scholarly journals Development of Post Processing for Wave Propagation Problem: Response Filtering Method

2020 ◽  
Vol 10 (24) ◽  
pp. 9032
Author(s):  
Hyeong Seok Koh ◽  
Jong Wook Lee ◽  
Kiwoon Kwon ◽  
Gil Ho Yoon
Keyword(s):  
Analytical Solution ◽  
Numerical Solution ◽  
Numerical Approach ◽  
Mechanical Stresses ◽  
Structural Safety ◽  
Benchmark Problems ◽  
Filtering Method ◽  
Wave Propagation Problem ◽  
Time Domains ◽  
Frequency Components

This study develops a new response filtering approach for recovering dynamic mechanical stresses under impact loading. For structural safety, it is important to consider the propagation of transient mechanical stresses inside structures under impact loads. Commonly, mechanical stress waves can be obtained by solving Newton’s second law using explicit or implicit finite element procedures. Regardless of the numerical approach, large discrepancies called the Gibb’s phenomenon are observed between the numerical solution and the analytical solution. To reduce these discrepancies and enhance the accuracy of the numerical solution, this study develops a response filtering method (RFM). The RFM averages the transient responses within split time domains. By solving several benchmark problems and analyzing the stresses in the frequency domain, it was possible to verify that the RFM can provide an improved solution that converges toward the analytical solution. A mathematical theory is also presented to correlate the relationship between the filtering length and the frequency components of the filtered stress values.

A Numerical Approach to Determine Some Properties of Cylindrical Pieces of Bananas During Drying

2015 ◽  
Vol 11 (3) ◽  
pp. 335-347 ◽  
Author(s):  
Wilton Pereira da Silva ◽  
Cleide M. D. P. S. e Silva ◽  
Aluizio Freire da Silva Junior ◽  
Alexandre José de Melo Queiroz
Keyword(s):  
Numerical Solution ◽  
Numerical Approach ◽  
Moisture Diffusivity ◽  
Convective Drying ◽  
Chi Square ◽  
Experimental Conditions ◽  
Liquid Diffusion ◽  
Air Temperatures ◽  
C 50 ◽  
Volume Method

Abstract This article uses several liquid diffusion models to describe convective drying of bananas cut into cylindrical pieces. A two-dimensional numerical solution of the diffusion equation with boundary condition of the third kind, obtained through the finite volume method, was used to describe the process. The cylindrical pieces were cut into the following dimensions: length of about 21 mm and average radius of 15 mm. Drying air temperatures were 40°C, 50°C, 60°C and 70°C. In order to determine the process parameters, an optimizer was coupled with the numerical solution. A model that considers the shrinkage and variable effective moisture diffusivity well describes drying for all the experimental conditions, and enables to predict the moisture distributions at any given time. For this model, the determination coefficient has varied from 0.99937 (70°C) to 0.99995 (40°C), while the chi-square ranged from 3.41 × 10−4 (40°C) to 4.15 × 10−3 (70°C).

scholarly journals Use of Jacobians for inverse kinematics of articulated robots : a study on approximate solutions

2020 ◽  
Author(s):  
◽  
Uriel Jacket Tresor Demby's
Keyword(s):  
Numerical Solution ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Fuzzy Inference ◽  
Numerical Approach ◽  
Data Driven ◽  
Approximate Methods ◽  
Inference System ◽  
First Case

In the context of articulated robotic manipulators, the Forward Kinematics (FK) is a highly non-linear function that maps joint configurations of the robot to poses of its endeffector. Furthermore, while in the most useful cases these functions are neither injective (one-to-one) nor surjective (onto), depending on the robot configuration -- i.e. the sequence of prismatic versus revolute joints, and the number of Degrees of Freedom (DoF) -- the associated Inverse Kinematics (IK) problem may be practically or even theoretically impossible to be solved analytically. Therefore, in the past decades, several approximate methods have been developed for many instances of IK problems. The approximate methods can be divided into two distinct categories: data-driven and numerical approaches. In the first case, data-driven approaches have been successfully used for small workspace domains (e.g., task-driven applications), but not fully explored for large ones, i.e. in task-independent applications where a more general IK is required. Similarly, and despite many successful implementations over the years, numerical solutions may fail if an improper matrix inverse is employed (e.g., Moore-Penrose generalized inverse). In this research, we propose a systematic, robust and accurate numerical solution for the IK problem using the Unit-Consistent (UC) and the Mixed (MX) Inverse methods to invert the Jacobians derived from the Denavit-Hartenberg (D-H) representation of the FK for any robot. As we demonstrate, this approach is robust to whether the system is underdetermined (less than 6 DoF) or overdetermined (more than 6 DoF). We compare the proposed numerical solution to data driven solutions using different robots -- with DoF varying from 3 to 7. We conclude that numerical solutions are easier to implement, faster, and more accurate than most data-driven approaches in the literature, specially for large workspaces as in task-independent applications. We particularly compared the proposed numerical approach against two data-driven approaches: Multi-Layer Perceptron (MLP) and Adaptive Neuro-Fuzzy Inference System (ANFIS), while exploring various architectures of these Neural Networks (NN): i.e. number of inputs, number of outputs, depth, and number of nodes in the hidden layers.

