Free vibration analysis of porous beams with gradually varying mechanical properties

This work is aimed to present analysis on free vibration behavior of porous beams with gradually varying mechanical properties based on a robust finite beam element. The governing equations are developed using a mixed variational formulation considering high-order displacement distribution. A new parabolic distribution of the transverse shear strains is introduced and the zero condition of the shear stresses at the upper and bottom surfaces of the beam is satisfied. The porosity can be spread into the beam with evenly and unevenly distributions. According to a modified power function, the material properties are varying along the thickness direction of the FGM porous beam. The presented results show the effect of gradient index, porosity coefficient and forms, boundary conditions, and geometrical parameters on the vibration of FGM beams. It is found that porous beams can be useful as a passive method for control of vibration for structural components.

Evaluation of the Floor Acceleration Amplification Demand of Instrumented Buildings

The floor acceleration amplification (FAA) factor is one of the most critical parameters in computing the equivalent seismic force of nonstructural component (NC). To evaluate the heightwise FAA distribution profile, the recorded acceleration response of the instrumented buildings was analyzed using the California Strong Motion Instrumentation Program (CSMIP) database. The FAA demands for three groups of buildings consisting of reinforced concrete, steel, and masonry buildings were analyzed. In each group, the buildings were classified into four subgroups according to their heights. Parabolic distribution profiles were suggested that could envelop most of the FAA data, as demonstrated by the processed results. An earthquake experience-based importance factor was suggested in terms of the percentage of the enveloped records. The obtained FAAs at the roof were generally larger than those in other levels. The percentile distributions of the roof acceleration amplification (RAA) were computed. The results showed that the roof FAA was underestimated in ASCE 7-16. The magnitudes of the FAA and the RAA correlated to the fundamental period of the building, which was considered by classifying the buildings according to the period ranges. The RAA profile against the period was obtained from a regression analysis. The developed FAA profile is expected to be useful in the seismic design of NCs, and it is expected to be adopted in future code provisions.

Numerical simulation of characteristics of propagation of symmetric waves in microwave circular shielded waveguide with a radially inhomogeneous dielectric filling

The paper presents a numerical simulation of the propagation characteristics of symmetric E-type and H-type waves in microwave circular shielded waveguide with radially inhomogeneous dielectric filling. Using the modified Galerkin method, the calculation of a circular two-layer shielded waveguide was carried out, as a result of which the distribution of the electromagnetic field of the waveguide with linear and parabolic distribution of permeability was determined. The results obtained using the modified Galerkin method were compared with the results obtained using the classical partial domain method, which agree well enough.

Model Test and Back Analysis of Shield Tunnel Load Distribution in Soft Clay

Combined with the soft clay layer of Foshan metro, a back-analysis method combining model test and numerical simulation is developed. First, the similitude criterion for the model used in this study was derived from similarity theory and elasticity mechanics equations. Artificial clay is prepared by mixing kaolin, bentonite, loess, and river sand in proportions of 4 : 2: 3 : 1. Gypsum, water, and borax are mixed in proportions of 1 : 0.7 : 0.015 to simulate the tunnel lining. The model tests were carried out based on four load modes: the combination of mode 1, vertical load distribution and horizontal load linear distribution, mode 2, vertical load distribution and horizontal load parabolic distribution, mode 3, vertical load parabolic distribution and horizontal load linear distribution, and mode 4, vertical and horizontal load parabolic distribution. Then, the calculation model corresponding to the four load modes is established using ABAQUS, and the measured data is back-analyzed as the known quantity. The specific load values obtained were 359 kPa, 380 kPa, 361 kPa, and 368 kPa by the load-internal force curve. The bending moment and axial force are calculated by substituting the back-analysis load values back into the model and comparing the results with the measured values; it was found that the internal forces under the back-calculation load still deviated by varying degrees. By using the comprehensive error function E to evaluate the advantages and disadvantages of the four distribution modes, the comprehensive errors are 4.3%, 1.7%, 6.5%, and 5.9%, respectively. That is, the error of load distribution of mode 2 (the combination of vertical load distribution and horizontal load parabolic distribution) is the lowest and is highly consistent with the measured value, which is the closest to the characteristics of the load pattern of the stratum.

The Study of Hydrodynamic Processes Occurring on Transition of Sudden Expanding of Hydraulic Section of Plane – Parallel Full Pipe Flow

The study regarding the regularity of changes in the hydrodynamic processes in the area of a sudden expanding in hydraulic section of the planeparallel full pipe flow of the liquid is carried out on the basis of the equations on the boundary layer. A method has been developed for determining the changes in the hydrodynamic parameters of the flow in the transition section which makes it possible to obtain the profile of the distribution of fluid velocities in any cross section of the channel based on the results of deformation of the areas of velocity under common initial and boundary conditions. The hydrodynamic processes occurring on transition of sudden expanding on hydraulic section of plane-parallel full pipe flow are studied in cases when: a) the velocity at any point of the inlet section of the channel is constant; b) the velocity at the inlet section is distributed according to the parabolic law. The calculation results for various values of the coefficient of expansion are given: Based on the results of computer simulation, the course of deformation of the velocity diagram along the length of the transition section was obtained for a constant and parabolic distribution of the velocities of the fluid flowing into the expanded section of the channel. The regularities of pressure distribution along the length of the studied section were also determined.

Full-field tracking and analysis of shrinkage strain during moisture content loss in wood

Anisotropic shrinkage is a typically feature in wood, which is of critical importance in wood drying. In this study, the shrinkage strains over each growth ring were determined by a full-field strain measurement system during moisture content (MC) loss. Color maps were used to visualize the full-field distribution of displacement and shrinkage strain under different MC conditions. The variation of tangential and radial shrinkage strain from pith to bark, as well as the anisotropic shrinkage in heartwood and sapwood were studied. Both of the displacement and strain values increased as the MC decreased. From pith to bark, the tangential strains were higher at two poles as compared to the center, showing a parabolic distribution below fiber saturation point. While for radial shrinkage strain, a minor difference was observed except for the MC of 10%. An intersection between tangential and radial shrinkage ratio curve was observed at the MC of 28%. Both expansion and shrinkage in tangential direction were larger than radial counterparts, and the transformation from expansion to shrinkage occurred at the MC region of 32–28%. In addition, the shrinkage in heartwood was larger than sapwood, whereas anisotropic shrinkage in sapwood was more pronounced as compared to heartwood.

FRICTION PILE BEARING CAPACITY BASED ON THE PARABOLIC DISTRIBUTION OF SKIN FRICTION

The article describes the approach to evaluation of a friction pile bearing capacity based on the parabolic distribution of a skin friction in multi-layer soil bases. The design equationsare obtained for evaluated the ultimate load on an axial loaded pile in multi-layer soil using the new design scheme. The advantage of the proposed approach is to obtain some experimental parameters that take into account the actual interaction of the pile and soil on the construction site. Negative friction forces (from the reaction force under the pile end) negatively affect the pile bearing capacity. The numerical example is given for a friction pile in the soil base with two layers. The proposed equation also allows calculating various parameters: the soil stress under the piletoe, the pile effective length, relative deformations along the pile, etc.