TAILIEUCHUNG - Free vibration of prestress timoshenko beams resting on elastic foundation

This paper presents a finite element formulation for investigating the free vibration of uniform Timoshenko beams resting on a Vinkler-type elastic foundation and prestressing by axial force. | Vietnam Journal of Mechanics, VAST, Vol. 29, No . 1 (2007), pp. 1 - 12 FREE VIBRATION OF PRESTRESS TIMOSHENKO BEAMS RESTING ON ELASTIC FOUNDATION NGUYEN DINH KIEN Institute of Mechanics Vietnamese Academy of Science and Technology Abstract. This paper presents a finite element formulat ion for investigating the free vibration of uniform Timoshenko beams resting on a V.' inkler-type elastic foundation and prestressing by axial force. Taking the effect of prestress, foundation support and shear deformation into account, a stiffness matrix for Timoshenko-type beam element is formulated using the energy method . The element consistent mass matrix is obtained from the kinetic energy using simple li near shape functions . Employing the formulated element, the natural frequencies of the beams having various boundary conditions are det ermined for different values of the axial force and foundation stiffness . The vibration characteristics of the beams pa rtially supported on the foundation arc a lso st udi ed and highlighted. Specially, the effects of shear deformation on the vibration frequenci es of prestress beams fully and partially supported on the elast ic foundation are investigated in det a il. 1. INTRODUCTION Practical problems like railroad tracks, hight way pavements, continuously pipelines . can be modelled by means of beams on elastic foundation. Static analysis of beams on various types of foundation has been extensively carried out by many researcher [L 2]. In the context of dynamic analysis, in [3] Rosa described an analytical approach for investigating the effect of foundation support on the vibration characteristics of T imoshenko beams resting on a Pasternak foundation. Using the so-called Ray leigh-Ritz method, Rao has investigated the large vibration characteristics of simply supported and cantilever Timoshenko beams resting on a two-parameter foundation [4]. By solving the governing equation, Hung [5] derived the stiffness and mass matrices used

• Cơ khí - Chế tạo máy
• Vietnam Journal of Mechanics
• Prestress timoshenko beams resting on elastic foundation
• Vinkler type elastic foundation
• Uniform Timoshenko beams
• The axial force and foundation stiffness
• Dang Dinh Ang
• Nonlinear analysis and mechanics
• Dynamic problems involving stationary cracks
• The Wiener Hopt technique
• Dual integral equations
• Dual integrals in non linear fracture mechanics
• Non linear fracture mechanics
• Energy release rate
• Discuss the obtained
• The alpha finite element method (αFEM)
• Solid mechanics using triangular and tetrahedral elements
• Suitable computational cost
• NS FEM makes
• The upper bound property
• Non linear constitutive problems in solid mechanics
• Non linear constitutive problems
• Languages Gibian and special operators
• The application FEM
• Betts miller janjic convective parameterization scheme
• H14 31 model to forecast heavy rainfall in Vietnam
• Betts Miller Janjic
• Three rain seasons
• Manufacturing dry mixed cement mortar
• High compressive strength
• High flexural strength
• Low shrinkage and high watertightness for restoration
• Damaged hydraulic structures in Vietnam
• Standard gradient models and crack simulation
• Standard gradient models
• The propagation of cracks
• Damage mechanics and crack simulation
• The interaction between two parametric excitations
• The second and third degrees
• The asymptotic method of nonlinear mechanics
• Dynamic system governed
• Comparison of two hydrological model simulations
• Nam and Xinanjiang for Nong Son catchment
• The Central Vietnam
• The runoff components
• 3 D numerical simulation
• The tidal circulation
• The gulf of Tonkin
• The kinetic energy distribution
• Duality in the analysis of responses to nonlinear systems
• The analysis of responses
• The original nonlinear systems
• The study of nonlinear mechanics
• Aerodynamics of a wing in surface effect ship
• Theory and experiment
• Wing in surface effect ship
• The aerodynamic characteristics
• The Institute of Mechanics
• The error estimate
• The convergence rate for h
• p refinement
• The finite element analysis
• Three dimensional elastostatic mechanics problems
• Some initial experimental results
• Free water layer formation in horizontal pipes
• Water layer formation
• Hanoi Institute of Mechanics
• Bending vibration of beam elements under moving loads
• Considering vehicle braking forces
• Fluctuations of structures
• Beam elements according
• Continuous element for vibration analysis
• Thick shells of revolution
• Continous Element Method
• Finite element solutions
• Natural frequencies and harmonic responses
• Cast3m implementation of the extended finite element method
• The extended finite element method for cohesive crack
• Quasi brittle materia
• The proposed implementation
• The displacement discontinuities
• Buckling analysis of simply supported composite laminates subjected
• In plane compression load
• A novel mesh ffree method
• Alternative numerical technique
• Mesh free method
• A three story building
• Hedge algebras based fuzzy controller
• The structural system
• The El Centro earthquake
• Three story building against earthquake
• Laminar separation phenomenon combining with numerical calculations
• The turbulent separation
• The laminar separation
• Experimental study on mechanical properties
• Three phase polymer composite reinforced
• Glass fibers and titanium oxide particles
• Polymer composite reinforced
• Three phase composite
• Dynamic characteristics of elastically supported beam subjected
• A compressive axial force and a moving load
• The implicit Newmark method
• The Galerkin finite element method
• The axial force
• Eccentrically stiffened functionally graded plates and shallow shells
• Von Karman Donnell sense
• The formulation of governing equations
• The classical shell theory
• Mathematical modelling and control of the evolution
• Dynamic systems interacting with medium
• Mathematical modeling evolutional systems interacting
• Two conjugate mechanical subsystems
• Evaluating structural safety based on fuzzy set theory
• Evaluating structural safety
• The fuzzy reliability
• Simple beam structure