تحلیل ارتعاش آزاد غیرخطی لایه خاک دانه‌ای با استفاده از تکنیک اغتشاشات

نوع مقاله : مقاله پژوهشی

نویسندگان

1 مهندسی عمران،فنی و مهندسی،خوارزمی،تهران،ایران

2 گروه مهندسی عمران دانشگاه خوارزمی، تهران، ایران

3 گروه مهندسی مکانیک دانشکده مهندسی دانشگاه خوارزمی، تهران،ایران

چکیده

در این تحقیق یک مدل تجربی به منظور تعیین خصوصیات تغییرشکل دینامیکی خاک دانه‌ای سیمانته و غیرسیمانته ارائه گردیده است. سپس به مطالعه و بررسی فرکانس طبیعی آبرفت‌های یک لایه، همگن و با سطح افقی تحت اثر ارتعاشات هارمونیک یک‌بعدی پرداخته شده است. مدل ارائه شده سازگاری بسیار خوبی با نتایج آزمایشگاهی در محدوده گسترده‌ای از انواع خاک دانه‌ای دارد. اگر سطح زمین، سطح سنگ بستر زیر خاک و مرز بین لایه خاک و سنگ به صورت افقی در نظر گرفته شود، محدوده جانبی رسوبات آبرفت یک لایه تأثیری در پاسخ ندارد و در این صورت لایه رسوبات ممکن است به صورت یک لایه افقی نیمه‌بی‌نهایت در نظر گرفته شود. در چنین مواردی وقتی خاک تحت تأثیر تحریکات لرزه‌ای در پایه قرار می‌گیرد، تنها تغییرشکل‌های برشی در خاک ایجاد می‌شوند. رفتار غیرخطی خاک که ناشی از بارگذاری سیکلی می‌باشد، از طریق اصلاح در خصوصیات تغییرشکلی دینامیکی خاک دانه‌ای یعنی نسبت میرایی و سختی نرمال شده، با استفاده از رویکرد جدیدی در معادله تعادل دینامیکی حرکت حاکم بر رفتار سیستم یک درجه آزاد تحت ارتعاش آزاد، قرار داده شده است. پس با تشکیل معادله یک درجه آزادی مرتبه اول غیرخطی حرکت تحت ارتعاش آزاد، امکان ارائه راه‌حل تقریبی این معادله با تکنیک اغتشاشات وجود خواهد داشت. فرکانس طبیعی این سیستم یک درجه آزاد به روش تحلیلی تعیین گردید و نتایج نشان می‌دهد که دقت لازم را دارا می‌باشد. روش تحلیلی برای تعیین پاسخ سیستم یک درجه آزاد از سازگاری بسیار خوبی با روش عددی مانند روش رانج کوتا برخوردار است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Nonlinear Free Vibration Analysis of Granular Soil Layer Using Perturbation Technique

نویسندگان [English]

  • Ali Shirzad 1
  • Amir Hamidi 2
  • S.A.A. Hosseini 3
1 Civil engineering, engineerin,kharazmi,Tehran,Iran
2 civil engineering department, Kharazmi University, Tehran, Iran
3 Mechanical engineering department, faculty of engineering, Kharazmi University, Tehran, Iran.
چکیده [English]

In this study, an experimental model has been proposed to determine the dynamic deformation properties of cemented and non-cemented granular soils and then the natural frequency of one-layered, homogeneous and horizontal surface alluvium under the influence of one-dimensional harmonic vibrations was studied. The proposed model is very compatible with laboratory results in a wide range of grain soils. The natural frequency of a one-degree-of-freedom system was determined analytically, and the results showed that it has careful accuracy. The analytical method to determine the response of a one-degree-of-freedom system has a very good agreement with the numerical method such as the Runge-Kutta method. In the present study, considering the one-layered alluvium as a lumped mass system and nonlinear spring and nonlinear damping, a clear solution of this system of a one-degree-of-freedom has been proposed. On the other hand, the natural frequency can not only be a function of the depth of the alluvium layer and can be considered as a function of time.

کلیدواژه‌ها [English]

  • Perturbation techniques
  • Natural frequency
  • Nonlinear effects
  • Experimental formulations
  • One-layer deposit surface response
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