scholarly journals Free vibration analysis of coupled sloshing-flexible membrane system in a liquid container

2018 ◽  
Vol 25 (1) ◽  
pp. 84-97 ◽  
Author(s):  
Amir Kolaei ◽  
Subhash Rakheja
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Free Vibration ◽  
Finite Element Model ◽  
Liquid Membrane ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Computational Time ◽  
Flexible Membrane ◽  
Liquid Free Surface

A finite element model is developed to study free vibration of a liquid in a tank of arbitrary geometry with a flexible membrane constraining the liquid free-surface. A variational formulation is initially developed using the Galerkin method, assuming inviscid, incompressible and irrotational flow. The resulting generalized eigenvalue problem is then reduced by considering only the elements on the liquid free-surface, which significantly reduces the computational time. The proposed physical model is subsequently implemented into the FEniCS framework to obtain coupled hydroelastic liquid-membrane frequencies and modes. The coupled frequencies are compared with those reported for rectangular and upright cylindrical tanks using analytical methods in order to illustrate the validity of the finite element model. The results are subsequently presented for a horizontal cylindrical tank with an elastic free-surface membrane for different fill ratios and tank lengths. The effects of the membrane tension on the free vibration of the liquid in the tank are further investigated by comparing the coupled liquid-membrane frequencies with slosh frequencies of the liquid alone. It is shown that sloshing frequencies can be effectively shifted to higher values to prevent resonance in partially filled moving containers.

scholarly journals On the Finite Element Model of Rotating Functionally Graded Graphene Beams Resting on Elastic Foundation

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Nguyen Van Dung ◽  
Nguyen Chi Tho ◽  
Nguyen Manh Ha ◽  
Vu Trong Hieu
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Elastic Foundation ◽  
Mechanical Response ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Engineering Practice

Rotating structures can be easily encountered in engineering practice such as turbines, helicopter propellers, railroad tracks in turning positions, and so on. In such cases, it can be seen as a moving beam that rotates around a fixed axis. These structures commonly operate in hot weather; as a result, the arising temperature significantly changes their mechanical response, so studying the mechanical behavior of these structures in a temperature environment has great implications for design and use in practice. This work is the first exploration using the new shear deformation theory-type hyperbolic sine functions to carry out the free vibration analysis of the rotating functionally graded graphene beam resting on the elastic foundation taking into account the effects of both temperature and the initial geometrical imperfection. Equations for determining the fundamental frequencies as well as the vibration mode shapes of the beam are established, as mentioned, by the finite element method. The beam material is reinforced with graphene platelets (GPLs) with three types of GPL distribution ratios. The numerical results show numerous new points that have not been published before, especially the influence of the rotational speed, temperature, and material distribution on the free vibration response of the structure.

A dissipative finite element model for free surface flow

1988 ◽  
Vol 104 (1-4) ◽  
pp. 289-299 ◽  
Author(s):  
Litsa Anastasiadou-Partheniou ◽  
George A. Terzidis
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Finite Element Model ◽  
Free Surface Flow ◽  
Element Model ◽  
Surface Flow

Methods for Reducing a Thermal Finite Element Model Including the Advection Network Contribution

2006 ◽  
Author(s):  
Daniele Botto ◽  
Stefano Zucca ◽  
Muzio M. Gola
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Real Time ◽  
Residual Life ◽  
Mathematical Formulation ◽  
Time Integration ◽  
Element Model ◽  
Computational Time ◽  
Fatigue Damage Accumulation ◽  
Secondary Air

The life monitoring concept needs on-line calculation to evaluate stresses and temperatures on aircraft engine components, in order to asses fatigue damage accumulation and residual life. Due to the amount of computational time required it is not possible for a full finite element model to operate in real time using the on-board CPU. Stresses and temperatures are then evaluated by using simplified algorithms. In the present work Guyan reduction and component mode synthesis have been applied to a thermal finite element model, including the cooling stream flow — the so called advection network — in order to reduce the size of the solving equation system. The appropriate mathematical formulation for the advection network reduction has been developed. Two reduction methods have been performed, discussed and subsequently applied to a thermal finite element model of a real low pressure turbine disk. The reduced system includes both the disk and the correlated fluid network model, simulating turbine secondary air system. The finite element model is axi-symmetric, with constant convective coefficients. Results of time integration for the reduced and the complete models have been compared. Results show that the proposed techniques gives models with a reduced number of degrees of freedom and at the same time good accuracy in temperature calculation. The reduced models are then suitable for real time computation.

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