NGHIÊN CỨU DAO ĐỘNG TỰ DO PHI TUYẾN SỬ DỤNG PHƯƠNG PHÁP PHÂN TÍCH ĐỒNG LUÂN=RESEARCH ON NONLINEAR FREE VIBRATIONS USING HOMOTOPY ANALYSIS METHOD

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Tác giả: Thế Hùng Dương, Thế Thịnh Nguyễn

Ngôn ngữ: vie

Ký hiệu phân loại:

Thông tin xuất bản: Tạp chí Khoa học và Công nghệ - Đại học Thái Nguyên, 2024

Mô tả vật lý: tr.321 - 329

Bộ sưu tập: Metadata

ID: 478475

Thêm vào giỏ

Bài báo này áp dụng phương pháp phân tích đồng luân để nghiên cứu dao động tự do phi tuyến. Bài báo dùng phương pháp phân tích đồng luân để tìm nghiệm giải tích của hệ hai bậc tự do phi tuyến. Kết quả giải tích đã tìm được tần số dao động riêng, công thức chuyển vị của hệ được xấp xỉ tính toán ở bậc 10. Việc nghiên cứu tìm nghiệm giải tích chỉ nhận được kết quả khả quan khi lựa chọn tham số phụ là yếu tố quuyết định đến giá trị của nghiệm. So sánh với kết quả tính bằng phương pháp số, sử dụng tính toán bằng phương pháp phân tích đồng luân là một lợi thế để tìm nghiệm của bài toán dao động phi tuyến. Từ kết quả tính toán của bài báo, khi tham số phụ nhận được kết quả trùng khớp với kết quả giải bằng phương pháp số. Ngoài ra, để đánh giá mức độ tin cậy trong phương pháp phân tích đồng luân, bài báo đã xác định được khi biến thời gian trong khoảng , kết quả so sánh về chuyển vị tính bằng phương pháp phân tích đồng luân với phương pháp số là đáng tin cậy.This paper applies the homotopy analysis method to study nonlinear free vibrations. The paper has used the homotopy analysis method to find analytical solutions of a nonlinear two-degree-of-freedom system. Analytical results have found the natural oscillation frequencies, the displacement formula of the system are approximately calculated at the 10th order. Research to find analytical solutions only receives positive results when selecting the auxiliary parameter is the deciding factor in the values of the solution. Compared with the results calculated by numerical methods, using calculations by homotopy analysis method is an advantage to find solutions to the nonlinear vibration problem. From calculating results, in case of auxiliary parameter , those results are matched very well when analyzed by the numerical methods. In additionally, to evaluate the reliability of the homotopy analysis method, this paper has determined that when the time variable is in the range t = [ ], the displacemental results are compared by calculated by the homotopy method with the numerical method would be confidence interval.

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