Search results for: Modal%20analysis
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 135

Search results for: Modal%20analysis

15 Vibration Analysis of Gas Turbine SIEMENS 162MW - V94.2 Related to Iran Power Plant Industry in Fars Province

Authors: Omid A. Zargar

Abstract:

Vibration analysis of most critical equipment is considered as one of the most challenging activities in preventive maintenance. Utilities are heart of the process in big industrial plants like petrochemical zones. Vibration analysis methods and condition monitoring systems of these kinds of equipments are developed too much in recent years. On the other hand, there are too much operation factors like inlet and outlet pressures and temperatures that should be monitored. In this paper, some of the most effective concepts and techniques related to gas turbine vibration analysis are discussed. In addition, a gas turbine SIEMENS 162MW - V94.2 vibration case history related to Iran power industry in Fars province is explained. Vibration monitoring system and machinery technical specification are introduced. Besides, absolute and relative vibration trends, turbine and compressor orbits, Fast Fourier transform (FFT) in absolute vibrations, vibration modal analysis, turbine and compressor start up and shut down conditions, bode diagrams for relative vibrations, Nyquist diagrams and waterfall or three-dimensional FFT diagrams in startup and trip conditions are discussed with relative graphs. Furthermore, Split Resonance in gas turbines is discussed in details. Moreover, some updated vibration monitoring system, blade manufacturing technique and modern damping mechanism are discussed in this paper.

Keywords: Gas turbine, turbine compressor, vibration data collector, utility, condition monitoring, non-contact probe, Relative Vibration, Absolute Vibration, Split Resonance, Time Wave Form (TWF), Fast Fourier transform (FFT).

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14 Rayleigh-Bénard-Taylor Convection of Newtonian Nanoliquid

Authors: P. G. Siddheshwar, T. N. Sakshath

Abstract:

In the paper we make linear and non-linear stability analyses of Rayleigh-Bénard convection of a Newtonian nanoliquid in a rotating medium (called as Rayleigh-Bénard-Taylor convection). Rigid-rigid isothermal boundaries are considered for investigation. Khanafer-Vafai-Lightstone single phase model is used for studying instabilities in nanoliquids. Various thermophysical properties of nanoliquid are obtained using phenomenological laws and mixture theory. The eigen boundary value problem is solved for the Rayleigh number using an analytical method by considering trigonometric eigen functions. We observe that the critical nanoliquid Rayleigh number is less than that of the base liquid. Thus the onset of convection is advanced due to the addition of nanoparticles. So, increase in volume fraction leads to advanced onset and thereby increase in heat transport. The amplitudes of convective modes required for estimating the heat transport are determined analytically. The tri-modal standard Lorenz model is derived for the steady state assuming small scale convective motions. The effect of rotation on the onset of convection and on heat transport is investigated and depicted graphically. It is observed that the onset of convection is delayed due to rotation and hence leads to decrease in heat transport. Hence, rotation has a stabilizing effect on the system. This is due to the fact that the energy of the system is used to create the component V. We observe that the amount of heat transport is less in the case of rigid-rigid isothermal boundaries compared to free-free isothermal boundaries.

Keywords: Nanoliquid, rigid-rigid, rotation, single-phase.

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13 Rail Corridors between Minimal Use of Train and Unsystematic Tightening of Population: A Methodological Essay

Authors: A. Benaiche

Abstract:

