Fonksiyonel Derecelendirilmiş Kirişlerin Serbest Titreşim Analizi

Yıl 2018, Cilt: 8 Sayı: 2, 119 - 130, 31.12.2018

Muhittin Turan , Volkan Kahya

https://doi.org/10.31466/kfbd.453833

Cited By: 7

Öz

Bu çalışmada, birinci mertebe kayma deformasyonu teorisine dayalı olarak fonksiyonel derecelendirilmiş kirişlerin serbest titreşim analizi Navier tipi çözüm yöntemi kullanılarak yapılmıştır. Hareket denklemleri Lagrange eşitlikleri ile türetilmiş, problemin çözümünde ise trigonometrik fonksiyonlar kullanılmıştır. Farklı sınır şartlarına, hacimsel oran fonksiyonunun farklı k değerlerine ve kirişin açıklığının yüksekliğine oranına bağlı olarak doğal frekanslar sayısal olarak hesaplanmıştır. Sayısal sonuçlar literatürle kıyaslanmış ve oldukça uyumlu oldukları görülmüştür.

Anahtar Kelimeler

Fonksiyonel derecelendirilmiş malzeme, Navier metodu, Birinci mertebe kayma deformasyonu teorisi

Free Vibration Analysis of Functionally Graded Beams

Öz

In this study, the free vibration analysis of functionally graded (FG) beams is performed Navier type solution method according to the first-order shear deformation beam theory. The governing equations are derived from the Lagrange’s equations, and they are solved by using trigonometric series. Natural frequencies are calculated numerically for different boundary conditions, power-law indices and span-to-height ratios. Comparisons show in good agreement with the literature.

Anahtar Kelimeler

Functionally graded material, Navier method, Free vibration, First-order shear deformation theory

Kaynakça

• Aydogdu, M. ve Taskin, V., (2007). Free Vibration Analysis of Functionally Graded Beams with Simply Supported Edges, Materials & Design, 28,5, 1651-1656.
• Chen, W. R. ve Chang, H., (2017). Closed-Form Solutions for Free Vibration Frequencies of Functionally Graded Euler-Bernoulli Beams, Mechanics of Composite Materials, 53,1, 79-98.
• Hadji, L., Khelifa, Z. ve El Abbes, A. B., (2015). A New Higher Order Shear Deformation Model for Functionally Graded Beams, KSCE Journal of Civil Engineering, 20,5, 1835-1841.
• Kahya, V. ve Turan, M., (2017). Finite Element Model for Vibration and Buckling of Functionally Graded Beams Based on the First-Order Shear Deformation Theory, Composites Part B: Engineering, 109, 108-115.
• Kahya, V. ve Turan, M., (2018). Vibration and Stability Analysis of Functionally Graded Sandwich Beams by a Multi-Layer Finite Element, Composites Part B: Engineering, 146, 198-212.
• Lee, J. W. ve Lee, J. Y., 2017. Free Vibration Analysis of Functionally Graded Bernoulli-Euler Beams Using an Exact Transfer Matrix Expression, International Journal of Mechanical Sciences, 122, 1-17.
• Li, X. F., (2008). A Unified Approach for Analyzing Static and Dynamic Behaviors of Functionally Graded Timoshenko and Euler–Bernoulli Beams, Journal of Sound and Vibration, 318,4-5, 1210-1229.
• Nguyen, T.-K., Vo, T. P. ve Thai, H.-T., (2013). Static and Free Vibration of Axially Loaded Functionally Graded Beams Based on the First-Order Shear Deformation Theory, Composites Part B: Engineering, 55, 147-157.
• Nguyen, T.-K., Truong-Phong Nguyen, T., Vo, T. P. ve Thai, H.-T., (2015). Vibration and Buckling Analysis of Functionally Graded Sandwich Beams by a New Higher-Order Shear Deformation Theory, Composites Part B: Engineering, 76, 273-285.
• Şimşek, M., (2010a). Fundamental Frequency Analysis of Functionally Graded Beams by Using Different Higher-Order Beam Theories, Nuclear Engineering and Design, 240,4, 697-705.
• Şimşek, M., (2010b). Vibration Analysis of a Functionally Graded Beam under a Moving Mass by Using Different Beam Theories, Composite Structures, 92,4, 904-917.
• Sina, S. A., Navazi, H. M. ve Haddadpour, H., (2009). An Analytical Method for Free Vibration Analysis of Functionally Graded Beams, Materials & Design, 30,3, 741-747.
• Thai, H.-T. ve Vo, T. P., (2012). Bending and Free Vibration of Functionally Graded Beams Using Various Higher-Order Shear Deformation Beam Theories, International Journal of Mechanical Sciences, 62,1, 57-66.
• Vo, T. P., Thai, H.-T., Nguyen, T.-K., Maheri, A. ve Lee, J., (2014). Finite Element Model for Vibration and Buckling of Functionally Graded Sandwich Beams Based on a Refined Shear Deformation Theory, Engineering Structures, 64, 12-22.