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Structural Engineering and Mechanics
  Volume 75, Number 3, August10 2020, pages 357-367

Transient response of 2D functionally graded beam structure
Mohamed A. Eltaher and Şeref D. Akbaş

    The objective of this article is investigation of dynamic response of thick multilayer functionally graded (FG) beam under generalized dynamic forces. The plane stress problem is exploited to describe the constitutive equation of thick FG beam to get realistic and accurate response. Applied dynamic forces are assumed to be sinusoidal harmonic, sinusoidal pulse or triangle in time domain and point load. Equations of motion of deep FG beam are derived based on the Hamilton principle from kinematic relations and constitutive equations of plane stress problem. The numerical finite element procedure is adopted to discretize the space domain of structure and transform partial differential equations of motion to ordinary differential equations in time domain. Numerical time integration method is used to solve the system of equations in time domain and find the time responses. Numerical parametric studies are performed to illustrate effects of force type, graduation parameter, geometrical and stacking sequence of layers on the time response of deep multilayer FG beams.
Key Words
    forced vibration; transient response; 2D deep beam; multilayered functionally graded; finite element; implicit time integration
Mohamed A. Eltaher: Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia
Mohamed A. Eltaher: Department of Mechanical Design & Production, Faculty of Engineering, Zagazig University,P.O. Box 44519, Zagazig, Egypt
Şeref D. Akbaş: Deparment of Civil Engineering, Bursa Technical University, Bursa, Turkey

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