scholarly journals Dynamic Response of an Inhomogeneous Elastic Pile in a Multilayered Saturated Soil to Transient Torsional Load

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Kaifu Liu ◽  
Zhiqing Zhang
Keyword(s):  
Dynamic Response ◽  
Time Domain ◽  
Separation Of Variables ◽  
Saturated Soil ◽  
Function Technique ◽  
Soil System ◽  
Torsional Load ◽  
Cross Sectional Dimension ◽  
Velocity Response ◽  
The Time Domain

In this paper, we solve the dynamic response of an inhomogeneous elastic pile embedded in a multilayered saturated soil and subjected to a transient torsional load via a semianalytical method. To portray the inhomogeneity of the pile and the stratification of surrounding soil, the pile-soil system is subdivided into Nth layers along the depth direction in view of the variation of shear modulus or cross-sectional dimension of the pile or differences in soil properties. Then, the vibration displacement solution with undermined constants for any saturated soil layer subjected to the time-harmonic torsional load is obtained by virtue of the separation of variables scheme. To establish the connection of adjacent longitudinal soil layers, the circumferential contact traction at the interface of the adjacent layers is treated as the distributed Winkler subgrade model independent of the radial distance. Then, by utilizing the continuity conditions of the pile-soil system and the method of recursion typically used in the transfer function technique, the torsional impedance of the pile top can be derived in the frequency domain. By virtue of inverse Fourier transform and convolution theorem, the velocity response of an inhomogeneous pile subjected to a transient half-sine exciting torque and embedded in a layered saturated soil is gained in the time domain. Finally, selected numerical results are gained to investigate the influence of typical defects in pile and soil layering on the velocity response of the pile top in the time domain.

scholarly journals Vertical Dynamic Response of Pile Embedded in Layered Transversely Isotropic Soil

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Wenbing Wu ◽  
Guosheng Jiang ◽  
Shenggen Huang ◽  
Chin Jian Leo
Keyword(s):  
Shear Modulus ◽  
Dynamic Response ◽  
Separation Of Variables ◽  
Constitutive Relations ◽  
Soil Layer ◽  
Vertical Plane ◽  
Transversely Isotropic ◽  
Laplace Transform Technique ◽  
Velocity Response ◽  
The Time Domain

The dynamic response of pile embedded in layered transversely isotropic soil and subjected to arbitrary vertical harmonic force is investigated. Based on the viscoelastic constitutive relations for a transversely isotropic medium, the dynamic governing equation of the transversely isotropic soil is obtained in cylindrical coordinates. By introducing the fictitious soil pile model and the distributed Voigt model, the governing equations of soil-pile system are also derived. Firstly, the vertical response of the soil layer is solved by using the Laplace transform technique and the separation of variables technique. Secondly, the analytical solution of velocity response in the frequency domain and its corresponding semianalytical solution of velocity response in the time domain are derived by means of inverse Fourier transform and convolution theorem. Finally, based on the obtained solutions, a parametric study has been conducted to investigate the influence of the soil anisotropy on the vertical dynamic response of pile. It can be seen that the influence of the shear modulus of soil in the vertical plane on the dynamic response of pile is more notable than the influence of the shear modulus of soil in the horizontal plane on the dynamic response of pile.

Dynamic Torsional Response of a Pile Partially Embedded in Saturated Soil

2014 ◽  
Vol 509 ◽  
pp. 27-33
Author(s):  
Rui Fu Qin ◽  
Zhi Qing Zhang ◽  
Rong Fa Chen
Keyword(s):  
Inverse Fourier Transform ◽  
Vertical Direction ◽  
Sine Wave ◽  
Saturated Soil ◽  
Soil System ◽  
Impedance Function ◽  
Torsional Response ◽  
Time Harmonic ◽  
Velocity Response ◽  
The Time Domain