In the current situation, the automobile has become the main means of locomotion. It allows traveling long distances, encouraging urban sprawl. To counteract this trend, the train is often proposed as an alternative to the car. Simultaneously, the favoring of urban development around public transport nodes such as railway stations is one of the main issues of the coordination between urban planning and transportation and the keystone of the sustainable urban development implementation. In this context, this paper focuses on the study of the spatial structuring dynamics around the railway. Specifically, it is a question of studying the demographic dynamics in rail corridors of Nantes, Angers and Le Mans (Western France) basing on the radiation of railway stations. Consequently, the methodology is concentrated on the knowledge of demographic weight and gains of these corridors, the index of urban intensity and the mobility behaviors (workers’ travels, scholars' travels, modal practices of travels). The perimeter considered to define the rail corridors includes the communes of urban area which have a railway station and communes with an access time to the railway station is less than fifteen minutes by car (time specified by the Regional Transport Scheme of Travelers). The main tools used are the statistical data from the census of population, the basis of detailed tables and databases on mobility flows. The study reveals that the population is not tightened along rail corridors and train use is minimal despite the presence of a nearby railway station. These results lead to propose guidelines to make the train, a real vector of mobility across the rail corridors.

Keywords: Coordination between urban planning and transportation, Rail corridors, Railway stations, Travels.

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12 Meta Model for Optimum Design Objective Function of Steel Frames Subjected to Seismic Loads

Authors: Salah R. Al Zaidee, Ali S. Mahdi

Abstract:

Except for simple problems of statically determinate structures, optimum design problems in structural engineering have implicit objective functions where structural analysis and design are essential within each searching loop. With these implicit functions, the structural engineer is usually enforced to write his/her own computer code for analysis, design, and searching for optimum design among many feasible candidates and cannot take advantage of available software for structural analysis, design, and searching for the optimum solution. The meta-model is a regression model used to transform an implicit objective function into objective one and leads in turn to decouple the structural analysis and design processes from the optimum searching process. With the meta-model, well-known software for structural analysis and design can be used in sequence with optimum searching software. In this paper, the meta-model has been used to develop an explicit objective function for plane steel frames subjected to dead, live, and seismic forces. Frame topology is assumed as predefined based on architectural and functional requirements. Columns and beams sections and different connections details are the main design variables in this study. Columns and beams are grouped to reduce the number of design variables and to make the problem similar to that adopted in engineering practice. Data for the implicit objective function have been generated based on analysis and assessment for many design proposals with CSI SAP software. These data have been used later in SPSS software to develop a pure quadratic nonlinear regression model for the explicit objective function. Good correlations with a coefficient, R2, in the range from 0.88 to 0.99 have been noted between the original implicit functions and the corresponding explicit functions generated with meta-model.

Keywords: Meta-modal, objective function, steel frames, seismic analysis, design.

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11 Modeling of Masonry In-Filled R/C Frame to Evaluate Seismic Performance of Existing Building

Authors: Tarek M. Alguhane, Ayman H. Khalil, M. N. Fayed, Ayman M. Ismail

Abstract:

This paper deals with different modeling aspects of masonry infill: no infill model, Layered shell infill model, and strut infill model. These models consider the complicated behavior of the in-filled plane frames under lateral load similar to an earthquake load. Three strut infill models are used: NBCC (2005) strut infill model, ASCE/SEI 41-06 strut infill model and proposed strut infill model based on modification to Canadian, NBCC (2005) strut infill model. Pushover and modal analyses of a masonry infill concrete frame with a single storey and an existing 5-storey RC building have been carried out by using different models for masonry infill. The corresponding hinge status, the value of base shear at target displacement as well as their dynamic characteristics have been determined and compared. A validation of the structural numerical models for the existing 5-storey RC building has been achieved by comparing the experimentally measured and the analytically estimated natural frequencies and their mode shapes. This study shows that ASCE/SEI 41-06 equation underestimates the values for the equivalent properties of the diagonal strut while Canadian, NBCC (2005) equation gives realistic values for the equivalent properties. The results indicate that both ASCE/SEI 41-06 and Canadian, NBCC (2005) equations for strut infill model give over estimated values for dynamic characteristic of the building. Proposed modification to Canadian, NBCC (2005) equation shows that the fundamental dynamic characteristic values of the building are nearly similar to the corresponding values using layered shell elements as well as measured field results.

Keywords: Masonry infill, framed structures, RC buildings, non-structural elements.

