Vibroacoustic coupling and transmission paths

This dissertation deals with four topics. The first three are in the same environment, the transmission paths. The fourth refers to the synthesis of subsystems and more specifically to two subsystems linked by any number of elastic elements. In the first topic it is proved that the solution of any linear mechanical system can be expressed as a linear combination of signal transmission paths. This is done in the framework of the Global Transfer Direct Transfer (GTDT) formulation for vibroacoustic problems. Transmission paths are expressed as powers of the transfer matrix. The key idea of the proof is to generalise the Neumann series of the transfer matrix ,which is convergent only if its spectral radius is smaller than one, into a modified Neumann series that is convergent regardless of the eigenvalues of the transfer matrix. The modification consists in choosing the appropriate combination coefficients for the powers of the transfer matrix in the series. A recursive formula for the computation of these factors is derived. The theoretical results are illustrated by means of numerical examples. Finally, we show that the generalised Neumann series can be understood as an acceleration of Jacobi iterative method. For complex geometries, the definition of the subsystems is not a straightforward task. We present as a second topic a subsystem identification method based on the direct transfer matrix, which represents the first-order paths. The key ingredient is a cluster analysis of the rows of the powers of the transfer matrix. These powers represent high-order paths in the system. Once subsystems are identified, the proposed approach also provides a quantification of the degree of coupling between subsystems. This information is relevant to decide whether a subsystem may be analysed independently of the rest or subsystems or not. The two features (subsystem identification and quantification of the degree of coupling) are illustrated by means of numerical examples: plates coupled by means of springs and rooms connected by means of a cavity. In the third work, Advanced Transfer Path Analysis (ATPA) is applied to a cuboid-shaped box. The simplicity of this vibroacoustic system helps to make a detailed analysis of the ATPA method in a more controlled environment than in situ measurements in trains, wind turbines or other mechanical systems with complex geometry, big dimensions and movement. At the same time, a numerical model (based on finite elements) of the box is developed. The agreement between the experimental measurements and the numerical results is good. The numerical model is used in order to perform tests that cannot be accomplished in practise. The results are helpful in order to verify hypotheses, provide recommendations for the testing procedures and study some aspects of ATPA such as the reconstruction of operational signals by means of direct transfer functions or to quantify and understand which are the transmission mechanisms in the box. The fourth topic introduces a method to synthesize the modal characteristics of a system from the modal characteristics of its subsystems. The interest is focused on those systems with elastic links between the parts which is the main feature of the proposed method. An algebraic proof is provided for the case of arbitrary number of connections. The solution is a system of equations with a reduced number of degrees of freedom that correspond to the number of elastic links between the subsystems. In addition the method is also interpreted from a physical point of view (equilibrium of the interaction forces). An application to plates linked by means of springs shows how the global eigenfrequencies and eigenmodes are properly computed by means of the subsystems eigenfrequencies and eigenmodes.Aquest treball estudia quatre temes. Els tres primers estan en el àmbit de les vies de transmissió. El quart fa referencia a la síntesi de subsistemes i mes concretament a dos subsistemes lligats per un nombre qualsevol de molles. En el primer treball es demostra que la solució de qualsevol sistema mecànic lineal es pot expressar com una combinació lineal de vies de transmissió de senyal. Això es fa en el marc de la formulació per problemes vibroacústics del Global Transfer Direct Transfer (GTDT). Les vies de transmissió s'expressen com les potencies de la matriu de transferències. La idea clau de la demostració es generalitzar la sèrie de Neumann aplicada a la matriu de transferència, que és una sèrie convergent només si el radi espectral és menor que u, amb una sèrie de Neumann modificada que convergeix amb independència del radi espectral de la matriu de transferència. La modificació consisteix en escollir els coeficients apropiats per a les potències de la matriu de transferència a la sèrie. Una fórmula recursiva facilita el càlcul. Els resultats teòrics s'il·lustren amb exemples numèrics. Finalment es mostra que la sèrie de Neumann generalitzada es pot aplicar per accelerar el mètode iteratiu de Jacobi. En geometries complexes, la definició dels subsistemes no es directe. Com a segon tòpic es presenta un mètode per a identificar els subsistemes que es basa en la matriu de transferència que representa els camins de primer ordre. La clau es un estudi clúster de les files de les potencies de la matriu de transferència. Aquestes potencies representen els camins d'ordre superior en el sistema i són més afectats per l'esmorteïment que els camins d'ordre inferior. Quan el subsistemes estan identificats, el mètode proposat també dona una quantificació del grau d'acoblament entre els subsistemes. Aquesta informació és important per decidir quan un subsistema es pot analitzar amb independència de la resta de subsistemes. Les dues aplicacions (identificació i quantificació del grau d'acoblament,) s?il·lustren mitjanant exemples numèrics: plaques lligades amb molles i habitacions connectades per un forat. En el tercer treball s'aplica ATPA a una caixa. La simplicitat d'aquest sistema vibroacústic ajuda a poder fer una anàlisi detallada del mètode ATPA en un entorn més controlat que el que es disposa amb assaigs en trens, turbines eòliques o altres sistemes mecànics de geometria complexa, grans dimensions i que estan en moviment. Es fa un model numèric basat en Elements Finits que correspon bé amb els assaigs fets sobre la caixa real. El model numèric s'empra per provar resultats del mètode que son difícils de demostrar en experiments reals, també per trobar procediments per limitar les imprecisions inevitables als assaigs i que poden afectar a la reconstrucció dels senyals en funcionament real i per aprofundir en els mecanismes de transmissió del senyal. El quart treball introdueix un mètode per a sintetitzar les característiques modals d'un sistema a partir de les característiques modals dels subsistemes. L'interès s'adreça als sistemes que tenen les seves parts lligades elàsticament sent aquest aspecte el factor diferencial. Es fa una demostració algebraica per a qualsevol nombre de connexions. El resultat és un sistema d'equacions de dimensió igual al nombre de connexions que, normalment, és molt inferior al nombre de graus de llibertat. El mètode s'interpreta a més des del punt de vista físic (equilibri entre les forces de interacció). Amb un exemple consistent en dues plaques lligades amb molles es demostra que freqüències i modes propis es calculen de forma adient

