Semi-analytical Boundary Element Method Research Articles

Hydrodynamic forces in higher modes of a thin cantilever beam resonator

The hydrodynamic force in a thin uniform beam cantilever is essential quantity for designing a resonator. We obtained the hydrodynamic drag forces in a uniform cantilever vibrating at the first four transverse modes using a semi-analytical boundary element method (BEM) and finite element method (FEM) in ANSYS. The present three-dimensional (3D) BEM inertial and damping forces are compared with FEM over a frequency range with less than 9.5% deviation until frequency parameter of 100; thereafter, it deviates numerically due to neglecting the non-linear convective forces. Considering the hydrodynamic damping force, the quality factor is estimated for the first four transverse modes of a uniform cantilever beam. As a result, the present 3D BEM model behaves well at the first bending mode compared to FEM. We also study the effect of the aspect ratio (ratio of width to length) of the beam for all four modes. However, the first mode quality factor sufficiently correlates with the numerical value for all aspect ratios. For uniform beams operating with higher modes, the influence of nonlinear and resonance frequency by the numerical model is more pronounced at smaller lengths. Hence, the 3D BEM approach can estimate the hydrodynamic forces on cantilever-based resonators, for example, atomic force microscopy and biosensors.

Research on Singularity in Calculation of Induced Electric Field in Pointed Conductors

In the electric field environment of thunderstorm, the tip of a grounded object at a high place is more likely to produce corona discharge and finally cause lightning flash. Therefore, the study of the surface electric field of the grounded object tip in the electric field environment has important theoretical value and practical significance for the analysis of the characteristics of the head-on discharge. Due to the strong singularity of the tip structure, the traditional numerical analysis method cannot accurately calculate its surface electric field. Therefore, the traditional literature usually chamfers the conductor tip, but in lightning physics, researchers are most concerned about the maximum field strength in the local area. In order to study the electric field distribution on the tip conductor surface, a semi-analytical boundary element method is proposed to calculate the tip structure directly. Firstly, the analytical formula of the electric field on the tip conductor surface and the boundary element semi-analytical common method are derived, and the tip conductor model is established to calculate the tip electric field excited by the external electric field using the analytical solution and the semi-analytical method. The correctness of the semi-analytical method is verified by calculating the L2 loss function of the two, and the influence of the tip angle on the semi-analytical calculation results is studied. The results show that for the three-dimensional cone model, the L2 loss function is 10-5, which meets the calculation accuracy. The special treatment of the semi-analytical method at the strong singular integral makes the calculation accuracy much higher than that of the Gaussian integral, where the L2 loss function is greatly reduced. Further, based on the change of tip angle, as the conductor tip becomes sharper, the greater the electric field distortion is, and the greater the L2 loss function is. The research results provide a method reference for the calculation of the electric field on the tip conductor surface.

Analytical Model of Perturbed EMF in a Transmit-Receive Coil System Due to Thin Flaws

This work proposes a model based on the semianalytical boundary element method (BEM) to predict the perturbation of the voltage induced in an eddy current coil due to narrow opening flaws that are usually encountered in eddy current nondestructive tests. The modeling is performed for rectangular narrow opening flaws that are located on the surface of an aluminum plate of finite thickness. The excitation to the coil varies time harmonically and the BEM results are corroborated by experiments performed in a controlled environment in the laboratory.

Field Tests and Three-Dimensional Semi-Analytical Boundary Element Method Analysis of a Row of Holes as Active Barrier in Saturated Soil

