Dynamic Analysis of a Protein-Ligand Molecular Chain Attached to an Atomic Force Microscope

2004 ◽  
Vol 126 (4) ◽  
pp. 496-513 ◽  
Author(s):  
Deman Tang ◽  
Earl H. Dowell
Keyword(s):  
Nonlinear Systems ◽  
Atomic Force Microscope ◽  
Reduced Order Model ◽  
Molecular Chain ◽  
Static Equilibrium ◽  
Reduced Order Models ◽  
Base Excitation ◽  
Order Model ◽  
Reduced Order ◽  
Atomic Force

Dynamic numerical simulation of a protein-ligand molecular chain connected to a moving atomic force microscope (AFM) has been studied. A sinusoidal base excitation of the cantilevered beam of the AFM is considered in some detail. A comparison between results for a single molecule and those for multiple molecules has been made. For a small number of molecules, multiple stable static equilibrium positions are observed and chaotic behavior may be generated via a period-doubling cascade for harmonic base excitation of the AFM. For many molecules in the chain, only a single static equilibrium position exists. To enable these calculations, reduced-order (dynamic) models are constructed for fully linear, combined linear/nonlinear and fully nonlinear systems. Several distinct reduced-order models have been developed that offer the option of increased computational efficiency at the price of greater effort to construct the particular reduced-order model. The agreement between the original and reduced-order models (ROM) is very good even when only one mode is included in the ROM for either the fully linear or combined linear/nonlinear systems provided the excitation frequency is lower than the fundamental natural frequency of the linear system. The computational advantage of the reduced-order model is clear from the results presented.

Order Reduction of Parametrically Excited Nonlinear Systems Subjected to External Periodic Excitations

2009 ◽  
Author(s):  
Sangram Redkar ◽  
S. C. Sinha
Keyword(s):  
Nonlinear Systems ◽  
Fundamental Solution ◽  
Invariant Manifold ◽  
Large Scale ◽  
Order Reduction ◽  
Reduced Order Model ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order ◽  
And Control

In this work, some techniques for order reduction of nonlinear systems with periodic coefficients subjected to external periodic excitations are presented. The periodicity of the linear terms is assumed to be non-commensurate with the periodicity of forcing vector. The dynamical equations of motion are transformed using the Lyapunov-Floquet (L-F) transformation such that the linear parts of the resulting equations become time-invariant while the forcing and/or nonlinearity takes the form of quasiperiodic functions. The techniques proposed here; construct a reduced order equivalent system by expressing the non-dominant states as time-varying functions of the dominant (master) states. This reduced order model preserves stability properties and is easier to analyze, simulate and control since it consists of relatively small number of states in comparison with the large scale system. Specifically, two methods are outlined to obtain the reduced order model. First approach is a straightforward application of linear method similar to the ‘Guyan reduction’, the second novel technique proposed here, utilizes the concept of ‘invariant manifolds’ for the forced problem to construct the fundamental solution. Order reduction approach based on invariant manifold technique yields unique ‘reducibility conditions’. If these ‘reducibility conditions’ are satisfied only then an accurate order reduction via ‘invariant manifold’ is possible. This approach not only yields accurate reduced order models using the fundamental solution but also explains the consequences of various ‘primary’ and ‘secondary resonances’ present in the system. One can also recover ‘resonance conditions’ associated with the fundamental solution which could be obtained via perturbation techniques by assuming weak parametric excitation. This technique is capable of handing systems with strong parametric excitations subjected to periodic and quasi-periodic forcing. These methodologies are applied to a typical problem and results for large-scale and reduced order models are compared. It is anticipated that these techniques will provide a useful tool in the analysis and control system design of large-scale parametrically excited nonlinear systems subjected to external periodic excitations.

Reduced Order Model Analysis for Two Dimensional Molecular Dynamic Chain Structure Attached to an Atomic Force Microscope

2003 ◽  
Author(s):  
Deman Tang ◽  
Earl H. Dowell
Keyword(s):  
Atomic Force Microscope ◽  
Excitation Frequency ◽  
Chain Structure ◽  
Reduced Order Model ◽  
Two Dimensional ◽  
Order Model ◽  
Global Mode ◽  
Reduced Order ◽  
Atomic Force ◽  
Global Modes

Dynamic analysis and numerical simulation of a protein-ligand chain structure connected to a moving atomic force microscope (AFM) has been conducted. The elements of the chain are free to extend and rotate relative to each other in a two-dimensional plane. Sinusoidal base excitation of the cantilevered beam of the AFM is considered in some detail. Reduced order (dynamic) models are constructed using global modes for both linear and nonlinear dynamic systems with and without the “nearest neighbor assumption”. The agreement between the original and reduced order models (ROM) is very good even when only one global mode is included in the ROM for either the linear case or for the nonlinear case, provided the excitation frequency is lower than the fundamental natural frequency of the linear system. For higher excitation frequencies, more global modes are required. The computational advantage of the reduced order model is clear from the results presented.

