NONLINEAR FREE VIBRATION OF A MODERATELY THICK DOUBLY CURVED SHALLOW SHELL OF ELLIPTICAL PLAN-FORM

2009 ◽  
Vol 06 (04) ◽  
pp. 615-632 ◽  
Author(s):  
S. M. CHORFI ◽  
A. HOUMAT
Keyword(s):  
Free Vibration ◽  
Harmonic Balance ◽  
Shallow Shell ◽  
Geometrical Nonlinearity ◽  
Harmonic Balance Method ◽  
The Finite Element Method ◽  
Nonlinear Free Vibration ◽  
Mode Method ◽  
Convergence Study ◽  
Doubly Curved

The p-version of the finite element method is used in conjunction with the blending function method to investigate the nonlinear free vibration of a doubly curved shallow shell of elliptical plan-form. The effects of transverse shear deformations, rotary inertia, and geometrical nonlinearity are taken into account. The harmonic balance method is used to derive the equations of free motion. The resultant nonlinear equations are solved iteratively using the linearized updated mode method. The efficiency of the method is demonstrated through convergence study and comparison with published results. The effects of geometric parameters such as thickness, ellipse aspects, and curvatures on the backbone curves of a clamped doubly curved shallow shell of elliptical plan-form are studied. It is shown that the increase or decrease of the hardening behavior is dependent upon these parameters.

Dynamic Response and Stability Analysis with Newton Harmonic Balance Method for Nonlinear Oscillating Dielectric Elastomer Balloons

2018 ◽  
Vol 18 (12) ◽  
pp. 1850152 ◽  
Author(s):  
Dafeng Tang ◽  
C. W. Lim ◽  
Ling Hong ◽  
Jun Jiang ◽  
S. K. Lai
Keyword(s):  
Stability Analysis ◽  
Free Vibration ◽  
Harmonic Balance ◽  
Dynamical Behavior ◽  
Harmonic Balance Method ◽  
Stretch Ratio ◽  
Dielectric Elastomer ◽  
Nonlinear Free Vibration ◽  
Free Vibration Frequency ◽  
Dielectric Elastomer Membrane

Subject to various pressure and voltage values, the deformation of a hyperelastic dielectric elastomer membrane may attain different stable and unstable equilibria. In this paper, the neo-Hookean material model is adopted to describe the hyperelastic behavior of a dielectric elastomer membrane. The effects of initial stretch ratio, pressure and voltage on the nonlinear free vibration of a spherical dielectric elastomer balloon are investigated qualitatively and quantitatively. Through a linear stability analysis of the equilibrium states, the safe regime of initial stretch ratio for the deformation of dielectric elastomer balloon is confined. Under specific static driving pressure and voltage, the system oscillates about the stable equilibrium and there is no oscillation in the neighborhood of the unstable equilibrium. Besides, the critical pressure and voltage values are determined. Beyond the critical values, there is no periodic oscillation. Along with the stability analysis, complex dynamical behavior such as drastic change of output regime, sporadic instability and sudden bifurcations can be predicted. By applying the Newton Harmonic Balance (NHB) method for quantitative analysis, the frequency response can be readily predicted. It is found that the nonlinear free vibration frequency decreases with increasing initial stretch ratio and control parameters (pressure and voltage).

scholarly journals Free Vibration Analysis of Laminated Functionally Graded Carbon Nanotube-Reinforced Composite Doubly Curved Shallow Shell Panels Using a New Four-Variable Refined Theory

2019 ◽  
Vol 3 (4) ◽  
pp. 104 ◽  
Author(s):  
Vu Van Tham ◽  
Tran Huu Quoc ◽  
Tran Minh Tu
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Shallow Shell ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Refined Theory ◽  
Reinforced Composite ◽  
Doubly Curved

In this paper, a new four-variable refined shell theory is developed for free vibration analysis of multi-layered functionally graded carbon nanotube-reinforced composite (FG-CNTRC) doubly curved shallow shell panels. The theory has only four unknowns and satisfies zero stress conditions at the free surfaces without correction factor. Five different types of carbon nanotube (CNTs) distribution through the thickness of each FG-CNT layer are considered. Governing equations of simply supported doubly curved FG-CNTRC panels are derived from Hamilton’s principle. The resultant eigenvalue system is solved to obtain the frequencies and mode shapes of the anti-symmetric cross-ply laminated panels by using the Navier solution. The numerical results in the comparison examples have proved the accuracy and efficiency of the developed model. Detailed parametric studies have been carried out to reveal the influences of CNTs volume fraction, CNTs distribution, CNTs orientation, dimension ratios and curvature on the free vibration responses of the doubly curved laminated FG-CNTRC panels.

Sign in / Sign up

Export Citation Format

Share Document