Một phương pháp xấp xỉ liên tiếp kết hợp để giải phương trình Duffing và ứng dụng của nó

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Tác giả:

Ngôn ngữ: vie

Ký hiệu phân loại: 511.4 Approximations formerly also 513.24 and expansions

Thông tin xuất bản: Vietnam Juornal of Mechanics, 2014

Mô tả vật lý: 77-93

Bộ sưu tập: Metadata

ID: 506333

The paper proposes an algorithm to solve a general Duffing equation, in which a process of transforming the initial equation to a resulting equation is proposed, and then the coupling successive approximation method is applied to solve the resulting equation. By using this algorithm a special physical factor and complex-valued solutions to the general Duffing equation are revealed. The proposed algorithm does not use any assumption of small parameters in the equation solving. The coupling successhre procedure provides an analytic approximated solution in both real-valued or complex-valued solution. The procedure also reveals a formula to evaluate the vibration frequency, tp, of the non-linear equation. Since the first approximation solution is in a closed-form, the chaos index of the general Duffing equation and the chaotic characteristics of solutions can be predicted. Some examples are used to illustrate the proposed method. IIi the case of chaotic solution, the Pointcare conjecture is used for solution verification.
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