Eigenvalue and eigenmode synthesis in elastically coupled subsystems

A method to synthesize the modal characteristics of a system from the modal characteristics of its subsystems is proposed. The interest is focused on those systems with elastic links between the parts which is the main feature of the proposed method. An algebraic proof is provided for the case of arbitrary number of connections. The solution is a system of equations with a reduced number of degrees of freedom that correspond to the number of elastic links between the subsystems. In addition the method is also interpreted from a physical point of view (equilibrium of the interaction forces). An application to plates linked by means of springs shows how the global eigenfrequencies and eigenmodes are properly computed by means of the subsystems eigenfrequencies and eigenmodes.Peer ReviewedPostprint (author's final draft

The solution of linear mechanical systems in terms of path superposition

We prove that the solution of any linear mechanical system can be expressed as a linear combination of signal transmission paths. This is done in the framework of the Global Transfer Direct Transfer (GTDT) formulation for vibroacoustic problems. Transmission paths are expressed as powers of the transfer matrix. The key idea of the proof is to generalise the Neumann series of the transfer matrix --which is convergent only if its spectral radius is smaller than one-- into a modified Neumann series that is convergent regardless of the eigenvalues of the transfer matrix. The modification consists in choosing the appropriate combination coefficients for the powers of the transfer matrix in the series. A recursive formula for the computation of these factors is derived. The theoretical results are illustrated by means of numerical examples. Finally, we show that the generalised Neumann series can be understood as an acceleration (i.e. convergence speedup) of the Jacobi iterative method.Peer ReviewedPostprint (author's final draft

The solution of vibroacoustic linear systems as a finite sum of transmission paths

© 2021 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Linear systems are frequently encountered in low, mid and high vibroacoustics modelling of mechanical built-up structures. It has recently been proved that the solution to those systems can be always factorized as an infinite (weighted) Neumann series summation, which accounts for signal transmission through paths connecting system elements. The key to path expansion relies on the concept of direct transmissibility. In this work, we explore some additional theoretical aspects of transmissibility-based transmission path analysis (TPA), which is known to constitute a valuable tool to remedy noise and vibration problems. In particular, we show that it is also possible to expand the solution of a matrix linear system as a finite summation of transmission paths. Furthermore, our goal is to provide mathematical and physical insight into such path factorization. As regards the former, we exploit the relationship between graph theory and matrix algebra to interpret the terms appearing in the series expansion as combinations of open and closed paths in a graph. In what concerns the second, two benchmark examples are addressed that benefit from the graph theory outcomes. The first one consists of a mass-damping-stiffness system representative of vibroacoustic modelling at low frequencies. A relation is established between the relative weights of the paths, the global system resonances and the resonances of complementary systems, which contain elements not belonging to the paths. The second example involves a statistical energy analysis (SEA) model made of connected plates. The meaning of the relative weights of open paths in the finite expansion for energy transmission between SEA subsystems is analyzed and compared to the results of infinite SEA path factorization.Peer ReviewedPostprint (author's final draft

