استخراج مودهای نرمال غیرخطی سازه های دارای مصالح غیرخطی بر پایه روش تناوب مستقل

قریب لو, آرش; وطنی اسکوئی, اصغر

doi:10.22065/jsce.2021.266675.2332

استخراج مودهای نرمال غیرخطی سازه های دارای مصالح غیرخطی بر پایه روش تناوب مستقل

نوع مقاله : علمی - پژوهشی

نویسندگان

¹ گروه مهندسی سازه، دانشکده مهندسی عمران، دانشگاه تربیت دبیر شهید رجایی، تهران، ایران

² دانشکده مهندسی عمران، دانشگاه تربیت دبیر شهید رجایی، تهران، ایران

10.22065/jsce.2021.266675.2332

چکیده

تقاضای روز‌افزون دنیای مدرن و افزایش نیاز صنایع به تحلیل‌هایی با سطوح دقت بالاتر، جامعه مهندسی را بر آن داشته تا با بسط روش-های خطی متداول پیشین به نواحی غیرخطی گامی اساسی را در راستای ارضای این نیاز بر‌دارد. در این میان، ارتقای مودهای نرمال خطی به‌عنوان یکی از فراگیرترین و محبوب‌ترین روش‌های تحلیلی، پنجره‌ای جدید به‌سوی تحلیلی نزدیک‌تر به واقعیت می‌گشاید. در این مقاله، پس از شناخت بنیادین مودهای نرمال غیرخطی، رویکردی جهت تحلیل سازه‌های چند درجه آزاد با مصالح غیرخطی تحت ارتعاش آزاد نامیرا پیشنهاد شده است. سپس با تمرکز بر روش‌های محاسبه، الگوریتمی نوین جهت شناسایی مودهای نرمال غیرخطی ارائه شده و با بسط این الگوریتم بر معادلات دیفرانسیل مانا به کار گرفته شده در تحلیل ارتعاش آزاد، امکان استخراج کلیه مودهای نرمال غیرخطی در حیطه مسئله فراهم گردیده است. پس از آن، به‌منظور بررسی عملکرد روش پیشنهادی، مدل اجزا محدودی یک سازه دو طبقه فولادی ایجاد شده و پس از اعتبارسنجی، در راستای تشکیل معادلات دیفرانسیل مانا به کار گرفته شده است. نهایتاً، پس از اعتبارسنجی روش تناوب مستقل، احجام مودهای نرمال غیرخطی شبه پیوستار و منحنی‌های انرژی - فرکانس سازه مذکور استخراج گشته‌اند. شایان‌ذکر است عدم وابستگی به پاسخ‌های پیشین در یافتن پاسخ بعدی، امکان دستیابی به مودهای نرمال غیرخطی با فرکانس‌های متفاوت در هر درجه آزادی، جذب تمامی رزونانس‌های داخلی، امکان بسط ساده مدل اجزا محدودی به یک مجموعه معادلات حرکت مانا و در نظر گرفتن مصالح غیرخطی در تحلیل، همگی از دستاورد‌های نوین این مقاله هستند.

کلیدواژه‌ها

موضوعات

روش های عددی در مهندسی سازه

عنوان مقاله [English]

Nonlinear Normal Modes of structures with nonlinear material based on Independent Periodic Method

نویسندگان [English]

Arash Ghariblou ¹
Asghar Vatani Oskouei ²

¹ Structural Engineering Department, Civil Engineering Faculty, Shahid Rajaee Teacher Training University, Tehran, Iran

² Faculty of Civil Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran.

چکیده [English]

Ever-increasing demands of the modern world and the growth of industry requirements toward more accurate analyses have made the engineering community develop the first fundamental step and meet the needs by extending the previous prevalent linear methods into nonlinear areas. In this regard, the improvement of linear modes as one of the most pervasive and widespread analytical methods opens a new window to analyses with more closeness to reality. In this paper, after the deep identification of Nonlinear Normal Modes, an approach is proposed to analyze the multi-degree-of-freedom structures with nonlinear material under undamped free vibration. Afterward, through an in-depth investigation of the calculation methods, a novel algorithm for identifying Nonlinear Normal Modes was proposed, and by expanding this algorithm to the existing invariable motion equation used in free vibration analysis, the possibility of the extraction of all Nonlinear Normal Modes has emerged. After that, to investigate the functionality of the proposed approach, the Finite Elements Method-based Model of a 2-story steel structure was developed and, after verification, it was used to form the invariable differential equations. Finally, after verifying the Independent Periodic Method, pseudo-continuous masses of Nonlinear Normal Modes and Frequency-Energy curves of the mentioned structure were calculated. It is worth noting that the independency of resulted response to previous points, the possibility of capturing Nonlinear Normal Modes with different frequencies in each degree-of-freedom, the potential of capturing all internal resonances, the expendability of Finite Elements Model to a set of invariable motion equations, and considering material nonlinearity are among achievements of the current paper.

کلیدواژه‌ها [English]

Nonlinear Normal Modes
Independent Periodic Method
Bifurcations
Nonlinear Dynamics
frequency-energy dependency
Internal Resonances

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