Abstract The adverse effects of ground vibrations can be eliminated or prevented by installation of various types of wave barriers, such as a row of holes. The analysis is accomplished with the aid of a series of field experiments and numerical simulation. Three-dimensional semi-analytical boundary element models are established to use a row of holes as active wave barrier to isolate the ground vibrations generated by the machine foundation laid on the surface of saturated soil foundation, and the effects of the model parameters on isolation effectiveness are investigated and discussed in detail. A simple single program multiple data parallel algorithm is developed with the aid of Matlab software to increase calculating efficiency. The results show that a row of holes can isolate the ground vibrations successfully. Increasing the radius and the depth and decreasing the net spacing between two successive holes can all result in an increase in the screening effectiveness. According to the results, it is suggested in the design that the hole radius should take the value of 0.1∼0.15λR (λR is the Rayleigh wave length), and the hole depth and the net spacing should take the value no more than 1.0λR and 0.1λR, respectively. Moreover, the distance between the machine foundation and barrier can affect the screening effectiveness, and the larger the distance is, the poorer the screening effectiveness is. The number of holes in a row has less effect on the screening effectiveness. However, the bigger the number of holes in a row is, the larger the screening zone behind the barriers is.

A semi-analytical numerical method for modelling the normal wheel–rail contact

ABSTRACT A new semi-analytical boundary element method is proposed for determining the wheel–rail contact zone and the normal stress distribution within it. The potential contact area is discretised using strip elements, employing an iterative algorithm to satisfy the contact constraints. At each iteration, the length of the contact strips is updated using an analytical expression based on Hertz's theory. This simplified formulation provides good approximation of the pressure distribution, and consequently the contact area, in non-elliptic cases. The reduction in the number of system unknowns by using a semi-analytical methodology also enables fast computation speeds, an indispensable requirement in railway dynamics.

Numerical Analysis on the Ground Vibration Isolation of Duxseal

A new kind of vibration screening material, Duxseal, with a high damping ratio is proposed to be used as an active vibration barrier in the free field. To investigate the influence of width, thickness, and embedded depth of using Duxseal on vibration reduction, numerical studies are performed using a three-dimensional (3D) semianalytical boundary element method (BEM) combined with a thin-layer method (TLM). The isolation effectiveness of Duxseal in ground vibration is also compared with the traditional wave impeding block (WIB). The numerical results show that Duxseal performed exceedingly well in screening ground vibrations in the free field. The effectiveness of the vibration isolation increases with the increase in the width, thickness, and embedded depth of the Duxseal material, within a certain range, under harmonic vertical excitation. In addition, Duxseal is much more effective for isolating ground vibration than the traditional WIB. The performance of Duxseal in isolating ground vibration is relatively stable along the distance away from the vibration source, while the amplitude attenuation ratio bounces upward when the distance away from the vibration source increases for the WIB isolation system.

Field experiment and numerical study on active vibration isolation by horizontal blocks in layered ground under vertical loading

In this paper, a series of field experiments were carried out to investigate the active vibration isolation for a surface foundation using horizontal wave impedance block (WIB) in a multilayered ground under vertical excitations. The velocity amplitude of ground vibration was measured and the root-mean-square (RMS) velocity is used to evaluate the vibration mitigation effect of the WIB. The influences of the size, the embedded depth and the shear modulus of the WIB on the vibration mitigation were also systematically examined under different loading conditions. The experimental results convincingly indicate that WIB is effective to reduce the ground vibration, especially at high excitation frequencies. The vibration mitigation effect of the WIB would be improved when its size and shear modulus increase or the embedded depth decreases. The results also showed that the WIB may amplify rather than reduce the ground vibration when its shear modulus is smaller or the embedded depth is larger than a threshold value. Meanwhile, an improved 3D semi-analytical boundary element method (BEM) combined with a thin layer method (TLM) was proposed to account for the rectangular shape of the used WIB and the laminated characteristics of the actual ground condition in analyzing the vibration mitigation of machine foundations. Comparisons between the field experiments and the numerical analyses were also made to validate the proposed BEM.