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10 An Iterative Updating Method for Damped Gyroscopic Systems

Authors: Yongxin Yuan

Abstract:

The problem of updating damped gyroscopic systems using measured modal data can be mathematically formulated as following two problems. Problem I: Given Ma ∈ Rn×n, Λ = diag{λ1, ··· , λp} ∈ Cp×p, X = [x1, ··· , xp] ∈ Cn×p, where p<n and both Λ and X are closed under complex conjugation in the sense that λ2j = λ¯2j−1 ∈ C, x2j = ¯x2j−1 ∈ Cn for j = 1, ··· , l, and λk ∈ R, xk ∈ Rn for k = 2l + 1, ··· , p, find real-valued symmetric matrices D,K and a real-valued skew-symmetric matrix G (that is, GT = −G) such that MaXΛ2 + (D + G)XΛ + KX = 0. Problem II: Given real-valued symmetric matrices Da, Ka ∈ Rn×n and a real-valued skew-symmetric matrix Ga, find (D, ˆ G, ˆ Kˆ ) ∈ SE such that Dˆ −Da2+Gˆ−Ga2+Kˆ −Ka2 = min(D,G,K)∈SE (D− Da2 + G − Ga2 + K − Ka2), where SE is the solution set of Problem I and · is the Frobenius norm. This paper presents an iterative algorithm to solve Problem I and Problem II. By using the proposed iterative method, a solution of Problem I can be obtained within finite iteration steps in the absence of roundoff errors, and the minimum Frobenius norm solution of Problem I can be obtained by choosing a special kind of initial matrices. Moreover, the optimal approximation solution (D, ˆ G, ˆ Kˆ ) of Problem II can be obtained by finding the minimum Frobenius norm solution of a changed Problem I. A numerical example shows that the introduced iterative algorithm is quite efficient.

Keywords: Model updating, iterative algorithm, gyroscopic system, partially prescribed spectral data, optimal approximation.

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9 Economic Effects of Maritime Environmental Legislation in the North and Baltic Sea Area: An Exploratory Sequential Mixed Methods Approach

Authors: Thea Freese

Abstract:

Environmental legislation to protect North and Baltic Sea areas from harmful vessel-source emissions has received increased political attention in recent years. Legislative measures are expected to show positive effects on the health of the marine environment and society. At the same time, compliance might increase the costs to industry and have effects on freight rates and volumes shipped with potential negative repercussions on the environment. Building on an exploratory sequential mixed methods approach, this research project will study the economic effects of maritime environmental legislation in two phases. In Phase I, exploratory in-depth interviews were conducted with 12 experts from various stakeholder groups aiming at identifying variables influencing the relationship between environmental legislation, freight rates and volumes shipped. Influencing factors like compliance, enforcement and modal shift were identified and studied. Phase II will comprise of a quantitative study conducted with the aim of verifying the theory build in Phase I and quantifying economic effects of rules on shipping pollution. Research in this field might inform policy-makers about determinants of behaviour of ship operators in the face of the law and might further the development of a comprehensive legal system for marine environmental protection. At the present stage of research, first tentative results from the qualitative phase may be examined and open research questions to be addressed in the quantitative phase as well as possible research designs for phase II may be discussed. Input from other researchers will be highly valuable at this point.

Keywords: Clean shipping operations, compliance, maritime environmental legislation, maritime law and economics, mixed methods research, North and Baltic Sea area.

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8 Toward Indoor and Outdoor Surveillance Using an Improved Fast Background Subtraction Algorithm

Authors: A. El Harraj, N. Raissouni

Abstract:

