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Optimal extended homotopy analysis method for Multi-Degree-of-Freedom nonlinear dynamical systems and its application

Qian, Y.H.;Zhang, Y.F.
- Structural Engineering and Mechanics
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- v.61 no.1
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- pp.105-116
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- 2017
In this paper, the optimal extended homotopy analysis method (OEHAM) is introduced to deal with the damped Duffing resonator driven by a van der Pol oscillator, which can be described as a complex Multi-Degree-of-Freedom (MDOF) nonlinear coupling system. Ecumenically, the exact solutions of the MDOF nonlinear coupling systems are difficult to be obtained, thus the development of analytical approximation becomes an effective and meaningful approach to analyze these systems. Compared with traditional perturbation methods, HAM is more valid and available, and has been widely used for nonlinear problems in recent years. Hence, the method will be chosen to study the system in this article. In order to acquire more suitable solutions, we put forward HAM to the OEHAM. For the sake of verifying the accuracy of the above method, a series of comparisons are introduced between the results received by the OEHAM and the numerical integration method. The results in this article demonstrate that the OEHAM is an effective and robust technique for MDOF nonlinear coupling systems. Besides, the presented methods can also be broadly used for various strongly nonlinear MDOF dynamical systems.
https://doi.org/10.12989/sem.2017.61.1.105 인용 KSCI

Impact Force Reconstruction of Composite materials based on Improved Regularization Technology

Sun, Yajie;Yin, Tao;Yang, Jian;Cai, Zhiyu;Wu, Shaoen
- KSII Transactions on Internet and Information Systems (TIIS)
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- v.15 no.8
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- pp.2718-2731
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- 2021
In the structural health monitoring of composite materials, in order to solve the ill-posed problem of impact force reconstruction, regularization techniques are often used to deal with it. Due to the poor convergence of the traditional Tikhonov regularization method, in order to accurately reconstruct the time history of the impact force, this paper improves Tikhonov regularization method and constructs homotopy function with strong convergence. Since the optimal regularization parameters need to be found in the homotopy function, the Newton downhill method is used to find the optimal parameters and the homotopy function can be calculated, which can accurately reconstruct the time history of the impact force. In order to verify the universality of the method in this paper, impact hammers of different materials were used in the experiment in this paper to study and compare the reconstruction effect of impact time history of different impact hammers.
https://doi.org/10.3837/tiis.2021.08.001 인용 PDF KSCI HTML

CO-CLUSTER HOMOTOPY QUEUING MODEL IN NONLINEAR ALGEBRAIC TOPOLOGICAL STRUCTURE FOR IMPROVING POISON DISTRIBUTION NETWORK COMMUNICATION

V. RAJESWARI;T. NITHIYA
- Journal of applied mathematics & informatics
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- v.41 no.4
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- pp.861-868
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- 2023
Nonlinear network creates complex homotopy structural communication in wireless network medium because of complex distribution approach. Due to this multicast topological connection structure, the queuing probability was non regular principles to create routing structures. To resolve this problem, we propose a Co-cluster homotopy queuing model (Co-CHQT) for Nonlinear Algebraic Topological Structure (NLTS-) for improving poison distribution network communication. Initially this collects the routing propagation based on Nonlinear Distance Theory (NLDT) to estimate the nearest neighbor network nodes undernon linear at x_(a,b)→ax²+bx² = c. Then Quillen Network Decomposition Theorem (QNDT) was applied to sustain the non-regular routing propagation to create cluster path. Each cluster be form with co variance structure based on Two unicast 2(n+1)-Z2(n+1)-Z network. Based on the poison distribution theory X_(a,b) ≠ µ(C), at number of distribution routing strategies weights are estimated based on node response rate. Deriving shorte;'l/st path from behavioral of the node response, Hilbert -Krylov subspace clustering estimates the Cluster Head (CH) to the routing head. This solves the approximation routing strategy from the nonlinear communication depending on Max- equivalence theory (Max-T). This proposed system improves communication to construction topological cluster based on optimized level to produce better performance in distance theory, throughput latency in non-variation delay tolerant.
https://doi.org/10.14317/jami.2023.861 인용 PDF