Nonlinear Axisymmetric Free Vibration Analysis of Liquid-Filled Spherical Shell With Volume Constraint

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
W. Jiammeepreecha ◽  
S. Chucheepsakul
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Internal Pressure ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Axisymmetric Vibration ◽  
Volume Constraint ◽  
Constraint Condition ◽  
Spherical Shells

Nonlinear axisymmetric free vibration analysis of liquid-filled spherical shells with volume constraint condition using membrane theory is presented in this paper. The energy functional of the shell and contained liquid can be expressed based on the principle of virtual work using surface fundamental form and is written in the appropriate forms. Natural frequencies and the corresponding mode shapes for specified axisymmetric vibration amplitude of liquid-filled spherical shells can be calculated by finite element method (FEM). A nonlinear numerical solution can be obtained by the modified direct iteration technique. The results indicate that the Lagrange multiplier is a parameter for adapting the internal pressure in order to sustain the shell in equilibrium state for each mode of vibration with the volume constraint condition. The axisymmetric mode shapes of the liquid-filled spherical shells under volume constraint condition were found to be in close agreement with those in existing literature for an empty spherical shell. Finally, the effects of support condition, thickness, initial internal pressure, bulk modulus of internal liquid, and elastic modulus on the nonlinear axisymmetric free vibration and change of pressure of the liquid-filled spherical shells with volume constraint condition were demonstrated. The parametric studies showed that the change of pressure has a major impact on the fundamental vibration mode when compared with the higher vibration modes.

Free Vibration Analysis of an Inflated Toroidal Shell

2002 ◽  
Vol 124 (3) ◽  
pp. 387-396 ◽  
Author(s):  
Akhilesh K. Jha ◽  
Daniel J. Inman ◽  
Raymond H. Plaut
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Circular Cross Section ◽  
Free Vibration Analysis ◽  
Longitudinal Direction ◽  
Variable Coefficients ◽  
Mode Shapes ◽  
Toroidal Shell

Free vibration analysis of a free inflated torus of circular cross-section is presented. The shell theory of Sanders, including the effect of pressure, is used in formulating the governing equations. These partial differential equations are reduced to ordinary differential equations with variable coefficients using complete waves in the form of trigonometric functions in the longitudinal direction. The assumed mode shapes are divided into symmetric and antisymmetric groups, each given by a Fourier series in the meridional coordinate. The solutions (natural frequencies and mode shapes) are obtained using Galerkin’s method and verified with published results. The natural frequencies are also obtained for a circular cylinder with shear diaphragm boundary condition as a special case of the toroidal shell. Finally, the effects of aspect ratio, pressure, and thickness on the natural frequencies of the inflated torus are studied.

Free vibration analysis of a rectangular plate carrying multiple various concentrated elements

2003 ◽  
Vol 217 (2) ◽  
pp. 171-183 ◽  
Author(s):  
J-S Wu ◽  
H-M Chou ◽  
D-W Chen
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Normal Mode ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Equation Of Motion ◽  
Mode Shapes

The dynamic characteristic of a uniform rectangular plate with four boundary conditions and carrying three kinds of multiple concentrated element (rigidly attached point masses, linear springs and elastically mounted point masses) was investigated. Firstly, the closed-form solutions for the natural frequencies and the corresponding normal mode shapes of a rectangular ‘bare’ (or ‘unconstrained’) plate (without any attachments) with the specified boundary conditions were determined analytically. Next, by using these natural frequencies and normal mode shapes incorporated with the expansion theory, the equation of motion of the ‘constrained’ plate (carrying the three kinds of multiple concentrated element) were derived. Finally, numerical methods were used to solve this equation of motion to give the natural frequencies and mode shapes of the ‘constrained’ plate. To confirm the reliability of previous free vibration analysis results, a finite element analysis was also conducted. It was found that the results obtained from the above-mentioned two approaches were in good agreement. Compared with the conventional finite element method (FEM), the approach employed in this paper has the advantages of saving computing time and achieving better accuracy, as can be seen from the existing literature.

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.

Free Vibration Analysis of Hybrid And Non-Hybrid GFRP Composite Wind Turbine Blade

2021 ◽  
pp. 11560-11567
Author(s):  
Sravanthi K., V. Mahesh, B. Nageswara Rao
Keyword(s):  
Free Vibration ◽  
Wind Turbine ◽  
Vibration Analysis ◽  
Energy Demand ◽  
Turbine Blades ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Analysis And Design ◽  
Gfrp Composite ◽  
Study Results

Wind energy is one prominent solution to mitigate the increasing energy demand. Composite materials are exhibiting enormous advantages with their tailor-made properties. With the development of renewable energy power generation, the issue of blade vibration reduction has gotten a lot of technical attention. It has become an essential technique for blade analysis and design. Various attempts were recorded to reduce the vibration of the blade and enhance its natural frequencies. The present work aimed to characterize the mechanical properties of the GFRP composite material and the GFRP composite with 4wt% of the MWCNT filler. Both hybrid and non-hybrid GFRP are subjected to characterization, with the same free vibration analysis of NACA 63-415 wind turbine blades being analyzed. The study results revealed that the hybrid GFRP has more stiffness, which causes it to enhance the free vibrations in all mode shapes.

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