Acoustic anisotropy and birefringence in fibre-reinforced composite materials

All nine elastic moduli of an orthotropic composite material, namely, polypropylene reinforced with glass fiber, are determined from the measured values of the bulk acoustic wave velocities along specific directions in the planes of symmetry of the material. These data are used to calculate the angular dependences of phase velocities, polarization vectors, and directions of ray velocities of bulk waves in the composite. It is demonstrated that the difference in the velocities of shear waves polarized along and across the glass fiber gives rise to an acoustic birefringence and can lead to an elliptical polarization of waves. The measurement of the phase velocities of shear waves as functions of the wave polarization is suggested as a method for the determination of the fiber orientation in a composite material.     

Lower bounds for positive and negative parts of measures and the arrangement of singularities of their Laplace transforms

For a real measure with variation V(x) satisfying the estimate V(x) ≤ c ₀ exp(Cx) and for the Laplace transform holomorphic in the disk {¦ -C¦ ≤ C} and having at least one pole of order m, we obtain lower bounds for the positive and negative parts of the measure V _± (x) > cx ^m , x > x ₀. We establish lower bounds for V _+- (x) on “short” intervals. Applications to number theory of the results obtained are considered.     

Rotational dependences of line half-widths for CO and CO2 confined in SiO2/Al2O3 xerogel

The absorption spectra of CO and CO₂ confined in nanopores of SiO₂/Al₂O₃ xerogel have been measured using a Bruker IFS-125 HR Fourier spectrometer. Dependences of the half-width values on rotational quantum numbers and the line shift mean values are studied and compared with the data available in literature. Possible causes which can affect the rotational dependences are discussed.     

Ionization spectrum transformation and compression of powerful femtosecond laser pulses in experiments on the propagation in gas-filled dielectric capillaries

The propagation of an intense (I≤10⁶ W/cm²) femtosecond laser radiation with a duration of ～100 fs through gas-filled dielectric capillaries was studied. The radiation with a power up to 0.2 TW propagates along the paths up to 20 cm with a transmission efficiency of ～45%. The beam transverse structure at the output is close to the capillary fundamental mode under gas-ionization conditions. The transformation of pulse spectrum was studied as a function of input intensity. It is demonstrated experimentally that the pulse is compressed to a duration of ～30 fs due to the compensation of ionization-induced self-phase modulation in a linear dispersive element at the capillary output.     

Nonlinear acoustic approach to material characterisation of polymers and composites in tensile tests

The paper reports on experimental study of elastic nonlinearity of polymers and glass fibre-reinforced (GFR-) composites in a wide range of tensile stress applied (up to a fracture limit). Focused slanted transmission mode (FSTM) of air-coupled ultrasound is adapted for remote generation and detection of flexural waves in the samples of plastics. Local noncontact measurements of flexural wave velocity as a function of static strain are used to calculate the second-order nonlinearity parameters beta2 and study their behaviour through a loading cycle. Molecular untangling and crazing phenomena are identified, respectively, with maxima of positive and negative beta2 in thermoplastics. In composites, mechanics of fibre-matrix interaction is considered for brittle and plastic fractures. Hysteresis in velocity variation during loading-unloading cycle is used as an indicator of residual defect accumulation.     

Nonlinear modulation technique for NDE with air-coupled ultrasound

The present study is aimed at expanding flexibility and application area of nonlinear acoustic modulation (NAM-) technique by combining the benefits of noncontact ultrasound excitation (remote locating and imaging of defects) with sensitivity of nonlinear methods in a new air-coupled NAM-version. A pair of focused air-coupled transducers was used to generate and receive (high-frequency) longitudinal or flexural waves in plate-like samples. Low-frequency (LF-) vibrations were excited with a shaker or a loudspeaker. Temporal and spectral analysis of the output signal revealed an extremely efficient nonlinear amplitude modulation and multiple frequency side-bands for sound transmission and flexural wave propagation through cracked defects. On the contrary, a negligible modulation was observed for large and medium scale inclusions and material inhomogeneities (linear defects). A new subharmonic mode of the NAM was observed at high excitation levels. It was also shown for the first time that nonlinear vibrations of cracks resulted in radiation of a very high-order harmonics (well above 100) of the driving excitation in air that enabled imaging of cracks remotely by registration their highly nonlinear "acoustic emission" with air-coupled transducers.     

On local convergence of sequential quadratically-constrained quadratic-programming type methods,with an extension to variational problems

We consider the class of quadratically-constrained quadratic-programming methods in the framework extended from optimization to more general variational problems. Previously, in the optimization case, Anitescu (SIAM J. Optim. 12, 949–978, 2002) showed superlinear convergence of the primal sequence under the Mangasarian-Fromovitz constraint qualification and the quadratic growth condition. Quadratic convergence of the primal-dual sequence was established by Fukushima, Luo and Tseng (SIAM J. Optim. 13, 1098–1119, 2003) under the assumption of convexity, the Slater constraint qualification, and a strong second-order sufficient condition. We obtain a new local convergence result, which complements the above (it is neither stronger nor weaker): we prove primal-dual quadratic convergence under the linear independence constraint qualification, strict complementarity, and a second-order sufficiency condition. Additionally, our results apply to variational problems beyond the optimization case. Finally, we provide a necessary and sufficient condition for superlinear convergence of the primal sequence under a Dennis-Moré type condition. Research of the second author is partially supported by CNPq Grants 300734/95-6 and 471780/2003-0, by PRONEX–Optimization, and by FAPERJ.     

Strongly nonlinear shear perturbations in discrete and continuous cubic nonlinear systems

Systems with constraints, the masses in which move only along guides, can execute strongly nonlinear vibrations. This means that nonlinear phenomena manifest themselves at arbitrary small deviations from equilibrium. The form of vibrations of a single mass is described by elliptical Jacobi functions. The spectrum of these vibrations is found. With an increase in amplitude, the period of vibrations decreases. We deduce equations of strongly nonlinear vibrations of a chain of connected masses. In the continuum limit, we obtain a new nonlinear equation in partial derivatives. We devise transformation of variables leading to linearization of this equation. We implemented a factorization procedure that decreases the order of the equation in partial derivatives from second to first. Exact solutions to the first-order equation describe the slow evolution of the displacement profile in a distributed system. In the absence of preliminary tension of elastic elements in the continued model, traveling waves cannot be achieved; however, time-oscillating solutions like standing waves are possible. We obtain an equation for a field of strongly nonlinear deformations. Its exact solution describes periodic movement in time and space. As well, the period of time oscillations decreases with an increase in amplitude, and the spatial period, in contrast, increases. The product of the vibration frequency multiplied by the spatial period is a constant that depends on the deformation energy. We propose a scheme of the mechanical system producing strongly nonlinear torsional vibrations. We experimentally measured the period of torsional vibrations of a single disc. We show that with an increase in amplitude in the process of vibration attenuation, an increase in the period occurs, which agrees with calculations. We measure the shapes of nonlinear vibrations of a chain of connected discs. A strongly nonlinear behavior of the chain is observed.