modal description logics feature modalities that capture dependence of knowledge on parameters such as time, place, or the information state of agents. E.g., the logic S5-ALC combines the standard description logic ALC with an S5-modality that can be understood as an epistemic operator or as representing (undirected) change. This logic embeds into a corresponding modal first-order logic S5-FOL. We prove a modal characterization theorem for this embedding, in analogy to results by van Benthem and Rosen relating ALC to standard first-order logic: We show that S5-ALC with only local roles is, both over finite and over unrestricted models, precisely the bisimulation-invariant fragment of S5-FOL, thus giving an exact description of the expressive power of S5-ALC with only local roles.

MODAL TRIGGERED NONLINEARITIES FOR DAMAGE LOCALIZATION IN THIN WALLED FRC STRUCTURES – A NUMERICAL STUDY

This paper presents a novel method for detecting locations of damages in thin walled structural components made of fiber reinforced composites (FRC). Therefore, the change of harmonic distortion, which is found by current research to be very sensitive to delamination, under resonant excitation will be derived from FEM-simulation. Based on the linear modal description of the undamaged structure and the damage-induced nonlinearities represented by a nonlinear measure, two spatial damage indexes have been formulated.The main advantage of this novel approach is that the information about the defect is represented mainly by changes in the modal harmonic distortion (MHD), which just needs to be measured in one (or few) structural points. The spatial resolution is given by the pairwise coupling of the MHD with the corresponding mode shapes.

Trapped waves on jet currents: asymptotic modal approach

An asymptotic theory of surface waves trapped on vertically uniform jet currents is developed as a first step towards a systematic description of wave dynamics on oceanic jet currents. It has been shown that in a linear setting an asymptotic separation of vertical and horizontal variables, which underpins the modal description of the wave field on currents, is possible if either the current velocity is small compared to the wave celerity or the current width is large compared to the wavelength along the current. The scheme developed enables us to obtain solutions as an asymptotic series with any desired accuracy. The initially three-dimensional problem is reduced to solving one-dimensional equations with the lateral and vertical dependence being prescribed by the corresponding modal structure. To leading order in current magnitude to wave celerity, the boundary value problem specifying the modes and eigenvalues reduces to classical Sturm–Liouville type based upon the one-dimensional stationary Schrödinger equation. The modes, both trapped and ‘passing-through’, form a complete orthogonal set. This makes the modal description of waves on currents a mathematically attractive alternative to the approaches currently adopted. Properties of trapped eigenmodes and their dispersion relations are examined both for broad currents of arbitrary magnitude, where the modes are not orthogonal, and for weak currents, where the modes are orthogonal. Several model profiles for which nice analytical solutions of the leading-order boundary value problem are known were used to get an insight. The asymptotic solutions proved not only to capture qualitative behaviour well but also to provide a good quantitative description even for unrealistically strong and narrow currents. The results are discussed for various oceanic currents, with particular attention paid to the Agulhas Current, for which specific estimates were derived. For typical dominant wind waves and swell, all oceanic-jet-type currents are weak and, correspondingly, the developed asymptotic scheme based upon one-dimensional stationary Schrödinger equation for modes applies.