Quasi-periodicity and multi-scale resonators for the reduction of seismic vibrations in fluid-solid systems

This paper presents a mathematical model for an industry-inspired problem of vibration isolation applied to elastic fluid-filled containers. A fundamental problem of suppression of vibrations within a finite-width frequency interval for a multi-scale fluid-solid system has been solved. We have developed a systematic approach employing full fluid-solid interaction and dispersion analysis, which can be applied to finite and periodic multi-scale systems. The analytical findings are accompanied by numerical simulations, including frequency response analyses and transient regime computations

The 2003-4 multisite photometric campaign for the Beta Cephei and eclipsing star 16 (EN) Lacertae with an Appendix on 2 Andromedae, the variable comparison star

A multisite photometric campaign for the Beta Cephei and eclipsing variable 16 Lacertae is reported. 749 h of high-quality differential photoelectric Stromgren, Johnson and Geneva time-series photometry were obtained with ten telescopes during 185 nights. After removing the pulsation contribution, an attempt was made to solve the resulting eclipse light curve by means of the computer program EBOP. Although a unique solution was not obtained, the range of solutions could be constrained by comparing computed positions of the secondary component in the Hertzsprung-Russell diagram with evolutionary tracks. For three high-amplitude pulsation modes, the uvy and the Geneva UBG amplitude ratios are derived and compared with the theoretical ones for spherical-harmonic degrees l <= 4. The highest degree, l = 4, is shown to be incompatible with the observations. One mode is found to be radial, one is l = 1, while in the remaining case l = 2 or 3. The present multisite observations are combined with the archival photometry in order to investigate the long-term variation of the amplitudes and phases of the three high-amplitude pulsation modes. The radial mode shows a non-sinusoidal variation on a time-scale of 73 yr. The l = 1 mode is a triplet with unequal frequency spacing, giving rise to two beat-periods, 720.7 d and 29.1 yr. The amplitude and phase of the l = 2 or 3 mode vary on time-scales of 380.5 d and 43 yr. The light variation of 2 And, one of the comparison stars, is discussed in the Appendix.Comment: 18 pages, 19 figures, accepted for publication in MNRA

Mesoscale models and approximate solutions for solids containing clouds of voids

For highly perforated domains the paper addresses a novel approach to study mixed boundary value problems for the equations of linear elasticity in the framework of mesoscale approximations. There are no assumptions of periodicity involved in the description of the geometry of the domain. The size of the perforations is small compared to the minimal separation between neighboring defects and here we discuss a class of problems in perforated domains, which are not covered by the homogenization approximations. The mesoscale approximations presented here are uniform. Explicit asymptotic formulas are supplied with the remainder estimates. Numerical illustrations, demonstrating the efficiency of the asymptotic approach developed here, are also given

Asteroseismology of the Beta Cephei star 12 (DD) Lacertae: photometric observations, pulsational frequency analysis and mode identification

We report a multisite photometric campaign for the Beta Cephei star 12 Lacertae. 750 hours of high-quality differential photoelectric Stromgren, Johnson and Geneva time-series photometry were obtained with 9 telescopes during 190 nights. Our frequency analysis results in the detection of 23 sinusoidal signals in the light curves. Eleven of those correspond to independent pulsation modes, and the remainder are combination frequencies. We find some slow aperiodic variability such as that seemingly present in several Beta Cephei stars. We perform mode identification from our colour photometry, derive the spherical degree l for the five strongest modes unambiguously and provide constraints on l for the weaker modes. We find a mixture of modes of 0 <= l <= 4. In particular, we prove that the previously suspected rotationally split triplet within the modes of 12 Lac consists of modes of different l; their equal frequency splitting must thus be accidental. One of the periodic signals we detected in the light curves is argued to be a linearly stable mode excited to visible amplitude by nonlinear mode coupling via a 2:1 resonance. We also find a low-frequency signal in the light variations whose physical nature is unclear; it could be a parent or daughter mode resonantly coupled. The remaining combination frequencies are consistent with simple light-curve distortions. The range of excited pulsation frequencies of 12 Lac may be sufficiently large that it cannot be reproduced by standard models. We suspect that the star has a larger metal abundance in the pulsational driving zone, a hypothesis also capable of explaining the presence of Beta Cephei stars in the LMC.Comment: 12 pages, 7 figures, MNRAS, in pres