Analytical Solution for Longitudinal Dynamic Responses of Long Tunnels under Arbitrary Excitations

In this paper, an analytical solution is proposed for longitudinal dynamic responses of long tunnels under arbitrary excitations. For the derivation, the tunnel is assumed as a Timoshenko beam resting on a visco-Pasternak foundation. The Timoshenko beam theory is employed to consider both effects of the shear distortion as well as the rotary inertia of the tunnel, which are neglected by the Euler–Bernoulli beam. The visco-Pasternak foundation is applied to represent the viscoelastic compressive and shear resistance of soil. The governing equations of motion are transformed from partial differential forms into algebraic forms through integral transformations, and thus the solutions are conveniently obtained. The analytical solutions of the tunnel under several specific dynamic loads, including impulsive loads, moving line loads as well as traveling loads, are presented in detail and verified by comparing to the known degraded solution in literature and finite element results. Several examples are also conducted to investigate the influence of the relative stiffness ratio between the soil and the tunnel structure on the tunnel responses.

General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part I

This two-part article series provides a generalized description of the scattering geometry of Bragg coherent diffraction imaging (BCDI) experiments, the shear distortion effects inherent in the 3D image obtained from presently used methods and strategies to mitigate this distortion. Part I starts from fundamental considerations to present the general real-space coordinate transformation required to correct this shear, in a compact operator formulation that easily lends itself to implementation with available software packages. Such a transformation, applied as a final post-processing step following phase retrieval, is crucial for arriving at an undistorted, correctly oriented and physically meaningful image of the 3D crystalline scatterer. As the relevance of BCDI grows in the field of materials characterization, the available sparse literature that addresses the geometric theory of BCDI and the subsequent analysis methods are generalized here. This geometrical aspect, specific to coherent Bragg diffraction and absent in 2D transmission CDI experiments, gains particular importance when it comes to spatially resolved characterization of 3D crystalline materials in a reliable nondestructive manner. This series of articles describes this theory, from the diffraction in Bragg geometry to the corrections needed to obtain a properly rendered digital image of the 3D scatterer. Part I of this series provides the experimental BCDI community with the general form of the 3D real-space distortions in the phase-retrieved object, along with the necessary post-retrieval correction method. Part II builds upon the geometric theory developed in Part I with the formalism to correct the shear distortions directly on an orthogonal grid within the phase-retrieval algorithm itself, allowing more physically realistic constraints to be applied. Taken together, Parts I and II provide the X-ray science community with a set of generalized BCDI shear-correction techniques crucial to the final rendering of a 3D crystalline scatterer and for the development of new BCDI methods and experiments.

Analysis Of Concrete Tunnel Frameworks Subject To Fault Removal

An earthquake fault rupture generates two types of ground motion: permanent quasi-static dislocations and dynamic oscillations, characterized by strong pulses. This study investigates tunnel’s response to two different conditions using a 2D finite element program; the first one has a static dislocation corresponding to different earthquake magnitudes, while the second combines near-field seismic motions with three specific peak ground accelerations along with permanent dislocations. The impulsive ground motions affect the lining response further to other influential factors such as fault type and dip angle, making changes in sectional forces, displacement, and shear distortion of the lining. Moreover, pulse intensity, period, and frequency content are effective characteristics of impulsive motions that change in final response of the lining, subjected to subsequent static dislocations. Based on the second condition, at low PGAs, the pulse type is more effective to final response of the lining, due to forward and backward momentum specifications in impulsive motions. For earthquakes with high PGA and larger values in nearfield parameters, both the pulse type and period are effective. The tunnel displacement increases at PGAs as large as 0.7 and 1g, unlike the low PGA as large as 0.35g, because of increasing soil stress and plastic strain, respectively.

Finite Element Analysis of Composite Replaceable Short Links

Eccentrically braced frames (EBF) with detachable short links are an efficient solution for buildings in seismic areas owing to their high energy dissipation capacity and ductility and ease of repair in the earthquake aftermath. Past studies revealed that short links can develop shear overstrength (i.e. Vu/Vp, where Vu is the ultimate shear strength and Vp the corresponding plastic resistance) larger than the value recommended in EC8 [1] (i.e. Vu/Vp =1.5). One of the factors causing the higher shear overstrength is the presence of axial restraints that leads to the development of tensile forces in the link at large levels of rotation. Another reason for higher shear overstrength is the composite slab that can resist the shear distortion together with the short link. Within the DUAREM project [2], full scale pseudo-dynamic experimental tests were carried out on 3D EBF allowing thus the investigation of replaceable links considering two arrangements: (i) steel solution – the link was uncoupled from the slab (ii) composite solution – the slab and link are connected. The aim of this paper is to present the results of finite element analyses (FEAs), based on calibrated models and the comparison between the obtained results and the experimental tests performed by [2]. The numerical investigation carried out aims to evaluate the shear overstrength and the level of axial force in the link for both tested configurations.

The bandgap distribution investigated across the strain-induced bending ZnO nanowire

In this work, the strain dependence of electronic and optical properties in wurtzite zinc oxide (ZnO) lattice were explored. Ab initio density functional theory (DFT) was used in evaluating the energy bandgap and the dielectric tensor, respectively. The influence on the bandgap due to the shear distortion was so small that the reducing linear trends on uniaxial compressive/tensile strain were reported, in which the evolution of the absorption curve with uniaxial strain agrees well with the experimental results across the bending section. This study provides a set of useful data in analyzing the evolution of the optical adsorption across the bending ZnO nanowire, and gives a systematic explanation to the available experiments from the electronic structure’s perspective.

Vibrations in a spatial K-shaped metallic frame: an exact analytical study with experimental validation

In a spatial K-shaped metallic frame, there exist in- and out-of-plane bending, axial, and torsional vibrations. A wave-based vibration analysis approach is applied to obtain free and forced vibration responses in a space frame. In order to validate the analytical approach, a steel K-shaped space frame was built by welding four beam elements of rectangular and square cross-section together. Bending vibrations are modeled using both the classical Euler–Bernoulli theory and the advanced Timoshenko theory. This allows the effects of rotary inertia and shear distortion, which were neglected in the classical Euler–Bernoulli theory, to be studied. In addition, the effect of torsional rigidity adjustment for structures of rotationally non-symmetric cross-section is also examined.

An Analytical Study of Dynamic Characteristics of Multi-Story Timoshenko Planar Frame Structures

This paper concerns in-plane vibration analysis of coupled bending and longitudinal vibrations in multi-story planar frame structures based on the advanced Timoshenko bending theory. It takes into account the effects of both rotary inertia and shear distortion. A wave based vibration analysis approach is proposed. From a wave vibration standpoint, vibrations propagate along a uniform waveguide (or structural element), and are reflected and transmitted at discontinuities (such as joints and boundaries). Reflection matrices at various boundaries, as well as transmission and reflection matrices at joint discontinuities are derived. Natural frequencies of coupled bending and longitudinal in-plane vibrations are obtained by assembling these propagation, reflection, and transmission matrices. Numerical examples are presented along with comparisons to results available in literature. The examples show good agreement with the results presented in the available literature.