Oxidative Dehydrogenation of an Amine Group of a Macrocyclic Ligand in the Coordination Sphere of a Cu\u3csup\u3eII\u3c/sup\u3e Complex

The spontaneous oxidation of an amine group to an imine has been observed experimentally in an octa-aza macrocyclic dinucleating ligand LH4 coordinated to CuII. The reaction is bimolecular and spontaneous in which amine groups of one macrocycle are oxidised and the CuII centres of a second macrocyclic complex are reduced. No additional oxidating or external base agents are required. DFT calculations are carried out to compare the reaction with that recently reported for a ligand coordinated to an FeIII centre, but which requires an external base as proton acceptor. The computational results show that the copper and iron catalysed amine to imine reactions proceed via different mechanisms

Experimental and numerical study of Advanced Transfer Path Analysis applied to a box prototype

Advanced Transfer Path Analysis (ATPA) is a technique that allows the characterisation of vibroacoustic systems not only from the point of view of contributions but also topologically by means of the path concept. Some of the aspects addressed in the current research such as the proper characterisation of the less contributing paths remained not proven. ATPA is applied to a cuboid-shaped box. The simplicity of this vibroacoustic system helps to make a detailed analysis of the ATPA method in a more controlled environment than in situ measurements in trains, wind turbines or other mechanical systems with complex geometry, big dimensions and movement. At the same time, a numerical model (based on finite elements) of the box is developed. The agreement between the experimental measurements and the numerical results is good. The numerical model is used in order to perform tests that cannot be accomplished in practise. The results are helpful in order to verify hypotheses, provide recommendations for the testing procedures and study some aspects of ATPA such as the reconstruction of operational signals by means of direct transfer functions or to quantify and understand which are the transmission mechanisms in the box.Peer ReviewedPostprint (author's final draft

Mono- and Dinuclear Complexes of Tricarbonylrhenium(I) with 4-Methyl-2,2'-bipyridine-4'-carbonitrile

Novel mono- and dinuclear tricarbonylrhenium(I) complexes of formula [Re(Mebpy-CN)(CO)3Cl] (1), [Re(Mebpy-CN)-(CO)3(CH3CN)](PF6) (2), and [(CH3CN)(CO)3Re(Mebpy-CN)Ru(NH3)5](PF6)3 (3), in which Mebpy-CN = 4-methyl-2,2-bipyridine-4-carbonitrile, were prepared and characterized by spectroscopic, photophysical, and computational techniques. The complete structure of complex 2 was determined by X-ray diffraction. The increased conjugation in the bipyridyl ring owing to the nitrile substituent increases the emission quantum yields of the 3MLCT (metal-to-ligand charge-transfer) lowest-lying excited states of 1 and 2 with respect to the corresponding bpy complexes (bpy = 2,2-bipyridine). The mixed-valent species of formula [(CH3CN)(CO)3Re(Mebpy-CN)Ru(NH3)5]4+ (4) was prepared in situ and as a mixed salt; the charge recombination from its metal-to-metal charge-transfer(MMCT) excited state is predicted to lie in the Marcus inverted region. The electronic structures and optical properties of all the reported complexes calculated by DFT and TD-DFT methods agree reasonably well with experimental results.Fil: Mecchia Ortiz, Juan Hugo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Tucumán. Instituto de Quimica del Noroeste; Argentina. Universidad Nacional de Tucumán; ArgentinaFil: Moran Vieyra, Faustino Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Transferencia de Santiago del Estero; Argentina. Universidad Nacional de Santiago del Estero; ArgentinaFil: Borsarelli, Claudio Darío. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Transferencia de Santiago del Estero; Argentina. Universidad Nacional de Santiago del Estero; ArgentinaFil: Romero, Isabel. Universidad de Girona; EspañaFil: Fontrodona, Xavier. Universidad de Girona; EspañaFil: Parella, Teodor. Universitat Autonoma de Barcelona; EspañaFil: Lis de Katz, Noemí D.. Universidad Nacional de Tucumán. Facultad de Bioquímica, Química y Farmacia; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Tucumán. Instituto de Quimica del Noroeste; ArgentinaFil: Fagalde, Florencia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Tucumán. Instituto de Quimica del Noroeste; Argentina. Universidad Nacional de Tucumán; ArgentinaFil: Katz, Néstor Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Tucumán. Instituto de Quimica del Noroeste; Argentina. Universidad Nacional de Tucumán; Argentin