Computationally Efficient Approaches to Simulate the Dynamics of Microbeams Under Mechanical Shock

2006 ◽  
Author(s):  
Mohammad I. Younis ◽  
Danial Jordy ◽  
James M. Pitarresi
Keyword(s):  
Hybrid Approach ◽  
Computational Cost ◽  
Nonlinear Behavior ◽  
Reduced Order Model ◽  
Beam Model ◽  
Mechanical Shock ◽  
Computationally Efficient ◽  
Order Model ◽  
Reduced Order ◽  
Dynamic Loading Conditions

We present computationally efficient models and approaches and utilize them to investigate the dynamics of microbeams under mechanical shock. We explore using a hybrid approach utilizing a beam model combined with the shock spectrum of a spring-mass-damper model. We conclude that this approach is computationally efficient and yields accurate results in both quasi-static and dynamic loading conditions. We utilize a reduced-order model based on the nonlinear Euler-Bernoulli beam model. We demonstrate that this model is capable of capturing accurately the dynamic behavior of microbeams under shock pulses of various amplitudes (low-g and high-g), in various damping conditions, structural boundaries (clamped-clamped and clamped-free), and can capture both linear and nonlinear behavior. We investigate high-g loading cases. We report significant increase in the computational cost of simulations when using traditional nonlinear finite-element models because of the activation of higher-order modes. We demonstrate that the developed reduced-order model can be very efficient in such cases.

scholarly journals A Comprehensive CFD Model for Dual-Phase Brass Indirect Extrusion Based on Constitutive Laws: Assessment of Hot-Zone Formation and Failure Prognosis

Metals ◽  
2018 ◽  
Vol 8 (12) ◽  
pp. 1043 ◽  
Author(s):  
George Pashos ◽  
George Pantazopoulos ◽  
Ioannis Contopoulos
Keyword(s):  
Stokes Equations ◽  
Metal Flow ◽  
Computational Cost ◽  
Constitutive Laws ◽  
Reduced Order Model ◽  
Preliminary Evaluation ◽  
Order Model ◽  
Zone Formation ◽  
Reduced Order ◽  
Prediction And Prevention

A numerical method for the precise calculation of temperature, velocity and pressure profiles of the α-β brass indirect hot extrusion process is presented. The method solves the Navier–Stokes equations for non-Newtonian liquids with strain-rate and temperature-dependent viscosity that is formulated using established constitutive laws based on the Zener–Hollomon type equation for plastic flow stress. The method can be implemented with standard computational fluid dynamics (CFD) software, has relatively low computational cost, and avoids the numerical artifacts associated with other methods commonly used for such processes. A response surface technique is also implemented, and it is thus possible to build a reduced order model that approximately maps the process with respect to all combinations of its parameters, including the extrusion speed and brass phase constitution. The reduced order model can be a very useful tool for production, because it instantaneously provides important quantities, such as the average pressure or the temperature of hot-spots that are formed due to the combined effect of die/billet friction and the generation of heat from plastic deformation (adiabatic shear deformation heating). This approach can assist in the preliminary evaluation of the metal flow pattern, and in the prediction and prevention of critical extrusion failures, thus leading to subsequent process and product quality improvements.

Analysis of Vibration of a Tank Caused by an Explosion

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
M. Utsumi ◽  
H. Tazuke
Keyword(s):  
Fluid Motion ◽  
Three Dimensional ◽  
Longitudinal Axis ◽  
Reduced Order Model ◽  
Fe Model ◽  
Computationally Efficient ◽  
Order Model ◽  
Reduced Order ◽  
Large Tank ◽  
The Galerkin Method

The vibration of a large tank caused by an explosion that occurs at a place apart from the tank is analyzed. Because the tank is double-walled and the liquid is contained in the inner shell, the vibration of the outer shell subjected to the explosion-induced pressure wave that travels outside the tank is analyzed without considering the liquid. A cylindrical tank with a spherical roof is considered as a realistic three-dimensional (3D) model, and a computationally efficient semi-analytical method that is applicable to the 3D geometry of the tank–fluid interface is investigated. First, cylindrical coordinates are introduced such that the longitudinal axis intersects the center of the tank base and is normal to the explosion source plane, thereby defining the inner and outer radii of the analysis domain of the fluid motion. Next, the solutions are expressed in terms of coordinate-dependent eigenvalues and a reduced order model is developed by applying the Galerkin method to the governing equations that take into account the compressibility and nonlinearity of the fluid motion. The method is verified by comparing with earlier results obtained by a numerical method. We also analyze the vibration of the tank shell by developing its finite element (FE) model and transforming the model into modal equations to develop a reduced order model for the fluid–tank system.

