TAILIEUCHUNG - Free vibration of two directional fgm beams using a higher order timoshenko beam element

Độ rung tự do của dầm vật liệu có chức năng hai chiều (2-D FGM) là nghiên cứu bằng phương pháp phần tử hữu hạn (FEM). Các thuộc tính vật liệu được giả định là được xếp loại cả chiều dày và hướng dọc theo phân bố pháp luật quyền lực. Phương trình chuyển động dựa trên lý thuyết chùm Timoshenko có nguồn gốc từ nguyên lý Hamilton. Một chùm tia bậc cao phần tử bằng cách sử dụng các hàm phân cấp để nội suy các chuyển vị và phép quay được xây dựng và được sử dụng trong phân tích. Để nâng cao hiệu quả của nguyên tố, biến dạng cắt bị ràng buộc thành hằng số. | Vietnam Journal of Science and Technology 56 (3) (2018) 380-396 DOI: FREE VIBRATION OF TWO-DIRECTIONAL FGM BEAMS USING A HIGHER-ORDER TIMOSHENKO BEAM ELEMENT Tran Thi Thom1, 2, *, Nguyen Dinh Kien1, 2 1 2 Institute of Mechanics, VAST, 18 Hoang Quoc Viet, Ha Noi Graduate University of Science and Technology, VAST, 18 Hoang Quoc Viet, Ha Noi * Email: thomtt0101@ Received: 25 September 2017; Accepted for publication: 26 March 2018 Abstract. Free vibration of two-directional functionally graded material (2-D FGM) beams is studied by the finite element method (FEM). The material properties are assumed to be graded in both the thickness and longitudinal directions by a power-law distribution. Equations of motion based on Timoshenko beam theory are derived from Hamilton's principle. A higher-order beam element using hierarchical functions to interpolate the displacements and rotation is formulated and employed in the analysis. In order to improve the efficiency of the element, the shear strain is constrained to constant. Validation of the derived element is confirmed by comparing the natural frequencies obtained in the present paper with the data available in the literature. Numerical investigations show that the proposed beam element is efficient, and it is capable to give accurate frequencies by a small number of elements. The effects of the material composition and aspect ratio on the vibration characteristics of the beams are examined in detail and highlighted. Keywords. 2-D FGM, Timoshenko beam, hierarchical functions, free vibration, FEM. Classification numbers: ; ; . 1. INTRODUCTION Functionally graded materials (FGMs), initiated in Japan in 1984 during a space project [1], are increasingly used as structural elements in modern industries such as aerospace structures, turbine blades and rocket engine components. Many researches on vibration behavior of FGM beam structures have been reported in the .

• Vật lý
• The free vibration
• The finite element method
• Timoshenko beam theory
• The natural frequencies obtained
• Two directional functionally graded material
• Free vibration analysis
• Free and constrained model
• Delaminated composite beam
• Vibration of the delaminated beam
• Breathing of delamination
• A novel meshfree approach
• Free vibration and buckling analysi
• Thin laminated composite plates
• User defined parameters
• Free vibration and buckling analysis
• Cartesian Transformation Method
• Vietnam Journal of Mechanics
• Fuzzy finite element algorithm
• Response surface method for free vibration analysis of structure
• Free vibration analysis of structure
• Fuzzy mode shapes
• Fuzzy natural frequencies
• Free vibration analysis of four parameter
• Functionally graded plates accounting transverse shear mode
• Functionally graded material
• Four parameter law
• higher order shear deformation theory
• Free vibration analysis of multi directional functionally graded plates
• Multi directional functionally graded plates
• 3D isogeometric analysis
• The free vibration behavior
• Three dimensional elasticity theory
• Nonlocal theory
• Isogeometric analysis
• Porous nanoplates using Nurbs formulations
• Free vibration analysis of porous nanoplates
• Free vibration of sandwich composite plates
• Dynamic response of sandwich composite plates
• Auxetic honeycomb core
• Free vibration
• Honeycomb core
• Mathematics – Physics
• Gradient auxetic plate
• Finite element method
• Gradient auxetic
• Free vibration and bending
• Free vibration of a cracked double beam carrying a concentrated mass
• Cracked double beam carrying a concentrated mass
• The double beam
• Free vibration of a 2D FGSW beam based
• Shear deformation theory
• Vibration modes of the beam
• Skin layers of 2D FGM
• Power gradation laws
• Free vibration of bidirectional functionally
• Buckling of bidirectional functionally graded sandwich plates
• Efficient Q9 element
• Linked interpolation
• Vibration and buckling analysis
• Mechanical sciences
• Scaled piping system
• Vibration attenuation via locally
• Resonant bandgap formation
• Finite element model updating
• Free and forced vibration testing
• Journal of Science and Technology
• Bending and free vibration analysis
• Functionally graded plates
• New eightunknown shear deformation theory
• Determination of mode shapes
• Multiple cracked beam element
• Application for free vibration analysis
• Multi span continuous beam
• Numerical analysis of free vibration
• Cross ply thick laminated composite cylindrical shells
• Continuous element method
• The dynamic transfer matrix
• The node based smoothed finite element method
• Free vibration problems
• The proposed formulation
• No spurious non zero energy modes
• New finite element for free vibration analysis
• Stiffened composite plates
• Arbitrarily oriented stifeners
• Mesh lines along the stiffeners
• Triangular cut out
• Laminated composite plate
• Eight nodded element
• Parametric design language code
• Static and free vibration of the sandwich folded plate
• The sandwich folded plate using the Layerwise theory
• The sandwich folded plate modeled by layer wise
• Discrete shear gap method
• The first order shear deformation theory
• Composite laminated plates
• Bending problems
• Composite plates using the C0 HSDT
• In plane rotations
• Rectangle plate
• Varying thickness
• Phase field theory
• Free vibration of rectangular plates
• Third order shear deformation theory
• Bending analysis
• Sandwich plate
• Auxetic material
• Modified couple stress theory
• Refined third order beam theory
• Nonlinear elastic foundation
• Nonlinear free vibration
• Hamilton’s principle
• Cross ply composite joined conical conical conical shells
• Dynamics stiffness matrix