Eigenfrequency spectrum of the reinforced concrete cantilever beam

For the calculation of building structures under the influence of external dynamic loads, it is necessary to know the eigen frequencies of the structures themselves in order to prevent such a phenomenon as resonance. Steel has distinctive properties from concrete, so its consideration is necessary to determine the eigen frequency of the whole structure. This article presents the calculation of the cantilever beam analytically and in the software package Abaqus for linear and volumetric problems with the interaction of concrete and reinforcement. Due to the reinforcement, the beam eigen frequencies differ from the eigen frequency of the conventional rigidly fixed rod, as evidenced by the results of the calculation.

Effect of intermediate supports location on natural frequencies of multiple cracked continuous beams

The present paper deals with free vibration of multiple cracked continuous beams with intermediate rigid supports. A simplified method is proposed to obtain general solution of free vibration in cracked beam with intermediate supports that is then used for natural frequency analysis of the beam in dependence upon cracks and support locations. Numerical results show that the support location or ratio of span lengths in combination with cracks makes a significant effect on eigenfrequency spectrum of beam. The discovered effects of support locations on eigenfrequency spectrum of cracked continuous beam are useful for detecting not only cracks but also positions of vanishing deflection on the beam.

ULF hydromagnetic oscillations with the discrete spectrum as eigenmodes of MHD-resonator in the near-Earth part of the plasma sheet

A new concept is proposed for the emergence of ULF geomagnetic oscillations with a discrete spectrum of frequencies (0.8, 1.3, 1.9, 2.6 ...mHz) registered in the magnetosphere's midnight-morning sector. The concept relies on the assumption that these oscillations are MHD-resonator eigenmodes in the near-Earth plasma sheet. This magnetospheric area is where conditions are met for fast magnetosonic waves to be confined. The confinement is a result of the velocity values of fast magnetosonic waves in the near-Earth plasma sheet which differ greatly from those in the magnetotail lobes, leading to turning points forming in the tailward direction for the waves under study. To compute the eigenfrequency spectrum of such a resonator, we used a model magnetosphere with parabolic geometry. The fundamental harmonics of this resonator's eigenfrequencies are shown to be capable of being clustered into groups with average frequencies matching, with good accuracy, the frequencies of the observed oscillations. A possible explanation for the stability of the observed oscillation frequencies is that such a resonator might only form when the magnetosphere is in a certain unperturbed state.

CCD Studies of δ Scuti Stars in Open Clusters

Asteroseismology on δ Scuti stars has until now produced very few convincing results – if we aim at doing strong tests of details of stellar modelling. The main reason for the lack of success is probably that these stars often rotate, which split nonradial oscillation frequencies into many more frequencies. These many frequencies and the fact that the more evolved δ Scuti stars contain a strong chemical composition gradient at the edge of the convective core, produce a very complicated eigenfrequency spectrum. In contrast to this, we expect, in principle, seismological studies of δ Scuti stars to be a very simple task: One has to compare theoretical oscillations in model stars with the observed oscillations. However, in order to produce convincing asteroseismological results, we need to do three things: (1) Detect as many eigenfrequencies as possible at high precision, (2) identify the eigenmodes and (3) improve the theoretical models. By observing δ Scuti stars in open clusters using CCDs, we have a possibility to improve on (1) and (2) as well as providing an opening for an improvement in the theoretical models by doing accurate calibrations of the basic cluster properties. In this paper I shall describe some of the results from CCD studies of δ Scuti stars in open clusters and identify some future prospects for this technique.