Forced Vibrations of Slacked Carbon Nanotube Resonators

2010 ◽  
Author(s):  
Hassen M. Ouakad ◽  
Mohammad I. Younis
Keyword(s):  
Perturbation Method ◽  
Multiple Scales ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Beam Model ◽  
Harmonic Load ◽  
Arch Model ◽  
Order Model ◽  
Reduced Order ◽  
Model Equations

In this paper, we present an investigation of the dynamics of electrically actuated carbon nanotubes (CNTs) resonators including the effect of their initial curvature due to fabrication (slack). A nonlinear arch model is used to simulate the motion of the slacked CNT. A reduced-order model using a multimode Galerkin procedure based on the mode shapes of the straight un-actuated CNTs is derived. The reduced-order model equations are integrated numerically with time to reveal the steady-state response of the CNT when actuated by a DC load superimposed to an AC harmonic load. A perturbation method, the method of multiple scales, is used to obtain analytically the forced vibration response due to DC and small AC loads for various slacked CNT. Results of the perturbation method are verified with those obtained by numerically integrating the reduced-order model equations. The effective nonlinearity of the CNT is calculated as function of the slack and the DC load while using a beam model for the CNTs showing a softening dominant behavior.

Nonlinear Dynamics of Electrically Actuated Carbon Nanotube Resonators

2009 ◽  
Vol 5 (1) ◽  
Author(s):  
Hassen M. Ouakad ◽  
Mohammad I. Younis
Keyword(s):  
Nonlinear Dynamics ◽  
Carbon Nanotube ◽  
Natural Frequency ◽  
Reduced Order Model ◽  
Plane Boundary ◽  
Beam Model ◽  
Harmonic Load ◽  
Order Model ◽  
Reduced Order ◽  
Wide Range

This work presents an investigation of the nonlinear dynamics of carbon nanotubes (CNTs) when actuated by a dc load superimposed to an ac harmonic load. Cantilevered and clamped-clamped CNTs are studied. The carbon nanotube is described by an Euler–Bernoulli beam model that accounts for the geometric nonlinearity and the nonlinear electrostatic force. A reduced-order model based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the carbon nanotube. The free-vibration problem is solved using both the reduced-order model and by solving directly the coupled in-plane and out-of-plane boundary-value problems governing the motion of the nanotube. Comparison of the results generated by these two methods to published data of a more complicated molecular dynamics model shows good agreement. Dynamic analysis is conducted to explore the nonlinear oscillation of the carbon nanotube near its fundamental natural frequency (primary-resonance) and near one-half, twice, and three times its natural frequency (secondary-resonances). The nonlinear analysis is carried out using a shooting technique to capture periodic orbits combined with the Floquet theory to analyze their stability. The nonlinear resonance frequency of the CNTs is calculated as a function of the ac load. Subharmonic-resonances are found to be activated over a wide range of frequencies, which is a unique property of CNTs. The results show that these resonances can lead to complex nonlinear dynamics phenomena, such as hysteresis, dynamic pull-in, hardening and softening behaviors, and frequency bands with an inevitable escape from a potential well.

scholarly journals Development of a Reduced Order Model for Fuel Burnup Analysis

Energies ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 890 ◽  
Author(s):  
Christian Castagna ◽  
Manuele Aufiero ◽  
Stefano Lorenzi ◽  
Guglielmo Lomonaco ◽  
Antonio Cammi
Keyword(s):  
Methodological Approach ◽  
Computational Cost ◽  
Reaction Rates ◽  
Reduced Order Model ◽  
Fuel Burnup ◽  
Order Model ◽  
Reduced Order ◽  
Solution Accuracy ◽  
Proper Orthogonal ◽  
Over Time

Fuel burnup analysis requires a high computational cost for full core calculations, due to the amount of the information processed for the total reaction rates in many burnup regions. Indeed, they reach the order of millions or more by a subdivision into radial and axial regions in a pin-by-pin description. In addition, if multi-physics approaches are adopted to consider the effects of temperature and density fields on fuel consumption, the computational load grows further. In this way, the need to find a compromise between computational cost and solution accuracy is a crucial issue in burnup analysis. To overcome this problem, the present work aims to develop a methodological approach to implement a Reduced Order Model (ROM), based on Proper Orthogonal Decomposition (POD), in fuel burnup analysis. We verify the approach on 4 years of burnup of the TMI-1 unit cell benchmark, by reconstructing fuel materials and burnup matrices over time with different levels of approximation. The results show that the modeling approach is able to reproduce reactivity and nuclide densities over time, where the accuracy increases with the number of basis functions employed.

