Numerical approach for partial eigenstructure assignment problems in singular vibrating structure using active control

2021 ◽  
pp. 014233122110646
Author(s):  
Peizhao Yu ◽  
Chuang Wang ◽  
Mengmeng Li
Keyword(s):  
Active Control ◽  
Numerical Solutions ◽  
Minimum Energy ◽  
Numerical Approach ◽  
Eigenstructure Assignment ◽  
Matrix Equations ◽  
Assignment Problems ◽  
Structure Information ◽  
Minimum Energy Consumption ◽  
The Matrix

In the paper, the partial eigenstructure assignment problems are investigated using acceleration–velocity–displacement active control in a singular vibrating structure. The problems are transformed into solving matrix equations using the receptance matrix method. Iterative sequences are constructed, and the iterative feasibility is presented for solving the matrix equations. The partial eigenvectors of the closed-loop system are reassigned by imposing modal constraints. An algorithm is proposed to get numerical solutions of the derived matrix equations. The initial value condition is discussed to obtain the minimum norm solution of the partial eigenstructure assignment problems. The designed acceleration–velocity–displacement active control can solve the partial eigenstructure assignment problems depending only on original vibrating structure information. The proposed numerical algorithm can obtain the minimum norms of controller gain, which implies minimum energy consumption. Numerical examples are given to illustrate the effectiveness of the proposed methods.

scholarly journals Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Berna Bülbül ◽  
Mehmet Sezer
Keyword(s):  
Matrix Method ◽  
Numerical Approach ◽  
Duffing Equation ◽  
Matrix Equations ◽  
Algebraic Equations ◽  
Solution Function ◽  
Numerical Examples ◽  
Collocation Points ◽  
Nonlinear Algebraic Equations ◽  
The Matrix

We have suggested a numerical approach, which is based on an improved Taylor matrix method, for solving Duffing differential equations. The method is based on the approximation by the truncated Taylor series about center zero. Duffing equation and conditions are transformed into the matrix equations, which corresponds to a system of nonlinear algebraic equations with the unknown coefficients, via collocation points. Combining these matrix equations and then solving the system yield the unknown coefficients of the solution function. Numerical examples are included to demonstrate the validity and the applicability of the technique. The results show the efficiency and the accuracy of the present work. Also, the method can be easily applied to engineering and science problems.

scholarly journals Eigenvalues and Eigenvectors for 3×3 Symmetric Matrices: An Analytical Approach

2020 ◽  
pp. 106-118
Author(s):  
Abu Bakar Siddique ◽  
Tariq A. Khraishi
Keyword(s):  
Analytical Solutions ◽  
Analytical Approach ◽  
Numerical Solutions ◽  
Linear Equations ◽  
Symmetric Matrices ◽  
Matrix Equations ◽  
Eigenvalues And Eigenvectors ◽  
Engineering Problems ◽  
The Matrix ◽  
Research Problems

Research problems are often modeled using sets of linear equations and presented as matrix equations. Eigenvalues and eigenvectors of those coupling matrices provide vital information about the dynamics/flow of the problems and so needs to be calculated accurately. Analytical solutions are advantageous over numerical solutions because numerical solutions are approximate in nature, whereas analytical solutions are exact. In many engineering problems, the dimension of the problem matrix is 3 and the matrix is symmetric. In this paper, the theory behind finding eigenvalues and eigenvectors for order 3×3 symmetric matrices is presented. This is followed by the development of analytical solutions for the eigenvalues and eigenvectors, depending on patterns of the sparsity of the matrix. The developed solutions are tested against some examples with numerical solutions.

scholarly journals Numerical Analysis of Viscoelastic Rotating Beam with Variable Fractional Order Model Using Shifted Bernstein–Legendre Polynomial Collocation Algorithm

