Application of Biot’s dynamic equation to seismic liquefaction problem

AbstractBy using of generalized Opial’s type inequality on time scales, a new oscillation criterion is given for a singular initial-value problem of second-order dynamic equation on time scales. Some oscillatory results of its generalizations are also presented. Example with various time scales is given to illustrate the analytical findings.

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Task-based torque minimization of a 3-PṞR spherical parallel manipulator

Robotica ◽

10.1017/s026357472100062x ◽

2021 ◽

pp. 1-30

Author(s):

Soheil Zarkandi

Keyword(s):

Closed Form ◽

Dynamic Modeling ◽

Dynamic Equation ◽

Parallel Manipulator ◽

Optimization Problem ◽

Dynamic Constraints ◽

Part C ◽

Euler Approach ◽

Three Degree Of Freedom ◽

Spherical Parallel Manipulator

Abstract A comprehensive dynamic modeling and actuator torque minimization of a new symmetrical three-degree-of-freedom (3-DOF) 3-PṞR spherical parallel manipulator (SPM) is presented. Three actuating systems, each of which composed of an electromotor, a gearbox and a double Rzeppa-type driveshaft, produce input torques of the manipulator. Kinematics of the 3-PṞR SPM was recently studied by the author (Zarkandi, Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 2020, https://doi.org/10.1177%2F0954406220938806). In this paper, a closed-form dynamic equation of the manipulator is derived with the Newton–Euler approach. Then, an optimization problem with kinematic and dynamic constraints is presented to minimize torques of the actuators for implementing a given task. The results are also verified by the SimMechanics model of the manipulator.

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Scaling law of gear transmission system obtained from dynamic equation and finite element method

Mechanism and Machine Theory ◽

10.1016/j.mechmachtheory.2021.104285 ◽

2021 ◽

Vol 159 ◽

pp. 104285

Author(s):

Chunpeng Zhang ◽

Jing Wei ◽

Shaoshuai Hou ◽

Jiaxiong Zhang

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Dynamic Equation ◽

Scaling Law ◽

Transmission System ◽

Gear Transmission ◽

Gear Transmission System ◽

Element Method

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Solution of general dynamic equation for nanoparticles in turbulent flow considering fluctuating coagulation

Applied Mathematics and Mechanics ◽

10.1007/s10483-016-2131-9 ◽

2016 ◽

Vol 37 (10) ◽

pp. 1275-1288 ◽

Cited By ~ 6

Author(s):

Jianzhong Lin ◽

Xiaojun Pan ◽

Zhaoqin Yin ◽

Xiaoke Ku

Keyword(s):

Turbulent Flow ◽

Dynamic Equation ◽

General Dynamic

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Oscillation and nonoscillation theorems of neutral dynamic equations on time scales

Advances in Difference Equations ◽

10.1186/s13662-019-2342-7 ◽

2019 ◽

Vol 2019 (1) ◽

Cited By ~ 1

Author(s):

Yong Zhou ◽

Ahmed Alsaedi ◽

Bashir Ahmad

Keyword(s):

Time Scales ◽

Dynamic Equation ◽

Dynamic Equations ◽

Nonoscillatory Solutions ◽

Oscillation Criteria ◽

Neutral Dynamic Equation ◽

The Given ◽

Neutral Dynamic Equations ◽

Oscillation And Nonoscillation

Abstract We present the oscillation criteria for the following neutral dynamic equation on time scales: $$ \bigl(y(t)-C(t)y(t-\zeta )\bigr)^{\Delta }+P(t)y(t-\eta )-Q(t)y(t-\delta )=0, \quad t\in {\mathbb{T}}, $$ ( y ( t ) − C ( t ) y ( t − ζ ) ) Δ + P ( t ) y ( t − η ) − Q ( t ) y ( t − δ ) = 0 , t ∈ T , where $C, P, Q\in C_{\mathit{rd}}([t_{0},\infty ),{\mathbb{R}}^{+})$ C , P , Q ∈ C rd ( [ t 0 , ∞ ) , R + ) , ${\mathbb{R}} ^{+}=[0,\infty )$ R + = [ 0 , ∞ ) , $\gamma , \eta , \delta \in {\mathbb{T}}$ γ , η , δ ∈ T and $\gamma >0$ γ > 0 , $\eta >\delta \geq 0$ η > δ ≥ 0 . New conditions for the existence of nonoscillatory solutions of the given equation are also obtained.

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Modelling of Seismic Liquefaction Using Classification Techniques

International Journal of Geotechnical Earthquake Engineering ◽

10.4018/ijgee.2021010102 ◽

2021 ◽

Vol 12 (1) ◽

pp. 12-21

Author(s):

Azad Kumar Mehta ◽

Deepak Kumar ◽

Pijush Samui

Keyword(s):

Classification Problem ◽

Group Method ◽

Type I ◽

Error Type ◽

Reliable Technique ◽

Case Record ◽

Classification Techniques ◽

Liquefaction Susceptibility ◽

Seismic Liquefaction ◽

Non Linear

Liquefaction susceptibility of soil is a complex problem due to non-linear behaviour of soil and its physical attributes. The assessment of liquefaction potential is commonly assessed by the in-situ testing methods. The classification problem of liquefaction is non-linear in nature and difficult to model considering all independent variables (seismic and soil properties) using traditional techniques. In this study, four different classification techniques, namely Fast k-NN (F-kNN), Naïve Bayes Classifier (NBC), Decision Forest Classifier (DFC), and Group Method of Data Handling (GMDH), were used. The SPT-based case record was used to train and validate the models. The performance of these models was assessed using different indexes, namely sensitivity, specificity, type-I error, type-II error, and accuracy rate. Additionally, receiver operating characteristic (ROC) curve were plotted for comparative study. The results show that the F-kNN models perform far better than other models and can be used as a reliable technique for analysis of liquefaction susceptibility of soil.

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