Reduced Order Model for the Geometric Nonlinear Response of Complex Structures

2012 ◽  
Author(s):  
Ricardo Perez ◽  
X. Q. Wang ◽  
Andrew Matney ◽  
Marc P. Mignolet
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Behavior ◽  
Reduced Order Model ◽  
Model Parameters ◽  
Complex Structures ◽  
Order Model ◽  
Plate Structures ◽  
Reduced Order ◽  
Nonlinear Static ◽  
Selection Of

This paper focuses on the development of nonlinear reduced order modeling techniques for the prediction of the response of complex structures exhibiting “large” deformations, i.e. a geometrically nonlinear behavior, and modeled within a commercial finite element code. The present investigation builds on a general methodology successfully validated in recent years on simpler beam and plate structures by: (i) developing a novel identification strategy of the reduced order model parameters that enables the consideration of the large number of modes (> 50 say) that would be needed for complex structures, and (ii) extending an automatic strategy for the selection of the basis functions used to represent accurately the displacement field. The above novel developments are successfully validated on the nonlinear static response of a 9-bay panel structure modeled with 96,000 degrees of freedom within Nastran.

A Reduced-Order Model for Turbomachinery Flows Using Proper Orthogonal Decomposition

2013 ◽  
Author(s):  
Thomas A. Brenner ◽  
Forrest L. Carpenter ◽  
Brian A. Freno ◽  
Paul G. A. Cizmas
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Stokes Equations ◽  
Computational Cost ◽  
Wheel Speed ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Computational Time ◽  
Order Model ◽  
Reduced Order ◽  
Proper Orthogonal

This paper presents the development of a reduced-order model based on the proper orthogonal decomposition (POD) method. The POD method has been developed to predict turbomachinery flows modeled by the Reynolds-averaged Navier–Stokes equations. The purpose of using a POD-based reduced-order model is to decrease the computational cost of turbomachinery flows. The POD model has been tested for two configurations: a canonical channel with a bump case and the transonic NASA Rotor 67 case. The Rotor 67 case has been simulated at design wheel speed and at three off-design conditions: 70, 80, and 90% of the wheel speed. The results of the POD-based reduced-order model where in excellent agreement with the full-order model results. The computational time of the reduced-order model was approximately one order of magnitude smaller than that of the full-order model.

The Construction of Nonlinear Normal Modes for Systems With Internal Resonance: Application to Rotating Beams

2002 ◽  
Author(s):  
Dongying Jiang ◽  
Christophe Pierre ◽  
Steven W. Shaw
Keyword(s):  
Invariant Manifold ◽  
Internal Resonance ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Reduced Order Model ◽  
Degree Of Freedom ◽  
Beam Model ◽  
Order Model ◽  
Reduced Order ◽  
Nonlinear Normal

A numerical method for constructing nonlinear normal modes for systems with internal resonances is presented based on the invariant manifold approach. In order to parameterize the nonlinear normal modes, multiple pairs of system state variables involved in the internal resonance are kept as ‘seeds’ for the construction of the multi-mode invariant manifold. All the remaining degrees of freedom are constrained to these ‘seed’ variables, resulting in a system of nonlinear partial differential equations governing the constraint relationships, which must be solved numerically. The solution procedure uses a combination of finite difference schemes and Galerkin-based expansion approaches. It is illustrated using two examples, both of which focus on the construction of two-mode models. The first example is based on the analysis of a simple three-degree-of-freedom example system, and is used to demonstrate the approach. An invariant manifold that captures two nonlinear normal modes is constructed, resulting in a reduced-order model that accurately captures the system dynamics. The methodology is then applied to a more large system, namely an 18-degree-of-freedom rotating beam model that features a three-to-one internal resonance between the first two flapping modes. The accuracy of the nonlinear two-mode reduced-order model is verified by time-domain simulations.

Sign in / Sign up

Export Citation Format

Share Document