ارائه فرمول‌بندی جدید برای تحلیل دینامیکی تاریخچه زمانی غیرخطی ارتعاشات سازه‌های تحت بارگذاری زلزله

نوع مقاله : مقاله کامل پژوهشی

نویسندگان

گروه مهندسی عمران، دانشکده فنی و مهندسی، دانشگاه بناب

چکیده

یک روش عددی سریع و کارآمد تحت عنوان روش نیوتن- کاتس- تتای چهار نقطه‌ای (Newton-Cotes-4P-θ Method)، برای تحلیل تاریخچه زمانی سیستم‌های سازه‌ای یک درجه آزادی (‏SDOF)‏ تحت اثر زلزله ارائه شده‌ است. این روش از فرمول عددی نیوتن- کاتس- تتای چهار نقطه‌ای برای حل معادله حرکت استفاده‌ کرده و سیستم‌های خطی و غیرخطی را نیز پوشش می‌دهد. در این روش هرگونه بارگذاری از نوع نیرو‌های خارجی وابسته به زمان و یا تحریک لرزه‌ای، قابل ‌اعمال به سیستم دینامیکی بوده و تحلیل آن امکان‌پذیر است. مزیت مهم فرمول‌بندی جدید سهولت اجرا، سادگی محاسبات و دقت بالای آن در مقایسه با سایر روش‌های مشابه خود مانند انتگرال دوهامل و روش‌های نیومارک- بتا (Newmark-) و ویلسون- تتا (Wilson-) می‌باشد. متعاقباً سطح دقت روش ارائه‌شده در حد روش‌های شبه تحلیلی انتگرال‌ دوهامل بوده و سرعت پردازش آن نیز، مشابه روش‌های انتگرال‌گیری گام‌‌به‌گام نیومارک- بتا و ویلسون- تتا می‌باشد. قابل‌ ذکر است که فرمول‌بندی جدید ارائه‌شده برخلاف روش نیومارک- بتا غیرخطی، نیاز به اجرای یک‌روند مستقل مانند تکرار نیوتن، برای لحاظ اثرات غیرخطی ندارد؛ بلکه تکرار یک سری محاسبات ساده منجربه همگرایی رفتار غیرخطی خواهد ‌شد. علاوه‌برآن، روش حاضر در هنگام تحلیل سیستم‌های دارای دوره تناوب کمتر از 0.15 ثانیه و نسبت میرایی کمتر از 0.02، عملکرد بهتری دارد و دارای پایداری مؤثر، سرعت همگرایی بالا و دقت کافی جهت تحلیل سیستم‌های دینامیکی بوده و به‌سادگی قابلیت اجرا دارد. نتایج عددی، مؤثربودن روش جدید را در مقایسه با انتگرال دوهامل و روش‌های نیومارک- بتا و ویلسون- تتا نشان می‌دهد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

New Formulation for Dynamic Analysis of Nonlinear Time-History of Vibrations of Structures under Earthquake Loading

نویسندگان [English]

  • Mohammad Reza Hanafi
  • Mehdi Babaei
  • Peyman Narjabadifam
Bachelor of Civil Engineering, Department of Civil Engineering, University of Bonab, Bonab, Iran
چکیده [English]

A fast and efficient numerical scheme is presented for time-history analysis of single-degree-of-freedom (SDOF) structural systems undergoing seismic excitation (Chopra, 2003). The new method is called Newton-Cotes-4P-θ Method. It uses the most known 4-point Newton-Cotes quadrature in its body to solve the vibration equation. Nonlinear analysis is covered as well as linear analysis. Any arbitrary external loadings of type force or seismic signals are welcome. The significant advantages of the new formulation are its great simplicity, running speed, and appropriate precision level compared with its counterparts such as Duhamel integral and Newmark-β methods. The accuracy level of the Newton-Cotes-4P-θ is close to the semi-analytical method of Duhamel integration and its speed is similar to the Newmark-β algorithm. Notably, against the nonlinear Newmark-β method, the new method does not require a standalone procedure to handle nonlinear analysis; instead, it simply triggers iteration of the same computation used in its first processing round. Moreover, the Newmark-β method loses its performance dealing with stiff and near-conservative () systems; however, the Newton-Cotes-4P-θ method does not loos its accuracy and keeps its well-performed analysis in this case. Numerical results reveal the superiority of the Newton-Cotes- 4P-θ method against its counterparts such as the Duhamel integral, Newmark-β, and Wilson-θ methods (Babaei et al., 2021; Babaei et al., 2022; Babaei et al., 2023).

کلیدواژه‌ها [English]

  • Structural dynamics
  • Seismic response
  • Nonlinear analysis
  • Time-history analysis
  • Newton-Cotes-4P-θ method
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