استفاده از روش تکرار تغییرات برای حل معادلات استورم لیوویل در ارتعاش سد خاکی

محورهای موضوعی : آنالیز

یاسر خلیلی ^{1 *} , عبدالعلی نعمتی ²

1 - گروه علوم پایه (آنالیز مجانبی)، دانشگاه علوم كشاورزي و منابع طبيعي ساري، ساری، ایران
2 - گروه ریاضی (آنالیز مجانبی)، دانشگاه مازندران، بابلسر، ایران

تاریخ دریافت : 1401/03/09 تاریخ پذیرش : 1402/06/21 تاریخ انتشار : 1403/10/30

کلید واژه: Shear stress, Variational iteration method, Pencil, earth dam,

چکیده مقاله :

جابجایی و حرکت سدهای خاکی در زمان وقوع زمین لرزه را می توان به کمک معادلات استورم-لیوویل بیان کرد. روش های تحلیلی و عددی ابزارهای مفید و مناسب برای حل این گونه مسئله‌ها می باشند. در تحقیق حاضر، معادله حرکت و جابجایی سد خاکی وقتی که فشاری به صورت τ_yz=G(∂u/∂z+∂u/∂t) بر آن وارد می شود، در نظر گرفته و به کمک روش عددی (روش تکرار تغییرات) جوابی برای معادله برآمده از این جابجایی که به صورت معادله پنسیل می باشد، ارائه می شود. جابجایی و حرکت سدهای خاکی در زمان وقوع زمین لرزه را می توان به کمک معادلات استورم-لیوویل بیان کرد. روش های تحلیلی و عددی ابزارهای مفید و مناسب برای حل این گونه مسئله‌ها می باشند. در تحقیق حاضر، معادله حرکت و جابجایی سد خاکی وقتی که فشاری به صورت τ_yz=G(∂u/∂z+∂u/∂t) بر آن وارد می شود، در نظر گرفته و به کمک روش عددی (روش تکرار تغییرات) جوابی برای معادله برآمده از این جابجایی که به صورت معادله پنسیل می باشد، ارائه می شود.

چکیده انگلیسی:

We can express the displacement and movement of the earth dams during the earthquake by Sturm-Liouville equations. Analytical and numerical methods are useful tools for solving such problems. In the present study the equation of motion and displacement of the earth dam is considered when it is applied the pressure as τ_yz=G(∂u/∂z+∂u/∂t) and it is given the solution for the equation derived from this displacement that is in the pencil form by the numerical method (variational iteration method). We can express the displacement and movement of the earth dams during the earthquake by Sturm-Liouville equations. Analytical and numerical methods are useful tools for solving such problems. In the present study the equation of motion and displacement of the earth dam is considered when it is applied the pressure as τ_yz=G(∂u/∂z+∂u/∂t) and it is given the solution for the equation derived from this displacement that is in the pencil form by the numerical method (variational iteration method).

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