The dynamic response of an elastic supporting pile partially embedded in a saturated soil and subjected to a time-harmonic torsional loading is investigated. At first, the pile is divided into two parts along the vertical direction, pile part above the soil and pile part embedded in the soil. Then, based on boundary and continuity conditions of the pile-soil system, the torsional impedance at the top end of the pile part embedded in the soil is obtained. By utilizing the transfer technique of impedance function, the admittance function of the pile top is defined in the frequency domain. By virtue of inverse Fourier transform and convolution theorem, a semi-analytical solution for the velocity response of a pile subjected to a semi-sine wave exciting torque is obtained in the time domain. Finally, selected numerical results are obtained to analyze the influence of main parameters on the torsional vibration characteristics of the pile.

scholarly journals Sensitivity with Respect to the Path Parameters and Nonlinear Stiffness of Vibration Transfer Path Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-11
Author(s):  
Yimin Zhang ◽  
Xianzhen Huang
Keyword(s):  
Dynamic Response ◽  
Time Domain ◽  
Evaluation Criteria ◽  
Nonlinear Stiffness ◽  
Vibration System ◽  
Transfer Path ◽  
Dynamic Sensitivity ◽  
The Time Domain

Generally speaking, a vibration system consists of three parts: vibration resource, vibration transfer path, and vibration receiver. Based on the dynamic sensitivity technique, this paper proposes a method for evaluating the contribution of each vibration transfer path to the dynamic response of the vibration receiver. Nonlinear stiffness is an important factor in causing the nonlinearity of vibration systems. Taking sensitivity as the evaluation criteria, we present an effective approach for estimating the influence of nonlinear stiffness in vibration transfer paths on the dynamic response of the vibration receiver. Using the proposed method, the sensitivity of the vibration system with multiple and/or multidimensional transfer paths could be determined in the time domain.

Time- and Frequency- Domain Analysis of Transient Electroosmotic Flow Induced by Sinusoidal AC Electric Field in a Curved Microtube

2005 ◽  
Author(s):  
Win-Jet Luo ◽  
Jia-Kun Chen ◽  
Ruey-Jen Yang
Keyword(s):  
Phase Shift ◽  
Electric Field ◽  
Transient Response ◽  
Time Domain ◽  
Electroosmotic Flow ◽  
Sustained Oscillation ◽  
Sustained Oscillations ◽  
Ac Electric Field ◽  
Velocity Response ◽  
The Time Domain

A backwards-Euler time-stepping numerical method is applied to simulate the transient response of electroosmotic flow in a curved microtube. The velocity responses of the flow fields induced by applied sinusoidal AC electric fields of different frequencies are investigated. The transient response of the system is fundamentally important since both the amplitude and the time duration of the transient response must be maintained within tolerable or prescribed limits. When a sinusoidal AC electric field is applied, the transient response of the output velocity oscillates in the time-domain. However, after a certain settling time, the output velocity attains a sustained oscillation with the same amplitude as the driving field. In this study, the transient response of the electroosmotic flow is characterized by the time taken by the velocity response to reach the first peak, the peak of the sustained oscillation, the maximum overshoot, the settling time, and the bandwidth of the sustained oscillations in the time-domain. Meanwhile, the performance of the system is identified by plotting the output velocity response and the output velocity phase-shift against the frequency of the applied signal. A finite time is required for the momentum to diffuse fully from the walls to the center of the curved microtube cross-section. As the applied frequency is increased, the maximum overshoot and the bandwidth and peak of the sustained oscillations gradually decrease since insufficient time exists for the momentum to diffuse fully to the center of the microtube. Additionally, the phase-shift between the applied electric field and the output velocity response gradually increases as the frequency of the applied signal is increased.

