A finite element formulation for large amplitude flexural vibrations of thin rectangular plates

1976 ◽  
Vol 6 (3) ◽  
pp. 163-167 ◽  
Author(s):  
G. Venkateswara Rao ◽  
I.S. Raju ◽  
K. Kanaka Raju
Keyword(s):  
Finite Element ◽  
Large Amplitude ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Rectangular Plates ◽  
Flexural Vibrations

Nonlinear Finite Element Formulation for the Large Displacement Analysis of Plates

1990 ◽  
Vol 57 (3) ◽  
pp. 707-718 ◽  
Author(s):  
Bilin Chang ◽  
A. A. Shabana
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Coordinate System ◽  
Deformable Body ◽  
Finite Element Formulation ◽  
Deformation Analysis ◽  
Element Formulation ◽  
Rectangular Plates ◽  
Shape Functions ◽  
Intermediate Element

In this investigation a nonlinear total Lagrangian finite element formulation is developed for the dynamic analysis of plates that undergo large rigid body displacements. In this formulation shape functions are required to include rigid body modes that describe only large translational displacements. This does not represent any limitation on the technique presented in this study, since most of commonly used shape functions satisfy this requirement. For each finite plate element an intermediate element coordinate system, whose axes are initially parallel to the axes of the element coordinate system, is introduced. This intermediate element coordinate system, which has an origin which is rigidly attached to the origin of the deformable body, is used for the convenience of describing the configuration of the element with respect to the deformable body coordinate system in the undeformed state. The nonlinear dynamic equations developed in this investigation for the large rigid body displacement and small elastic deformation analysis of the rectangular plates are expressed in terms of a unique set of time invariant element matrices that depend on the assumed displacement field. The invariants of motion of the deformable body discretized using the plate elements are obtained by assembling the invariants of its elements using a standard finite element procedure.

scholarly journals Finite Element Formulation for the Large-Amplitude Vibrations of FG Beams

2014 ◽  
Vol 61 (3) ◽  
pp. 469-482 ◽  
Author(s):  
Mehdi Javid ◽  
Milad Hemmatnezhad
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Power Law ◽  
Large Amplitude ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Geometrical Parameters ◽  
Element Formulation ◽  
Vibration Frequencies

Abstract On the basis of Euler-Bernoulli beam theory, the large-amplitude free vibration analysis of functionally graded beams is investigated by means of a finite element formulation. The von Karman type nonlinear strain-displacement relationship is employed where the ends of the beam are constrained to move axially. The material properties are assumed to be graded in the thickness direction according to the power-law and sigmoid distributions. The finite element method is employed to discretize the nonlinear governing equations, which are then solved by the direct numerical integration technique in order to obtain the nonlinear vibration frequencies of functionally graded beams with different boundary conditions. The influences of power-law index, vibration amplitude, beam geometrical parameters and end supports on the free vibration frequencies are studied. The present numerical results compare very well with the results available from the literature where possible.

Relatively simple finite element formulation for the large amplitude free vibrations of uniform beams

2009 ◽  
Vol 45 (10) ◽  
pp. 624-631 ◽  
Author(s):  
R.K. Gupta ◽  
Gunda Jagadish Babu ◽  
G. Ranga Janardhan ◽  
G. Venkateswara Rao
Keyword(s):  
Finite Element ◽  
Large Amplitude ◽  
Free Vibrations ◽  
Finite Element Formulation ◽  
Element Formulation
Sign in / Sign up

Export Citation Format

Share Document