2021 ◽  
Vol 5 (1) ◽  
pp. 8
Author(s):  
Cundi Han ◽  
Yiming Chen ◽  
Da-Yan Liu ◽  
Driss Boutat
Keyword(s):  
Numerical Analysis ◽  
Fractional Order ◽  
Governing Equation ◽  
Numerical Solutions ◽  
Bernstein Polynomials ◽  
Matrix Product ◽  
Algebraic Equations ◽  
Rotating Beam ◽  
The Matrix ◽  
The Time Domain

This paper applies a numerical method of polynomial function approximation to the numerical analysis of variable fractional order viscoelastic rotating beam. First, the governing equation of the viscoelastic rotating beam is established based on the variable fractional model of the viscoelastic material. Second, shifted Bernstein polynomials and Legendre polynomials are used as basis functions to approximate the governing equation and the original equation is converted to matrix product form. Based on the configuration method, the matrix equation is further transformed into algebraic equations and numerical solutions of the governing equation are obtained directly in the time domain. Finally, the efficiency of the proposed algorithm is proved by analyzing the numerical solutions of the displacement of rotating beam under different loads.

EUCOR: An Efficient Unequal Clustering and Optimal Routing in wireless sensor networks for energy conservation

2021 ◽  
pp. 1-9
Author(s):  
C. Jothikumar ◽  
Revathi Venkataraman ◽  
T. Sai Raj ◽  
J. Selvin Paul Peter ◽  
T.Y.J. Nagamalleswari
Keyword(s):  
Objective Function ◽  
Physical Phenomenon ◽  
Minimum Energy ◽  
Cluster Head ◽  
Industrial Applications ◽  
Base Station ◽  
Wireless Sensor ◽  
Unequal Clustering ◽  
Minimum Energy Consumption ◽  
Variable Cluster

Wireless sensor network is a wide network that works as a cutting edge model in industrial applications. The sensor application is mostly used for high security systems that provide safety support to the environment. The sensor system senses the physical phenomenon, processes the input signal and communicates with the base station through its neighbors. Energy is the most important criterion to support a live network for long hours. In the proposed system, the EUCOR (Efficient Unequal Clustering and Optimized Routing) protocol uses the objective function to identify the efficient cluster head with variable cluster size. The computation of the objective function deals with the ant colony approach for minimum energy consumption and the varying size of the cluster in each cycle is calculated based on the competition radius. The system prolongs the lifespan of the nodes by minimizing the utilization of energy in the transmission of packets in the networks when compared with the existing system.

scholarly journals Influence of Tool Geometry and Process Parameters on the Properties of Friction Stir Spot Welded Multiple (AA 5754 H111) Aluminium Sheets

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1157
Author(s):  
Danka Labus Zlatanovic ◽  
Sebastian Balos ◽  
Jean Pierre Bergmann ◽  
Stefan Rasche ◽  
Milan Pecanac ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Process Parameters ◽  
Spot Welding ◽  
Minimum Energy ◽  
Tool Geometry ◽  
Friction Stir ◽  
Minimum Energy Consumption ◽  
Punch Test ◽  
Wide Range ◽  
Lap Welding

Friction stir spot welding is an emerging spot-welding technology that offers opportunities for joining a wide range of materials with minimum energy consumption. To increase productivity, the present work addresses production challenges and aims to find solutions for the lap-welding of multiple ultrathin sheets with maximum productivity. Two convex tools with different edge radii were used to weld four ultrathin sheets of AA5754-H111 alloy each with 0.3 mm thickness. To understand the influence of tool geometries and process parameters, coefficient of friction (CoF), microstructure and mechanical properties obtained with the Vickers microhardness test and the small punch test were analysed. A scanning acoustic microscope was used to assess weld quality. It was found that the increase of tool radius from 15 to 22.5 mm reduced the dwell time by a factor of three. Samples welded with a specific tool were seen to have no delamination and improved mechanical properties due to longer stirring time. The rotational speed was found to be the most influential parameter in governing the weld shape, CoF, microstructure, microhardness and weld efficiency. Low rotational speeds caused a 14.4% and 12.8% improvement in joint efficiency compared to high rotational speeds for both tools used in this investigation.

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