Dynamic Response of 3D Surface/Embedded Rigid Foundations of Arbitrary Shapes on Multi-Layered Soils in Time Domain

2019 ◽  
Vol 19 (09) ◽  
pp. 1950106 ◽  
Author(s):  
Zejun Han ◽  
Mi Zhou ◽  
Xiaowen Zhou ◽  
Linqing Yang
Keyword(s):  
Dynamic Response ◽  
Frequency Domain ◽  
Time Domain ◽  
Dynamic Stiffness ◽  
Dynamic Responses ◽  
Rigid Foundation ◽  
Layered Soils ◽  
Stiffness Matrices ◽  
The Time Domain ◽  
Arbitrary Shapes

Significant differences between the predicted and measured dynamic response of 3D rigid foundations on multi-layered soils in the time domain were identified due to the existence of uncertainties, which makes the issue a complicated one. In this study, a numerical method was developed to determine the dynamic responses of 3D rigid surfaces and embedded foundations of arbitrary shapes that are bonded to a multi-layered soil in the time domain. First, the dynamic stiffness matrices of the rigid foundations in the frequency domain are calculated via integral domain transformation. Secondly, a dynamic stiffness equation for rigid foundations in the time domain is established via the mixed variables formulation, which is based on the discrete dynamic stiffness matrices in the frequency domain. The proposed method can be applied to the treatment of systems with multiple degrees of freedom without losing the true information that concerns the coupling characteristics. Numerical examples are presented to demonstrate the accuracy of the proposed method for predicting the horizontal, vertical, rocking, and torsional vibrations. Further, a parametric study was carried out to provide insight into the dynamic behavior of the soil–foundation interaction (SFI) while considering soil nonhomogeneity. The results indicate that the elastic modulus of the soil has a significant impact on the dynamic responses of the rigid foundation. Finally, a numerical example of a rigid foundation resting on a six-layered, semi-infinite soil demonstrates that the proposed method can be used to deal with multi-layered media in the time domain in a relatively easy way.

scholarly journals Soil-Pile Interaction in the Pile Vertical Vibration Based on Fictitious Soil-Pile Model

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Guodong Deng ◽  
Jiasheng Zhang ◽  
Wenbing Wu ◽  
Xiong Shi ◽  
Fei Meng
Keyword(s):  
Dynamic Response ◽  
Separation Of Variables ◽  
Vertical Vibration ◽  
Dynamic Responses ◽  
Dynamic Force ◽  
Laplace Transform Technique ◽  
Velocity Response ◽  
Pile Interaction ◽  
Pile Model ◽  
Fictitious Soil

By introducing the fictitious soil-pile model, the soil-pile interaction in the pile vertical vibration is investigated. Firstly, assuming the surrounding soil of pile to be viscoelastic material and considering its vertical wave effect, the governing equations of soil-pile system subjected to arbitrary harmonic dynamic force are founded based on the Euler-Bernoulli rod theory. Secondly, the analytical solution of velocity response in frequency domain and its corresponding semianalytical solution of velocity response in time domain are derived by means of Laplace transform technique and separation of variables technique. Based on the obtained solutions, the influence of parameters of pile end soil on the dynamic response is studied in detail for different designing parameters of pile. Lastly, the fictitious soil-pile model and other pile end soil supporting models are compared. It is shown that the dynamic response obtained by the fictitious soil-pile model is among the dynamic responses obtained by other existing models if there are appropriate material parameters and thickness of pile end soil for the fictitious soil-pile model.

ANALYTICAL TIME DOMAIN NORMAL MODE SOLUTION OF AN ACOUSTIC WAVEGUIDE WITH PERFECTLY REFLECTING WALLS

2013 ◽  
Vol 21 (02) ◽  
pp. 1250026 ◽  
Author(s):  
HÜSEYIN ÖZKAN SERTLEK ◽  
SERKAN AKSOY
Keyword(s):  
Normal Mode ◽  
Time Domain ◽  
Separation Of Variables ◽  
Wide Band ◽  
Frequency Component ◽  
Mode Method ◽  
Source Signal ◽  
Normal Mode Method ◽  
The Time Domain ◽  
Analytical Time

Solution of wide-band underwater acoustic problems with the classical Normal Mode method in the frequency domain needs to solve the problem repeating for every frequency component of the wide-band source signal. In this paper, a direct and causal analytical Time Domain Normal Mode Method is presented for arbitrary time-dependent acoustic sources for a single layered isovelocity waveguide. An incomplete separation of variables technique is used to solve the inhomogeneous wave equation, directly in the time domain. Therefore, it becomes possible to calculate the time domain acoustic pressure in a single run.

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