Transient thermal stresses in a reinforced hollow disk or cylinder containing a radial crack

The transient thermal stress problem in a hollow cylinder or a disk containing a radial crack is considered. It is assumed that the cylinder is reinforced on its inner boundary by a membrane which has thermoelastic constants different than those of the base material. The transient temperature, thermal stresses and the crack tip stress intensity factors are calculated in a cylinder which is subjected to a sudden change of temperature on the inside surface. The results are obtained for various dimensionless parameters and material constants. The special cases of the crack terminating at the cylinder-membrane interface and of the broken membrane are separately considered and some examples are given

A note on the bending of a cracked strip

A technique is described for calculating the stress intensity factors in a strip under bending by treating the strip as a two-dimensional continuum rather than a simple beam in evaluating the crack surface tractions used for the solution of the perturbation problem

Stress-intensity factors for a thick-walled cylinder containing an annular imbedded or external or internal surface crack

The elastostatic axisymmetric problem for a long thick-walled cylinder containing a ring-shaped internal or edge crack is considered. Using the standard transform technique the problem is formulated in terms of an integral equation which has a simple Cauchy kernel for the internal crack and a generalized Cauchy kernel for the edge crack as the dominant part. As examples the uniform axial load and the steady-state thermal stress problems have been solved and the related stress intensity factors have been calculated. Among other findings the results show that in the cylinder under uniform axial stress containing an internal crack the stress intensity factor at the inner tip is always greater than that at the outer tip for equal net ligament thicknesses and in the cylinder with an edge crack which is under a state of thermal stress the stress intensity factor is a decreasing function of the crack depth, tending to zero as the crack depth approaches the wall thickness

A clamped rectangular plate containing a crack

The general problem of a rectangular plate clamped along two parallel sides and containing a crack parallel to the clamps is considered. The problem is formulated in terms of a system of singular integral equations and the asymptotic behavior of the stress state near the corners is investigated. Numerical examples are considered for a clamped plate without a crack and with a centrally located crack, and the stress intensity factors and the stresses along the clamps are calculated

Stress intensity factors in a reinforced thick-walled cylinder

An elastic thick-walled cylinder containing a radial crack is considered. It is assumed that the cylinder is reinforced by an elastic membrane on its inner surface. The model is intended to simulate pressure vessels with cladding. The formulation of the problem is reduced to a singular integral equation. Various special cases including that of a crack terminating at the cylinder-reinforcement interface are investigated and numerical examples are given. Results indicate that in the case of the crack touching the interface the crack surface displacement derivative is finite and consequently the stress state around the corresponding crack tip is bounded; and generally, for realistic values of the stiffness parameter, the effect of the reinforcement is not very significant

Limiting absorption principle and Strichartz estimates for Dirac operators in two and higher dimensions

In this paper we consider Dirac operators in $\mathbb R^n$, $n\geq2$, with a potential $V$. Under mild decay and continuity assumptions on $V$ and some spectral assumptions on the operator, we prove a limiting absorption principle for the resolvent, which implies a family of Strichartz estimates for the linear Dirac equation. For large potentials the dynamical estimates are not an immediate corollary of the free case since the resolvent of the free Dirac operator does not decay in operator norm on weighted $L^2$ spaces as the frequency goes to infinity.Comment: Updated Corollary 1.3 with a slightly stronger statement. To appear in Comm. Math. Phys. arXiv admin note: text overlap with arXiv:0705.054

Deep Long Short-Term Memory Adaptive Beamforming Networks For Multichannel Robust Speech Recognition

Far-field speech recognition in noisy and reverberant conditions remains a challenging problem despite recent deep learning breakthroughs. This problem is commonly addressed by acquiring a speech signal from multiple microphones and performing beamforming over them. In this paper, we propose to use a recurrent neural network with long short-term memory (LSTM) architecture to adaptively estimate real-time beamforming filter coefficients to cope with non-stationary environmental noise and dynamic nature of source and microphones positions which results in a set of timevarying room impulse responses. The LSTM adaptive beamformer is jointly trained with a deep LSTM acoustic model to predict senone labels. Further, we use hidden units in the deep LSTM acoustic model to assist in predicting the beamforming filter coefficients. The proposed system achieves 7.97% absolute gain over baseline systems with no beamforming on CHiME-3 real evaluation set.Comment: in 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP