scholarly journals Building Spectral Element Dynamic Matrices Using Finite Element Models of Waveguide Slices and Elastodynamic Equations

2013 ◽  
Vol 20 (3) ◽  
pp. 439-458 ◽  
Author(s):  
P.B. Silva ◽  
A.L. Goldstein ◽  
J.R.F. Arruda
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Transfer Matrix ◽  
Cross Section ◽  
Element Model ◽  
Spectral Element ◽  
Forced Response ◽  
Spectral Elements ◽  
Element Formulation ◽  
Element Mesh

Structural spectral elements are formulated using the analytical solution of the applicable elastodynamic equations and, therefore, mesh refinement is not needed to analyze high frequency behavior provided the elastodynamic equations used remain valid. However, for modeling complex structures, standard spectral elements require long and cumbersome analytical formulation. In this work, a method to build spectral finite elements from a finite element model of a slice of a structural waveguide (a structure with one dimension much larger than the other two) is proposed. First, the transfer matrix of the structural waveguide is obtained from the finite element model of a thin slice. Then, the wavenumbers and wave propagation modes are obtained from the transfer matrix and used to build the spectral element matrix. These spectral elements can be used to model homogeneous waveguides with constant cross section over long spans without the need of refining the finite element mesh along the waveguide. As an illustrating example, spectral elements are derived for straight uniform rods and beams and used to calculate the forced response in the longitudinal and transverse directions. Results obtained with the spectral element formulation are shown to agree well with results obtained with a finite element model of the whole beam. The proposed approach can be used to generate spectral elements of waveguides of arbitrary cross section and, potentially, of arbitrary order.

Support-Condition Analyses of Rotating Beams Under Distributed Imbalance Loading

2011 ◽  
Author(s):  
Kai Jokinen ◽  
Erno Keskinen ◽  
Marko Jorkama ◽  
Wolfgang Seemann
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Cross Section ◽  
Cross Sections ◽  
Natural Frequencies ◽  
Element Model ◽  
Mode Shapes ◽  
Constant Cross Section ◽  
Support Condition ◽  
Beam Elements

In roll balancing the behaviour of the roll can be studied either experimentally with trial weights or, if the roll dimensions are known, analytically by forming a model of the roll to solve response to imbalance. Essential focus in roll balancing is to find the correct amount and placing for the balancing mass or masses. If this selection is done analytically the roll model used in calculations has significant effect to the balancing result. In this paper three different analytic methods are compared. In first method the mode shapes of the roll are defined piece wisely. The roll is divided in to five parts having different cross sections, two shafts, two roll ends and a shell tube of the roll. Two boundary conditions are found for both supports of the roll and four combining equations are written to the interfaces of different roll parts. Totally 20 equations are established to solve the natural frequencies and to form the mode shapes of the non-uniform roll. In second model the flexibility of shafts and the stiffness of the roll ends are added to the support stiffness as serial springs and the roll is modelled as a one flexibly supported beam having constant cross section. Finally the responses to imbalance of previous models are compared to finite element model using beam elements. Benefits and limitations of each three model are then discussed.

scholarly journals A Study on Fluid Self-Excited Flutter and Forced Response of Turbomachinery Rotor Blade

2014 ◽  
Vol 2014 ◽  
pp. 1-20 ◽  
Author(s):  
Chih-Neng Hsu
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Power Plants ◽  
Single Mode ◽  
Element Model ◽  
Forced Response ◽  
Structural Dynamic ◽  
Turbine Engine ◽  
Forcing Function ◽  
Structural Dynamic Characteristics

Complex mode and single mode approach analyses are individually developed to predict blade flutter and forced response. These analyses provide a system approach for predicting potential aeroelastic problems of blades. The flow field properties of a blade are analyzed as aero input and combined with a finite element model to calculate the unsteady aero damping of the blade surface. Forcing function generators, including inlet and distortions, are provided to calculate the forced response of turbomachinery blading. The structural dynamic characteristics are obtained based on the blade mode shape obtained by using the finite element model. These approaches can provide turbine engine manufacturers, cogenerators, gas turbine generators, microturbine generators, and engine manufacturers with an analysis system to remedy existing flutter and forced response methods. The findings of this study can be widely applied to fans, compressors, energy turbine power plants, electricity, and cost saving analyses.