Reduced Order Model Analysis for Two-Dimensional Molecular Dynamic Chain Structure Attached to an Atomic Force Microscope

2004 ◽  
Vol 126 (3) ◽  
pp. 531-546 ◽  
Author(s):  
Deman Tang ◽  
Earl H. Dowell
Keyword(s):  
Atomic Force Microscope ◽  
Excitation Frequency ◽  
Chain Structure ◽  
Reduced Order Model ◽  
Two Dimensional ◽  
Order Model ◽  
Global Mode ◽  
Reduced Order ◽  
Atomic Force ◽  
Global Modes

Dynamic analysis and numerical simulation of a protein-ligand chain structure connected to a moving atomic force microscope (AFM) has been conducted. The elements of the chain are free to extend and rotate relative to each other in a two-dimensional plane. Sinusoidal base excitation of the cantilevered beam of the AFM is considered in some detail. Reduced order (dynamic) models are constructed using global modes for both linear and nonlinear dynamic systems with and without the “nearest neighbor assumption.” The agreement between the original and reduced order models (ROM) is very good even when only one global mode is included in the ROM for either the linear case or for the nonlinear case, provided the excitation frequency is lower than the fundamental natural frequency of the linear system. For higher excitation frequencies, more global modes are required. The computational advantage of the reduced order model is clear from the results presented.

scholarly journals A Reduced Order Model of Mistuning Using a Subset of Nominal System Modes

1999 ◽  
Author(s):  
M.-T. Yang ◽  
J. H. Griffin
Keyword(s):  
Degrees Of Freedom ◽  
Reduced Order Model ◽  
Reduced Order Models ◽  
Order Model ◽  
Disk System ◽  
Element Analysis ◽  
Reduced Order ◽  
Nominal System ◽  
Harmonic Response ◽  
Bladed Disk

Reduced order models have been reported in the literature that can be used to predict the harmonic response of mistuned bladed disks. It has been shown that in many cases they exhibit structural fidelity comparable to a finite element analysis of the full bladed disk system while offering a significant improvement in computational efficiency. In these models the blades and disk are treated as distinct substructures. This paper presents a new, simpler approach for developing reduced order models in which the modes of the mistuned system are represented in terms of a sub-set of nominal system modes. It has the following attributes: the input requirements are relatively easy to generate; it accurately predicts mistuning effects in regions where frequency veering occurs; as the number of degrees of freedom increases it converges to the exact solution; it accurately predicts stresses as well as displacements; and it accurately models the deformation and stresses at the blades’ bases.

Accuracies of Reduced Order Models of a Bladed Rotor With Geometric Mistuning

2013 ◽  
Vol 136 (7) ◽  
Author(s):  
Yasharth Bhartiya ◽  
Alok Sinha
Keyword(s):  
Natural Frequencies ◽  
Domain Analysis ◽  
Forced Response ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order ◽  
Model Based ◽  
Bladed Rotor

The results from a reduced order model based on frequency mistuning are compared with those from recently developed modified modal domain analysis (MMDA). For the academic bladed rotor considered in this paper, the frequency mistuning analysis is unable to capture the effects of geometric mistuning, whereas MMDA provides accurate estimates of natural frequencies, mode shapes, and forced response.

Generation of Equivalent Circuit Models From Simulation Data of a Thermal System

2002 ◽  
Author(s):  
M. Bikdash ◽  
Y. P. Pang ◽  
E. P. Scott
Keyword(s):  
Complete Solution ◽  
Electrical Circuit ◽  
Reduced Order Model ◽  
Thermal System ◽  
Reduced Order Models ◽  
Order Model ◽  
Simulation Data ◽  
Cooling Fluid ◽  
Reduced Order ◽  
High Level

To enable the design and analysis of Integrated Power Electronics Models (IPEMs), a high level of software integration is needed. The solvers needed range form electrical circuit simulators, like Saber, to thermal analysis and CFD solvers like I-DEAS. As an electrical design parameter is changed, its effect will, in principle, be felt all the way to the temperature distribution in the cooling fluid, and hence a complete solution of the temperature field may have to be recomputed. This is of course computationally prohibitive. Hence a reduced-order model of the thermal behavior of the heat sink is of great interest. In this paper, we will present an algorithm that can automatically generate these reduced-order models from finite-element simulations.

scholarly journals Updating of aerodynamic reduced order models generated using computational fluid dynamics

2017 ◽  
Vol 232 (9) ◽  
pp. 1739-1763
Author(s):  
LM Griffiths ◽  
AL Gaitonde ◽  
DP Jones ◽  
MI Friswell
Keyword(s):  
Fluid Dynamics ◽  
Experimental Data ◽  
Computational Fluid Dynamics ◽  
Model Updating ◽  
Limited Range ◽  
Reduced Order Model ◽  
Reduced Order Models ◽  
Viscous Effects ◽  
Order Model ◽  
Reduced Order

