Internal resonance of an L-shaped beam with a limit stop .1. Free vibration

Real-life structures often possess piecewise stiffness because of clearances or interference between subassemblies. Such an aspect can alter a system's fundamental free vibration response and leads to complex mode interaction. The free vibration behaviour of an L-shaped beam with a limit stop is analyzed by using the frequency response function and the incremental harmonic balance method. The presence of multiple internal resonances, which involve interactions among the first five modes and are extremely complex, have been discovered by including higher harmonics in the analysis. The results show that mode interaction may occur if the higher harmonics of a vibration mode are close to the natural frequency of a higher mode. The conditions for the existence of internal resonance are explored, and it is shown that a prerequisite is the presence of bifurcation points in the form of intersecting backbone curves. A method to compute such intersections by using only one harmonic in the free vibration solution is proposed. (C) 1996 Academic Press Limited

Internal resonance of an L-shaped beam with a limit stop .2. Forced vibration

A limit stop is placed at the elbow of an L-shaped beam whose linear natural frequencies are nearly commensurable. As a result of this hardening device the non-linear system exhibits multiple internal resonances, which involve various degree of coupling between the first five modes of the beam in free vibration. A point load is so placed as to excite several modes and the resulting forced vibration is examined. In the undamped case, three in-phase and two out-of-phase solution branches have been found. The resonance curve is extremely complicated, with multiple branches and interactions between the first four modes. The amplitudes of the higher harmonics are highly influenced by damping, the presence of which can effectively attenuate internal resonances. Consequently parts of the resonance curve may be eliminated, with the resulting response comprising different distinctive branches. (C) 1996 Academic Press Limited

Spectroscopic properties of fluorophosphate glass with high Er(3+)supercript stop concentration

Fluorophosphate glass with 4 mol.% ErF3 content was prepared. The different scanning calorimetry was conducted. Raman spectrum, infrared transmission spectrum, absorption spectrum were measured. Fluorescence spectrum and lifetime of emission around 1.53 mu m were measured under 970 nm laser diode excitation. The metaphosphate content in the composition is limited, but the maximum phonon energy of glass amounts to 1290 cm- 1, and is comparatively high. The full width at half maximum is about 56 nm, and is wider than for most of the materials investigated. The measured lifetime of I-4(13/2) -> I-4(15/2) transition, contributed by the high phonon energy, inefficient interaction of Er3+ ions, and low water content, amounts to no less than 7.36 ms though the Er3+ concentration is high. This work might provide useful information for the development of compact optical devices.