The detection of moving objects from a video image sequences is very important for object tracking, activity recognition, and behavior understanding in video surveillance. The most used approach for moving objects detection / tracking is background subtraction algorithms. Many approaches have been suggested for background subtraction. But, these are illumination change sensitive and the solutions proposed to bypass this problem are time consuming. In this paper, we propose a robust yet computationally efficient background subtraction approach and, mainly, focus on the ability to detect moving objects on dynamic scenes, for possible applications in complex and restricted access areas monitoring, where moving and motionless persons must be reliably detected. It consists of three main phases, establishing illumination changes invariance, background/foreground modeling and morphological analysis for noise removing. We handle illumination changes using Contrast Limited Histogram Equalization (CLAHE), which limits the intensity of each pixel to user determined maximum. Thus, it mitigates the degradation due to scene illumination changes and improves the visibility of the video signal. Initially, the background and foreground images are extracted from the video sequence. Then, the background and foreground images are separately enhanced by applying CLAHE. In order to form multi-modal backgrounds we model each channel of a pixel as a mixture of K Gaussians (K=5) using Gaussian Mixture Model (GMM). Finally, we post process the resulting binary foreground mask using morphological erosion and dilation transformations to remove possible noise. For experimental test, we used a standard dataset to challenge the efficiency and accuracy of the proposed method on a diverse set of dynamic scenes.

Keywords: Video surveillance, background subtraction, Contrast Limited Histogram Equalization, illumination invariance, object tracking, object detection, behavior understanding, dynamic scenes.

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7 Multimodal Biometric System Based on Near- Infra-Red Dorsal Hand Geometry and Fingerprints for Single and Whole Hands

Authors: Mohamed K. Shahin, Ahmed M. Badawi, Mohamed E. M. Rasmy

Abstract:

Prior research evidenced that unimodal biometric systems have several tradeoffs like noisy data, intra-class variations, restricted degrees of freedom, non-universality, spoof attacks, and unacceptable error rates. In order for the biometric system to be more secure and to provide high performance accuracy, more than one form of biometrics are required. Hence, the need arise for multimodal biometrics using combinations of different biometric modalities. This paper introduces a multimodal biometric system (MMBS) based on fusion of whole dorsal hand geometry and fingerprints that acquires right and left (Rt/Lt) near-infra-red (NIR) dorsal hand geometry (HG) shape and (Rt/Lt) index and ring fingerprints (FP). Database of 100 volunteers were acquired using the designed prototype. The acquired images were found to have good quality for all features and patterns extraction to all modalities. HG features based on the hand shape anatomical landmarks were extracted. Robust and fast algorithms for FP minutia points feature extraction and matching were used. Feature vectors that belong to similar biometric traits were fused using feature fusion methodologies. Scores obtained from different biometric trait matchers were fused using the Min-Max transformation-based score fusion technique. Final normalized scores were merged using the sum of scores method to obtain a single decision about the personal identity based on multiple independent sources. High individuality of the fused traits and user acceptability of the designed system along with its experimental high performance biometric measures showed that this MMBS can be considered for med-high security levels biometric identification purposes.

Keywords: Unimodal, Multi-Modal, Biometric System, NIR Imaging, Dorsal Hand Geometry, Fingerprint, Whole Hands, Feature Extraction, Feature Fusion, Score Fusion

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6 Income Inequality and the Poverty of Youth in the Douala Metropolis of Cameroon

Authors: Nanche Billa Robert

Abstract:

More and more youth are doubtful of making a satisfactory labour market transition because of the present global economic instability and this is more so in Africa of the Sahara and metropolis like Douala. We use the explanatory sequential mixed method: in the first phase we randomly administered 610 questionnaires in the Douala metropolis respecting the population size of each division and its gender composition. We constructed the questionnaire using the desired values for living a comfortable life in Douala. In the second phase, we purposefully selected and interviewed 50 poor youth in order to explain in detail the initial quantitative results. We obtain the following result: The modal income class is 24,000-74,000 frs Central Africa Franc (CFA) and about 67% of the youth of the Douala metropolis earn below 75,000 frs CFA. They earn only 31.02% of the total income. About 85.7% earn below 126,000 frs CFA and about 92.14% earn below 177,000 frs CFA. The poverty-line is estimated at 177,000 frs CFA per month based on the desired predominant values in Douala and only about 9% of youth earn this sum, therefore, 91% of the youth are poor. We discovered that the salary a youth earns influences his level of poverty. Low income earners eat once or twice per day, rent low-standard houses of below 20,000 frs, are dependent and possess very limited durable goods, consult traditional doctors when they are sick, sleep and gamble during their leisure time. Intermediate income earners feed themselves either twice or thrice per day, eat healthy meals weekly, possess more durable goods, are independent, gamble and drink during their leisure time. High income earners feed themselves at least thrice per day, eat healthy food daily, inhabit high quality and expensive houses, are more stable by living longer in their neighbourhoods, like travelling and drinking during their leisure time. Unsalaried youth, are students, housewives or unemployed youth, they eat four times per day, take healthy meals daily, weekly, fortnightly or occasionally, are dependent or homeless depending on whether they are students or unemployed youth. The situation of the youth can be ameliorated through investing in the productive sector and promoting entrepreneurship as well as formalizing the informal sector.