scholarly journals Analytical and Experimental Analyses of Nonlinear Vibrations in a Rotary Inverted Pendulum

2021 ◽  
Author(s):  
Mohammadjavad Rahimi dolatabad ◽  
Abdolreza Pasharavesh ◽  
Amir Ali Akbar Khayyat
Keyword(s):  
Analytical Solution ◽  
Numerical Solution ◽  
Closed Loop ◽  
Inverted Pendulum ◽  
Multiple Scales ◽  
Nonlinear Oscillations ◽  
Wide Frequency Range ◽  
Perturbative Method ◽  
Full State Feedback ◽  
Rotary Inverted Pendulum

Abstract Gaining insight into possible vibratory responses of dynamical systems around their stable equilibria is an essential step, which must be taken before their design and application. The results of such a study can significantly help prevent instability in closed-loop stabilized systems through avoiding the excitation of the system in the neighborhood of its resonance. This paper investigates nonlinear oscillations of a Rotary Inverted Pendulum (RIP) with a full-state feedback controller. Lagrange’s equations are employed to derive an accurate 2-DoF mathematical model, whose parameter values are extracted by both the measurement and 3D modeling of the real system components. Although the governing equations of a 2-DoF nonlinear system are difficult to solve, performing an analytical solution is of great importance, mostly because, compared to the numerical solution, the analytical solution can function as an accurate pattern. Additionally, the analytical solution is generally more appealing to engineers because their computational costs are less than those of the numerical solution. In this study, the perturbative method of multiple scales is used to obtain an analytical solution to the coupled nonlinear motion equations of the closed-loop system. Moreover, the parameters of the controller are determined, using the results of this solution. The findings reveal the existence of hardening- and softening-type resonances at the first and second vibrational modes, respectively. This led to a wide frequency range with moderately large-amplitude vibrations, which must be avoided when adjusting a time-varying set-point for the system. The analytical results of the nonlinear vibration of the RIP are verified by experimental measurements, and a very good agreement is observed between the results of both approaches.

scholarly journals Comparative Study of Analytic Solution and Numerical Solution of Baseband Symbol Signal Based on Optimal Generic Function

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Mingxin Liu ◽  
Wei Xue ◽  
Sergey B. Makarov ◽  
Junwei Qi ◽  
Beiming Li
Keyword(s):  
Analytical Solution ◽  
Numerical Solution ◽  
Solution Process ◽  
Development Trend ◽  
Partial Solution ◽  
Research Process ◽  
Constraint Condition ◽  
Energy Limit ◽  
Function Model ◽  
Boundary Constraints

In this paper, the optimal mathematical generic function model is established using the minimum out-of-band energy radiation criterion. Firstly, the energy limit conditions, boundary constraints, and peak-to-average ratio constraints are applied to the generic function model; thus, the analytical solutions are obtained under different parameters. Secondly, a single symbol signal energy constraint condition and boundary constraint condition are added to the generic function model; thus, the numerical solution of the different parameters is obtained. In the process of solving the analytical solution, the partial solution process is simplified to solve the analytical solution, and there are also digital truncation problems. In addition, the corresponding order of the Lagrange differential equation increases by a multiple of 2 when the parameter n increases, which makes the solution extremely complicated or even impossible to solve. The numerical solution is in line with the current development trend of digital communication, and there is no need to simplify the solution process in the process of solving the numerical solution. When the parameter n and the Fourier series m take different values, the obtained symbol signals can also meet the needs of different communication occasions. The relevant data of the above research process were solved by a MATLAB software simulation, which proves the correctness of the method and the superiority of the numerical method.

