Component Mode Synthesis

Fig, 3 Frequency response function obtained by free boundary component mode synthesis... 

Two recent developments in fuzzy dynamic analysis are presented a Response Surface Modelling method (RSM) and a new Component Mode Synthesis procedure (CMS). 

The paper then focusses on 2 recent developments, namely response surface methods (RSM) and component mode synthesis (CMS). The former is a strategy to approximate the real structural behaviour as modelled by repeated finite element calculations by a response surface model that interpolates for structural response between well-chosen settings of uncertain parameters. The latter is an established theory for modelling structural dynamics using superelements. The paper extends the deterministic CMS to models with fuzzy uncertain parameters in the superelements. 

Component mode synthesis with uncertain sub structures... 

The aim of the well-known Component Mode Synthesis (CMS) method is to reduce the computational cost of large models and to enable a solntion strategy in which individual components can be optimised withont the need for the recalculation of the total structure. The CMS technique consists of three global steps. First the structure is divided into a residual structure and a number of components, also referred to as substructures or superelements. For each component, a confined set of component modes is calculated, which represent its static and dynamic behaviour. In the second step, these component modes are used to reduce the component stiffness and mass matrices. In the third step, all reduced super element models are combined with the non-reduced part of the structure to form the global reduced system, that is further used for global FE analyses. 

The other improvement is in the field of Component Mode Synthesis. A new scheme is developed to take into account the effect of uncertain parameters in the transformation matrices in the component mode reduction phase. It is shown that static and dynamic component modes may change with parameter uncertainties. In order to improve the accuracy of the analysis, it is required that these component mode sensitivities are explicitly taken into account. 

De Gersem, H., Moens, D., Desmet, W. Vandepitte, D. June 2007. On the use of devi-atoric component modes for the assessment of uncertainty in Component Mode Synthesis, Proceedings of the 1st International Conference on Uncertainty in Structural Dynamics, Sheffield. 

De Smet, M., C. Liefooghe, P. Sas and R. Snoeys, Dynamic Analysis of Flexible Structures Using Component Mode Synthesis, Journal of Applied Mechanics, Trans. ASME, Vol. 56, Dec. 1989, pp. 874-880. 

Component mode synthesis Domain decomposition Hybrid simulations... 

In all the DD methods described in this section, no reduction in the total number of degrees of freedom is made. Therefore, the error associated with static condensation of component mode synthesis where a set of degrees of freedom is eliminated firom the calculation does not appear here. However, approximations arise from usage of iterative solvers. The main goal here is to reduce the total computational cost by distributing the total computational burden among a... 

Apiwattanalunggam P, Shaw SW, Pierre C (2005) Component mode synthesis using nonlinear normal modes. Nonlinear Dyn 41(l-3) 17-46 Bennighof JK, Kaplan MF (1998) Frequency window implementation of adaptive multi-level substructuring. J Vib Acoust 120(2) 409-418 Bursi OS, Wagg D (eds) (2008) Modem testing techniques for structural systems dynamics and control. Springer, New York... 

M. Hao and S. C. Harvey. Analyzing the normal mode dynamics of macro-molecules by the component synthesis method. Biopolymers, 32 1393-1405, 1992. 

The microwave acceleration of Ugi condensations on a sohd support have been utilized in the synthesis of an 18-membered targeted hbrary of a-acylamino amides [60], Irradiation of the four components, immobilizing the amine on TentaGel S RAM, for 3-5 min in a single-mode microwave synthesizer gave the products in moderate to excellent yields and high purity (Scheme 7). 

Microwave and fluorous technologies have been combined in the solution phase parallel synthesis of 3-aminoimidazo[l,2-a]pyridines and -pyrazines [63]. The three-component condensation of a perfluorooctane-sulfonyl (Rfs = CgFiy) substituted benzaldehyde by microwave irradiation in a single-mode instrument at 150 °C for 10 min in CH2CI2 - MeOH in the presence of Sc(OTf)3 gave the imidazo-annulated heterocycles that could be purified by fluorous solid phase extraction (Scheme 9). Subsequent Pd-catalyzed cross-coupling reactions of the fluorous sulfonates with arylboronic acids or thiols gave biaryls or aryl sulfides, respectively, albeit it in relatively low yields. 

The rapid synthesis of 4-thiazolidinones by the MCR of an amine, aldehyde and mercaptoacetic acid has been developed under microwave-assisted conditions [73-75]. Irradiation of the three components in ethanol at 120 °C in the presence of molecular sieves [73] or in toluene at reflux under atmospheric conditions [74] in a single-mode microwave synthesizer gave the... 

The one-pot, three-component synthesis of a 20-membered dihydrotri-azine hbrary was also dramatically accelerated through the use of microwave irradiation [79]. Heating a subset of substituted anilines, cyanoguanidine and acetone in the presence of concentrated hydrochloric acid for 35 min at 90 °C in a single-mode microwave reactor gave the corresponding 2,2-dimethyl-1,2-dihydro-s-triazine hydrochloride 51 in comparable yield to conventional conductive heating methods but in a much shorter reaction time and increased purity (Scheme 21). 

The synthesis of functionahzed tetrahydrocarbazoles can be promoted by microwave irradiation [84], The organocatalytic four-component reaction of a solution of 2-substituted indole, aromatic aldehyde (2 equiv) and Mel-drum s acid in benzene in the presence of DL-proline proceeds when heated under Dean-Stark conditions for 5 min in a single-mode microwave reactor to give the tetrahydrocarbazole product as a mixture of diastereoisomers (Scheme 24). 

The reactor system, where the kinetic experiments were carried out can be described as a semi-batch reactor. Only the synthesis gas (H2 and CO) was fed into the reactor continuously during the experiments, while 1-butene and the solvent were in the batch mode. All reactions took place in the liquid phase. The mass balance for an arbitrary component in the gas is given by... 

In biological systems one of the primary modes of molecular recognition processes occurs via H-bond formation. Research concerning design and synthesis of molecular components that can self-assemble via H-bonding interactions has been reported [90,155]. 

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