Abstract




 
   

IJE TRANSACTIONS A: Basics Vol. 31, No. 4 (April 2018) 538-547    Article in Press

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  FREE VIBRATION OF A GENERALIZED PLANE FRAME
 
M. Rezaiee-Pajand, A. Aftabi Sani and S. M. Hozhabrossadati
 
( Received: October 05, 2017 – Accepted in Revised Form: November 30, 2017 )
 
 

Abstract    This article deals with the free in-plane vibration analysis of a frame with four arbitrary inclined members by differential transform method. Based on four differential equations and sixteen boundary and compatibility conditions, the related structural eigenvalue problem will be analytically formulated. The frequency parameters and mode shapes of the frame will be calculated for various values of the structural properties, such as joint angles, springs' stiffness and flexural rigidity of members. Finally, the obtained solution by the proposed method will be verified by authors' finite element program.

 

Keywords    Differential Transform Method; Free Vibration, Plane Frames, Elastic Supports and Joints

 

چکیده   

این مقاله به واکاوی نوسان آزاد درون صفحه‌ی یک قاب با چهار عضو کج با بهره‌جویی از راه‌کار تبدیل دیفرانسیلی می‌پردازد. بر پایه‌ی چهار معادله‌ی دیفرانسیل و شانزده شرط مرزی و سازگاری، مسأله‌ی مقدار ویژه‌ی وابسته به شکل تحلیلی رابطه‌سازی خواهد شد. عامل‌های بسامدی و شکل‌های حالت (مود) سازه برای مقدارهای گوناگون مشخصه‌های سازه، مانند زاویه‌ی گره‌های پیوند، سختی فنرها و سفتی خمشی عضوها حساب خواهد شد. سرانجام، پاسخ پیشنهادی با جواب برنامه‌ی جزءهای محدود نویسندگان راستی آزمایی خواهد شد.

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