Large Amplitude Free Flexural Vibration of Stiffened Plates Using Superparametric Element

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Saleema Panda ◽  
Manoranjan Barik
Keyword(s):  
Displacement Field ◽  
Large Amplitude ◽  
Shape Function ◽  
Flexural Vibration ◽  
Stiffened Plates ◽  
Plate Bending ◽  
Arbitrary Geometry ◽  
Numerical Examples

The present paper studies the nonlinear free flexural vibration of stiffened plates. The analysis is performed using a superparametric element. This element consists of an ACM plate-bending element along with in-plane displacements to represent the displacement field, and cubic serendipity shape function is used to define the geometry. The element can accommodate any arbitrary geometry, and the stiffeners either straight or curvilinear are modeled such that these can be placed anywhere on the plate. A number of numerical examples are presented to show its efficacy.

Finite strip analysis of continuous structures

1988 ◽  
Vol 15 (3) ◽  
pp. 424-429 ◽  
Author(s):  
M. S. Cheung ◽  
Wenchang Li
Keyword(s):  
Finite Element ◽  
Transverse Direction ◽  
Shape Function ◽  
Longitudinal Direction ◽  
Plate Bending ◽  
Continuous Beam ◽  
Numerical Examples ◽  
Finite Strip ◽  
Element Shape ◽  
Plate Type

The eigenfunctions of a continuous beam are found numerically. The folded plate type of finite strip with intermediate supports is formulated by combining such an eigenfunction in the longitudinal direction with an appropriate finite element shape function in the transverse direction. The numerical examples given in this paper, such as the continuous beam and plate, demonstrate the advantages of this method: simplicity, accuracy, and convenience. Key words: finite strip, continuous structure, eigenfunction, folded plate, plate bending.

Large amplitude free flexural vibration of stiffened plates

AIAA Journal ◽  
1996 ◽  
Vol 34 (11) ◽  
pp. 2377-2383 ◽  
Author(s):  
Abdul Hamid Sheikh ◽  
Madhujit Mukhopadhyay
Keyword(s):  
Large Amplitude ◽  
Flexural Vibration ◽  
Stiffened Plates

scholarly journals A New Discrete Plate Bending Model by Using a Lower Order Shape Function

1978 ◽  
Vol 1978 (143) ◽  
pp. 243-249 ◽  
Author(s):  
Kazuo Kondou ◽  
Shyoji Shiina ◽  
Tadahiko Kawai
Keyword(s):  
Lower Order ◽  
Shape Function ◽  
Plate Bending

Large Amplitude Forced Vibration Analysis of Stiffened Plates under Harmonic Excitation

2012 ◽  
pp. 26-61
Author(s):  
Anirban Mitra ◽  
Prasanta Sahoo ◽  
Kashinath Saha
Keyword(s):  
Free Vibration ◽  
Forced Vibration ◽  
Large Amplitude ◽  
Vibration Analysis ◽  
Mathematical Formulation ◽  
Free Vibration Analysis ◽  
Harmonic Excitation ◽  
Stiffened Plates ◽  
Backbone Curve ◽  
Forced Vibration Analysis

Large amplitude forced vibration behaviour of stiffened plates under harmonic excitation is studied numerically incorporating the effect of geometric non-linearity. The forced vibration analysis is carried out in an indirect way in which the dynamic system is assumed to satisfy the force equilibrium condition at peak excitation amplitude. Large amplitude free vibration analysis of the same system is carried out separately to determine the backbone curves. The mathematical formulation is based on energy principles and the set of governing equations for both forced and free vibration problems derived using Hamilton’s principle. Appropriate sets of coordinate functions are formed by following the two dimensional Gram-Schmidt orthogonalization procedure to satisfy the corresponding boundary conditions of the plate. The problem is solved by employing an iterative direct substitution method with an appropriate relaxation technique and when the system becomes computationally stiff, Broyden’s method is used. The results are furnished as frequency response curves along with the backbone curve in the dimensionless amplitude-frequency plane. Three dimensional operational deflection shape (ODS) plots and contour plots are provided in a few cases.

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