scholarly journals Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Qingxue Huang ◽  
Fuqiang Zhao ◽  
Jiaquan Xie ◽  
Lifeng Ma ◽  
Jianmei Wang ◽  
...  
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Fractional Differential Equations ◽  
Operational Matrix ◽  
Numerical Approach ◽  
Principal Characteristic ◽  
Legendre Functions ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Fractional Differential

In this paper, a robust, effective, and accurate numerical approach is proposed to obtain the numerical solution of fractional differential equations. The principal characteristic of the approach is the new orthogonal functions based on shifted Legendre polynomials to the fractional calculus. Also the fractional differential operational matrix is driven. Then the matrix with the Tau method is utilized to transform this problem into a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. The approach is tested via some examples. It is shown that the FLF yields better results. Finally, error analysis shows that the algorithm is convergent.

scholarly journals Transforming Arithmetic Asian Option PDE to the Parabolic Equation with Constant Coefficients

2011 ◽  
Vol 2011 ◽  
pp. 1-6 ◽  
Author(s):  
Zieneb Ali Elshegmani ◽  
Rokiah Rozita Ahmad ◽  
Saiful Hafiza Jaaman ◽  
Roza Hazli Zakaria
Keyword(s):  
Parabolic Equation ◽  
Analytical Solution ◽  
Heat Equation ◽  
Numerical Solution ◽  
Closed Form ◽  
Asian Option ◽  
Asian Options ◽  
New Approach ◽  
Constant Coefficients ◽  
Closed Form Analytical Solution

Arithmetic Asian options are difficult to price and hedge, since at present, there is no closed-form analytical solution to price them. Transforming the PDE of the arithmetic the Asian option to a heat equation with constant coefficients is found to be difficult or impossible. Also, the numerical solution of the arithmetic Asian option PDE is not very accurate since the Asian option has low volatility level. In this paper, we analyze the value of the arithmetic Asian option with a new approach using means of partial differential equations (PDEs), and we transform the PDE to a parabolic equation with constant coefficients. It has been shown previously that the PDE of the arithmetic Asian option cannot be transformed to a heat equation with constant coefficients. We, however, approach the problem and obtain the analytical solution of the arithmetic Asian option PDE.

An Integral Equation Method for Predicting Acoustic Emission within Enclosures

1985 ◽  
Vol 199 (2) ◽  
pp. 133-137 ◽  
Author(s):  
D T I Francis ◽  
M M Sadek
Keyword(s):  
Integral Equation ◽  
Finite Element ◽  
Acoustic Emission ◽  
Analytical Solution ◽  
Numerical Solution ◽  
Finite Element Methods ◽  
Exact Analytical Solution ◽  
Integral Equation Method ◽  
Absorption Characteristics ◽  
Good Agreement

A method is presented for calculating the acoustic emission of a vibrating body within an enclosure whose surface has known absorption characteristics. It is based on a numerical solution of the Helmholtz integral equation. Solutions are given for the case of a pulsating sphere within a sphere, and good agreement with the exact analytical solution is reported. The method is of value for small and medium scale problems at lower frequencies, where traditional techniques are less reliable. It is also potentially less demanding computationally than finite element methods.

scholarly journals A Semi-Analytical Solution of Thick Truncated Cones Using Matched Asymptotic Method and Disk Form Multilayers

2014 ◽  
Vol 61 (3) ◽  
pp. 495-513 ◽  
Author(s):  
Mohammad Zamani Nejad ◽  
Mehdi Jabbari ◽  
Mehdi Ghannad
Keyword(s):  
Finite Element Method ◽  
Shear Stress ◽  
Analytical Solution ◽  
Differential Equations ◽  
Numerical Solution ◽  
Asymptotic Method ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
The Finite Element Method ◽  
Truncated Cone

Abstract In this article, the thick truncated cone shell is divided into disk-layers form with their thickness corresponding to the thickness of the cone. Due to the existence of shear stress in the truncated cone, the equations governing disk layers are obtained based on first shear deformation theory. These equations are in the form of a set of general differential equations. Given that the truncated cone is divided into n disks, n sets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. The results obtained have been compared with those obtained through the analytical solution and the numerical solution. For the purpose of the analytical solution, use has been made of matched asymptotic method (MAM) and for the numerical solution, the finite element method (FEM).

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