3D Analysis of Vibration Isolation by Wave Impeding Block in Non-Uniform Layered Ground under Horizontal-Rocking Coupled Loading

The thin-layered method (TLM) is very efficient to the wave propagation in layered ground and boundary element method (BEM) is very precise to solve infinite domain problems. In order to study the isolation vibration effectiveness of non-uniform three-dimensional (3D) layered ground wave impeding block (WIB), this paper is accomplished with the aid of a 3D semi-analytical BEM based on TLM, on which the Green’s function is regarded as fundamental solution of a stratified half-space. Then the active isolation effectiveness by WIB is studied under horizontal-rocking coupled loading in elastic half-space in the upper stiff-layer and lower soft-layer. The results show that the foundation of the stratification parameter and the characteristics of non-uniform have significant influence on the vibration isolation effect of the WIB, and the isolation vibration effectiveness of lower soft-layer is better than the upper stiff-layer.

Experimental Investigation of Effect of WIB Embedded Depth on Ground Vibration Isolation

In this paper, an exploration was presented to access the actual screening effectiveness of concrete wave impeding block (WIB) and the influence of WIB embedded depth on the vertical vibration isolation effect under the continuous vertical loading. Furthermore, the displacements of measuring points were simulated with a semi-analytical boundary element method (BEM) and validated by the measured records. It was found that a concrete WIB with a reasonable embedded depth was able to decrease the ground vibration greatly. It was also proved that decreasing the embedded depth was an efficient measure for WIB to reduce the dynamic response of ground. Besides, the good qualitative agreement between the calculation and the experiment proved the reliability of the numerical method.

FEM/BEM Hybrid Method for Magnetic Field Evaluation Due to Underground Power Cables

This paper is a contribution to the evaluation of electromagnetic fields due to underground power cables. Open boundary 2-D problems may be treated combining the finite element method (FEM) inside a region surrounded by a regular (cylindrical) fictitious surface with a semi-analytical boundary element method (BEM) to describe the field outside this region. For the outside region, a generalization of Pollaczek's solution is applied, taking into account eddy currents in the soil and the proximity effect between the soil/air plane surface and the cylinder fictitious surface with finite radius. The method is validated by using typical underground power cables where analytical methods may be applied accurately.

Transient response of finitely long cylindrical cavity with arbitrary cross-section

A semi-analytical boundary element method is developed for the efficient time-domain dynamic response analysis of a finitely long cylindrical cavity with an arbitrary cross-section geometry. High computational efficiency is achieved by mapping a complex shape of the cross-section into a circular shape. For this purpose a special coordinate transformation equation is presented. This mapping enables us to discretize the boundary element equation only along the longitudinal axis of the cavity. The versatility and accuracy of the method are amply demonstrated through a number of examples. The transient stresses and displacements are found to be considerably influenced by the slenderness ratio, length over diameter of the cavity and the incidence angle of the incident wave.

Transient stress analysis of grooved and stepped shafts by time domain semi-analytical boundary element method

A formulation and numerical solution procedure for boundary integral equation using the semi-analytical method is given for the three-dimensional transient stress analysis of a grooved cylindrical shaft with arbitrary impact loads. In this method the fundamental solution of three-dimensional elastodynamics is directly used and the general three-dimensional problem is reduced to a one-dimensional numerical one using the semi-analytical technique at the stage of discretization of the boundary. Several numerical examples are presented for verification.

Dynamic response of underground structures by time domain SBEM and SFEM

The dynamic interaction problems of three-dimensional linear elastic structures with arbitrary shaped section embedded in a homogeneous, isotropic and linear elastic half space under dynamic disturbances are numerically solved. The numerical method employed is a combination of the time domain semi-analytical boundary element method (SBEM) used for the semi-infinite soil medium and the semi-analytical finite element method (SFEM) used for the three-dimensional structure. The two methods are combined through equilibrium and compatibility conditions at the soil-structure interface. Displacements, velocities, accelerations and interaction forces at the interface between underground structure and soil medium produced by the diffraction of wave by an underground structure for every time step are obtained. In dynamic soil-structure interaction problems, it is advantageous to combine the SBEM and the SFEM in an effort to produce an optimum numerical hybrid scheme which is characterized by the main advantages of the two methods. The effects of the thickness, the ratio of length and diameter of underground structure and the soil medium on dynamic responses are discussed.