Keywords: Income, inequality, poverty, metropolis.

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5 Application of Transportation Models for Analysing Future Intercity and Intracity Travel Patterns in Kuwait

Authors: Srikanth Pandurangi, Basheer Mohammed, Nezar Al Sayegh

Abstract:

In order to meet the increasing demand for housing care for Kuwaiti citizens, the government authorities in Kuwait are undertaking a series of projects in the form of new large cities, outside the current urban area. Al Mutlaa City located to the north-west of the Kuwait Metropolitan Area is one such project out of the 15 planned new cities. The city accommodates a wide variety of residential developments, employment opportunities, commercial, recreational, health care and institutional uses. This paper examines the application of comprehensive transportation demand modeling works undertaken in VISUM platform to understand the future intracity and intercity travel distribution patterns in Kuwait. The scope of models developed varied in levels of detail: strategic model update, sub-area models representing future demand of Al Mutlaa City, sub-area models built to estimate the demand in the residential neighborhoods of the city. This paper aims at offering model update framework that facilitates easy integration between sub-area models and strategic national models for unified traffic forecasts. This paper presents the transportation demand modeling results utilized in informing the planning of multi-modal transportation system for Al Mutlaa City. This paper also presents the household survey data collection efforts undertaken using GPS devices (first time in Kuwait) and notebook computer based digital survey forms for interviewing representative sample of citizens and residents. The survey results formed the basis of estimating trip generation rates and trip distribution coefficients used in the strategic base year model calibration and validation process.

Keywords: GPS based household surveys, transportation infrastructure, origin-destination trip matrices, traffic forecasts, transportation demand modeling, travel behavior patterns.

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4 Monetary Evaluation of Dispatching Decisions in Consideration of Mode Choice Models

Authors: Marcel Schneider, Nils Nießen

Abstract:

Microscopic simulation tool kits allow for consideration of the two processes of railway operations and the previous timetable production. Block occupation conflicts on both process levels are often solved by using defined train priorities. These conflict resolutions (dispatching decisions) generate reactionary delays to the involved trains. The sum of reactionary delays is commonly used to evaluate the quality of railway operations, which describes the timetable robustness. It is either compared to an acceptable train performance or the delays are appraised economically by linear monetary functions. It is impossible to adequately evaluate dispatching decisions without a well-founded objective function. This paper presents a new approach for the evaluation of dispatching decisions. The approach uses mode choice models and considers the behaviour of the end-customers. These models evaluate the reactionary delays in more detail and consider other competing modes of transport. The new approach pursues the coupling of a microscopic model of railway operations with the macroscopic choice mode model. At first, it will be implemented for railway operations process but it can also be used for timetable production. The evaluation considers the possibility for the customer to interchange to other transport modes. The new approach starts to look at rail and road, but it can also be extended to air travel. The result of mode choice models is the modal split. The reactions by the end-customers have an impact on the revenue of the train operating companies. Different purposes of travel have different payment reserves and tolerances towards late running. Aside from changes to revenues, longer journey times can also generate additional costs. The costs are either time- or track-specific and arise from required changes to rolling stock or train crew cycles. Only the variable values are summarised in the contribution margin, which is the base for the monetary evaluation of delays. The contribution margin is calculated for different possible solutions to the same conflict. The conflict resolution is optimised until the monetary loss becomes minimal. The iterative process therefore determines an optimum conflict resolution by monitoring the change to the contribution margin. Furthermore, a monetary value of each dispatching decision can also be derived.