Shock-Resistance Research of Ship Structural Subjected to Underwater Explosion

2014 ◽  
Vol 945-949 ◽  
pp. 1180-1184
Author(s):  
Yao Guo Xie
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Cross Section ◽  
Critical Radius ◽  
Underwater Explosion ◽  
Element Model ◽  
Current Standard ◽  
Envelope Analysis ◽  
Shock Resistance ◽  
Selection Of

A finite element model ships, for example design test condition of the underwater explosion, selection of explosive package quantity is 1000KG TNT, the explosive location along the direction of the ship with the bow, midship and stern, the angle of attack in three exploded cross section have 90 degrees, 60 degrees, 45 degrees, 30 degrees and 0 degrees. According to the current standard to calculate the ship damage radius, critical radius and safety radius of specific values under the effect of underwater explosion, interpolation calculation and draw the envelope. Analysis shows that the vitality of ships and shock-resistance is not only related to the explosive distance, also related to the attack position.

Multi-Objective Structural Optimization of Vehicle Wheels

2021 ◽  
Author(s):  
P. Stabile ◽  
F. Ballo ◽  
M. Gobbi ◽  
G. Previati
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Cross Section ◽  
Element Model ◽  
Computational Effort ◽  
Optimized Design ◽  
Support Design ◽  
Design Constraints ◽  
Multi Objective ◽  
Simplified Finite Element Model

Abstract This work focuses on the development of an innovative design methodology for lightweight wheels of road vehicles. In particular, the activity is carried out for the specific case of a wheel designed for an ultra-efficient vehicle for Shell Eco-marathon competition, with the aim of finding preliminary design solutions. A simplified finite element model of the tire structure is employed for an accurate modelling of the forces acting at the tire/rim interface. The material properties of the tire structure are identified by means of experimental tests. The computed tire/rim force distribution is applied to the rim exploiting a simplified finite element model of the wheel rim. A multi-objective optimization problem is formulated, based on mass and compliance minimization. Several wheel design layouts are investigated, which differ in terms of number of spokes (i.e. 3, 5 and 7), spokes layout (i.e. straight and Y-shape) and spokes cross section (i.e. rectangular, C and I). Geometric quantities related to the cross section dimensions of the spokes and to the rim thickness are optimized. Design constraints related to structural stiffness and elastic stability (both global and local buckling) are taken into account. The developed finite-element based model of the wheel is used to train a set of neural networks to approximate the objective functions and the design constraints to reduce the computational effort. A multi-objective genetic algorithm is adopted to obtain the Pareto-optimal solutions. The implemented method has proved to be a valuable tool to support design engineers in taking critical decisions in the early stages of the design process.

Numerical and experimental study on rotary draw bending of aluminium alloy tubes

2011 ◽  
Vol 2 (1) ◽  
pp. 33-38 ◽  
Author(s):  
L. Lăzărescu
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Aluminium Alloy ◽  
Cross Section ◽  
Angular Position ◽  
Element Model ◽  
Quality Parameters ◽  
Wall Thinning ◽  
Bending Process ◽  
Bending Radius

Abstract In this paper a 3D finite element model of the bending process for circular aluminium alloy tube has been built using the explicit code eta/Dynaform and validated by comparing the experiments. The experiments were carried out by using a hand bender with the same bending principle as a rotary draw numerical controlled (NC) bender. The relationship between quality parameters of bent tubes, in terms of cross-section distortion and wall thinning, and the angular position along the bent tube is discussed experimentally in combination with FE simulation. Then, the effects of bending radius (R) are investigated using simulation of the bending process based on the finite element model. The results show that with the increase of bending radius, the cross-section degradation factor (Ψ) and wall thinning degree (ξ) decreases rapidly.

Finite Element Analysis of Beams With Constrained Damping Treatment Modeled Via Fractional Derivatives

1997 ◽  
Vol 50 (11S) ◽  
pp. S216-S224 ◽  
Author(s):  
Luis E. Sua´rez ◽  
Arsalan Shokooh ◽  
Jose´ Arroyo
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Single Layer ◽  
Element Model ◽  
Beam Element ◽  
Element Formulation ◽  
Beam Model ◽  
Element Analysis ◽  
Damping Material ◽  
Derivatives Of

This paper presents a finite element formulation for the modeling of beams and frames with artificial damping provided by means of a constrained single layer of damping material. The behavior of the damping material is described using the fractional derivative model of viscoelasticity. In this model, the first order derivatives of the strains in the constitutive equations of the viscoelastic materials are replaced by derivatives of order α < 1. The finite element model developed is a one-dimensional beam element with three degrees of freedom per node. The dynamic response is calculated with a procedure involving a transformation of the original equations of motion to the state space and its decoupling with the eigenvectors of a special eigenvalue problem. The accuracy of the modal properties obtained with the beam model is compared with those calculated from a more elaborate plane stress finite element model. It was found that the proposed beam element provides very accurate results and with much lower computational costs than the 2-D model.

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