Reduced order models of computational fluid dynamics codes have been developed to decrease computational costs; however, each reduced order model has a limited range of validity based on the data used in its construction. Further, like the computational fluid dynamics from which it is derived, such models exhibit differences from experimental data due to uncertainty in boundary conditions and numerical accuracy. Model updating provides the opportunity to use small amounts of additional data to modify the behaviour of a reduced order model, which means that the range of validity of the reduced order model can be extended. Whilst here computational fluid dynamics data have been used for updating, the approach offers the possibility that experimental data can be used in future. In this work, the baseline reduced order models are constructed using the Eigensystem realisation algorithm and the steps used to update these models are given in detail. The methods developed are then applied to remove the effects of wind tunnel walls and to include viscous effects.

scholarly journals Model Reduction for Kinetic Models of Biological Systems

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 863
Author(s):  
Neveen Ali Eshtewy ◽  
Lena Scholz
Keyword(s):  
Nonlinear Systems ◽  
Model Reduction ◽  
Kinetic Models ◽  
Initial Conditions ◽  
Reduced Order Model ◽  
Order System ◽  
High Dimensional ◽  
Order Model ◽  
Model Order ◽  
Reduced Order

High dimensionality continues to be a challenge in computational systems biology. The kinetic models of many phenomena of interest are high-dimensional and complex, resulting in large computational effort in the simulation. Model order reduction (MOR) is a mathematical technique that is used to reduce the computational complexity of high-dimensional systems by approximation with lower dimensional systems, while retaining the important information and properties of the full order system. Proper orthogonal decomposition (POD) is a method based on Galerkin projection that can be used for reducing the model order. POD is considered an optimal linear approach since it obtains the minimum squared distance between the original model and its reduced representation. However, POD may represent a restriction for nonlinear systems. By applying the POD method for nonlinear systems, the complexity to solve the nonlinear term still remains that of the full order model. To overcome the complexity for nonlinear terms in the dynamical system, an approach called the discrete empirical interpolation method (DEIM) can be used. In this paper, we discuss model reduction by POD and DEIM to reduce the order of kinetic models of biological systems and illustrate the approaches on some examples. Additional computational costs for setting up the reduced order system pay off for large-scale systems. In general, a reduced model should not be expected to yield good approximations if different initial conditions are used from that used to produce the reduced order model. We used the POD method of a kinetic model with different initial conditions to compute the reduced model. This reduced order model is able to predict the full order model for a variety of different initial conditions.

A Reduced-Order Model of Mistuning Using a Subset of Nominal System Modes

1999 ◽  
Vol 123 (4) ◽  
pp. 893-900 ◽  
Author(s):  
M.-T. Yang ◽  
J. H. Griffin
Keyword(s):  
Degrees Of Freedom ◽  
Reduced Order Model ◽  
Reduced Order Models ◽  
Order Model ◽  
Disk System ◽  
Element Analysis ◽  
Reduced Order ◽  
Nominal System ◽  
Harmonic Response ◽  
Bladed Disk

Reduced-order models have been reported in the literature that can be used to predict the harmonic response of mistuned bladed disks. It has been shown that in many cases they exhibit structural fidelity comparable to a finite element analysis of the full bladed disk system while offering a significant improvement in computational efficiency. In these models the blades and disk are treated as distinct substructures. This paper presents a new, simpler approach for developing reduced-order models in which the modes of the mistuned system are represented in terms of a subset of nominal system modes. It has the following attributes: the input requirements are relatively easy to generate; it accurately predicts mistuning effects in regions where frequency veering occurs; as the number of degrees-of-freedom increases it converges to the exact solution; it accurately predicts stresses as well as displacements; and it accurately models the deformation and stresses at the blades’ bases.

The Study of Aeroelastic Reduced-Order Model Based on CFD/CSD Method and its Application

2014 ◽  
Vol 978 ◽  
pp. 131-134
Author(s):  
Rui Li ◽  
Chang Hong Tang
Keyword(s):  
Harmonic Balance ◽  
Unsteady Aerodynamics ◽  
Harmonic Balance Method ◽  
Reduced Order Model ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order ◽  
Advantages And Disadvantages ◽  
Aeroelastic Analysis ◽  
Proper Orthogonal

Unsteady aerodynamics research is the foundation of aeroelastic analysis. How to effectively improve the aeroelastic computational efficiency,it is the key of current research on aeroelasticity now.Reduced order models are proposed as a powerful tool to solve this problem. Analyzed the three reduced-order models for Volterra ,Proper Orthogonal Decomposition and Harmonic Balance method ,their advantages and disadvantages were pointed out. The direction of the reduced order model in the future was Proposed and some suggest was given out for its application.

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