تحلیل ارتعاشات عرضی آزاد تیرهای ناهمگن محوری نمایی با شرایط مرزی مختلف

نوع مقاله: مقاله مستقل

نویسندگان

1 باشگاه پژوهشگران جوان و نخبگان، واحد تهران جنوب، دانشگاه آزاد اسلامی، تهران

2 استادیار، مهندسی مکانیک، دانشگاه تربیت دبیر شهید رجایی، تهران

چکیده

در کار حاضر به تحلیل ارتعاشات آزاد تیرهای ناهمگن محوری پرداخته شده است. برای تیرهای مدرج تابعی نمایی، به ازای تمامی شرایط مرزی، معادلات مشخصه فرکانسی سیستم به صورت دقیق ارائه شده‌اند. همچنین تغییرات شکل مودهای مختلف سازه برحسب تغییرات پارامتر گرادیان مشخص شده‌اند و در نهایت نیز با مواد ایزوتروپیک مقایسه شده‌اند. .به منظور صحه‌سازی، نتایج استخراج شده در این پژوهش با مراجع موجود دیگر مقایسه شدند. نتایج نشان دادند که فرکانس طبیعی تیر و شکل مودهای سیستم به شرایط مرزی و نرخ گرادیان وابستگی شدید دارند. برای تیرهای مدرج تابعی به ازای هر پارامتر گرادیان، می‌توان یک فرکانس بحرانی یافت، به نحوی که منجر به پرش در طیف فرکانسی سیستم شود و در فرکانس‌های کمتر از حد بحرانی یا شبه فرکانس، امواج محوشونده رخ خواهند داد که این یک تفاوت بارز برای تیرهای همگن و ناهمگن است. نتایج پژوهش حاضر می‌توانند برای مهندسین و طراحان سازه‌های غیریکنواخت نیز مفید باشند.

کلیدواژه‌ها

موضوعات


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