Keywords: Choice of mode, monetary evaluation, railway operations, reactionary delays.

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3 Frequency Response of Complex Systems with Localized Nonlinearities

Authors: E. Menga, S. Hernandez

Abstract:

Finite Element Models (FEMs) are widely used in order to study and predict the dynamic properties of structures and usually, the prediction can be obtained with much more accuracy in the case of a single component than in the case of assemblies. Especially for structural dynamics studies, in the low and middle frequency range, most complex FEMs can be seen as assemblies made by linear components joined together at interfaces. From a modelling and computational point of view, these types of joints can be seen as localized sources of stiffness and damping and can be modelled as lumped spring/damper elements, most of time, characterized by nonlinear constitutive laws. On the other side, most of FE programs are able to run nonlinear analysis in time-domain. They treat the whole structure as nonlinear, even if there is one nonlinear degree of freedom (DOF) out of thousands of linear ones, making the analysis unnecessarily expensive from a computational point of view. In this work, a methodology in order to obtain the nonlinear frequency response of structures, whose nonlinearities can be considered as localized sources, is presented. The work extends the well-known Structural Dynamic Modification Method (SDMM) to a nonlinear set of modifications, and allows getting the Nonlinear Frequency Response Functions (NLFRFs), through an ‘updating’ process of the Linear Frequency Response Functions (LFRFs). A brief summary of the analytical concepts is given, starting from the linear formulation and understanding what the implications of the nonlinear one, are. The response of the system is formulated in both: time and frequency domain. First the Modal Database is extracted and the linear response is calculated. Secondly the nonlinear response is obtained thru the NL SDMM, by updating the underlying linear behavior of the system. The methodology, implemented in MATLAB, has been successfully applied to estimate the nonlinear frequency response of two systems. The first one is a two DOFs spring-mass-damper system, and the second example takes into account a full aircraft FE Model. In spite of the different levels of complexity, both examples show the reliability and effectiveness of the method. The results highlight a feasible and robust procedure, which allows a quick estimation of the effect of localized nonlinearities on the dynamic behavior. The method is particularly powerful when most of the FE Model can be considered as acting linearly and the nonlinear behavior is restricted to few degrees of freedom. The procedure is very attractive from a computational point of view because the FEM needs to be run just once, which allows faster nonlinear sensitivity analysis and easier implementation of optimization procedures for the calibration of nonlinear models.

Keywords: Frequency response, nonlinear dynamics, structural dynamic modification, softening effect, rubber.

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2 Archaic Ontologies Nowadays: Music of Rituals

Authors: Luminiţa Duţică, Gheorghe Duţică

Abstract:

Many of the interrogations or dilemmas of the contemporary world found the answer in what was generically called the appeal to matrix. This genuine spiritual exercise of re-connection of the present to origins, to the primary source, revealed the ontological condition of timelessness, ahistorical, immutable (epi)phenomena, of those pure essences concentrated in the archetypal-referential layer of the human existence. The musical creation was no exception to this trend, the impasse generated by the deterministic excesses of the whole serialism or, conversely, by some questionable results of the extreme indeterminism proper to the avant-garde movements, stimulating the orientation of many composers to rediscover a universal grammar, as an emanation of a new ‘collective’ order (reverse of the utopian individualism). In this context, the music of oral tradition and therefore the world of the ancient modes represented a true revelation for the composers of the twentieth century, who were suddenly in front of some unsuspected (re)sources, with a major impact on all levels of edification of the musical work: morphology, syntax, timbrality, semantics etc. For the contemporary Romanian creators, the music of rituals, existing in the local archaic culture, opened unsuspected perspectives for which it meant to be a synthetic, inclusive and recoverer vision, where the primary (archetypal) genuine elements merge with the latest achievements of language of the European composers. Thus, anchored in a strong and genuine modal source, the compositions analysed in this paper evoke, in a manner as modern as possible, the atmosphere of some ancestral rituals such as: the invocation of rain during the drought (Paparudele, Scaloianul), funeral ceremony (Bocetul), traditions specific to the winter holidays and new year (Colinda, Cântecul de stea, Sorcova, Folklore traditional dances) etc. The reactivity of those rituals in the sound context of the twentieth century meant potentiating or resizing the archaic spirit of the primordial symbolic entities, in terms of some complexity levels generated by the technique of harmonies of chordal layers, of complex aggregates (gravitational or non-gravitational, geometric), of the mixture polyphonies and with global effect (group, mass), by the technique of heterophony, of texture and cluster, leading to the implementation of some processes of collective improvisation and instrumental theatre.

Keywords: Archetype, improvisation, instrumental theatre, polyphony, ritual.

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1 Generative Syntaxes: Macro-Heterophony and the Form of ‘Synchrony’

Authors: Luminiţa Duţică, Gheorghe Duţică

Abstract:

One of the most powerful language innovation in the twentieth century music was the heterophony–hypostasis of the vertical syntax entered into the sphere of interest of many composers, such as George Enescu, Pierre Boulez, Mauricio Kagel, György Ligeti and others. The heterophonic syntax has a history of its growth, which means a succession of different concepts and writing techniques. The trajectory of settling this phenomenon does not necessarily take into account the chronology: there are highly complex primary stages and advanced stages of returning to the simple forms of writing. In folklore, the plurimelodic simultaneities are free or random and originate from the (unintentional) differences/‘deviations’ from the state of unison, through a variety of ornaments, melismas, imitations, elongations and abbreviations, all in a flexible rhythmic and non-periodic/immeasurable framework, proper to the parlando-rubato rhythmics. Within the general framework of the multivocal organization, the heterophonic syntax in elaborate (academic) version has imposed itself relatively late compared with polyphony and homophony. Of course, the explanation is simple, if we consider the causal relationship between the sound vocabulary elements – in this case, the modalism – and the typologies of vertical organization appropriate for it. Therefore, adding up the ‘classic’ pathway of the writing typologies (monody – polyphony – homophony), heterophony - applied equally to the structures of modal, serial or synthesis vocabulary – reclaims necessarily an own macrotemporal form, in the sense of the analogies enshrined by the evolution of the musical styles and languages: polyphony→fugue, homophony→sonata. Concerned about the prospect of edifying a new musical ontology, the composer Ştefan Niculescu experienced – along with the mathematical organization of heterophony according to his own original methods – the possibility of extrapolation of this phenomenon in macrostructural plan, reaching this way to the unique form of ‘synchrony’. Founded on coincidentia oppositorum principle (involving the ‘one-multiple’ binom), the sound architecture imagined by Ştefan Niculescu consists in one (temporal) model / algorithm of articulation of two sound states: 1. monovocality state (principle of identity) and 2. multivocality state (principle of difference). In this context, the heterophony becomes an (auto)generative mechanism, with macrotemporal amplitude, strategy that will be grown by the composer, practically throughout his creation (see the works: Ison I, Ison II, Unisonos I, Unisonos II, Duplum, Triplum, Psalmus, Héterophonies pour Montreux (Homages to Enescu and Bartók etc.). For the present demonstration, we selected one of the most edifying works of Ştefan Niculescu – Simphony II, Opus dacicum – where the form of (heterophony-)synchrony acquires monumental-symphonic features, representing an emblematic case for the complexity level achieved by this type of vertical syntax in the twentieth century music.

Keywords: Heterophony, modalism, serialism, synchrony, syntax.

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