Ultraspherical polynomials approach to the study of third-order non-linear systems

In this study, the Krylov-Bogoliubov-Mitropolskii-Popov asymptotic method is used to determine the transient response of third-order non-linear systems. Instead of averaging the non-linear functions over a cycle, they are expanded in ultraspherical polynomials and the constant term is retained. The resulting equations are solved to obtain the approximate solution. A numerical example is considered and the approximate solution is compared with the digital solution. The results show that there is good agreement between the two values.

Study of third-order non-linear systems- Variation of parameters approach

In this paper, the transient response of a third-order non-linear system is obtained by first reducing the given third-order equation to three first-order equations by applying the method of variation of parameters. On the assumption that the variations of amplitude and phase are small, the functions are expanded in ultraspherical polynomials. The expansion is restricted to the constant term. The resulting equations are solved to obtain the response of the given third-order system. A numerical example is considered to illustrate the method. The results show that the agreement between the approximate and digital solution is good thus vindicating the approximation.

Development of a transient gradient enhanced non local continuum damage mechanics model for masonry

Due to the advent of varied types of masonry systems a comprehensive failure mechanism of masonry essential for the understanding of its behaviour is impossible to be determined from experimental testing. As masonry is predominantly used in wall structures a biaxial stress state dominates its failure mechanism. Biaxial testing will therefore be necessary for each type of masonry, which is expensive and time consuming. A computational method would be advantageous; however masonry is complex to model which requires advanced computational modelling methods. This thesis has formulated a damage mechanics inspired modelling method and has shown that the method effectively determines the failure mechanisms and deformation characteristics of masonry under biaxial states of loading.

Vibration of Non-Uniform Thin-Walled Beams of Arbitrary Shape

A generalised theory for the natural vibration of non-uniform thin-walled beams of arbitrary cross-sectional geometry is proposed. The governing equations are obtained as four partial, linear integro-differential equations. The corresponding boundary conditions are also obtained in an integro-differential form. The formulation takes into account the effect of longitudinal inertia and shear flexibility. A method of solution is presented. Some numerical illustrations and an exact solution are included.

A differential transformation technique for the analysis of a class of non-linear time varying systems

The scope of the differential transformation technique, developed earlier for the study of non-linear, time invariant systems, has been extended to the domain of time-varying systems by modifications to the differential transformation laws proposed therein. Equivalence of a class of second-order, non-linear, non-autonomous systems with a linear autonomous model of second order is established through these transformation laws. The feasibility of application of this technique in obtaining the response of such non-linear time-varying systems is discussed.

Construction of stability multipliers for non-linear feedback systems

This paper is concerned with the analysis of the absolute stability of a non-linear autonomous system which consists of a single non-linearity belonging to a particular class, in an otherwise linear feedback loop. It is motivated from the earlier Popovlike frequency-domain criteria using the ' multiplier ' eoncept and involves the construction of ' stability multipliers' with prescribed phase characteristics. A few computer-based methods by which this problem can be solved are indicated and it is shown that this constitutes a stop-by-step procedure for testing the stability properties of a given system.

Evaluation of k-epsilon and RNG turbulence models for confined swirling and non-swirling flow

In a very recent study [1] the Renormalisation Group (RNG) turbulence model was used to obtain flow predictions in a strongly swirling quarl burner, and was found to perform well in predicting certain features that are not well captured using less sophisticated models of turbulence. The implication is that the RNG approach should provide an economical and reliable tool for the prediction of swirling flows in combustor and furnace geometries commonly encountered in technological applications. To test this hypothesis the present work considers flow in a model furnace for which experimental data is available [2]. The essential features of the flow which differentiate it from the previous study [1] are that the annular air jet entry is relatively narrow and the base wall of the cylindrical furnace is at 90 degrees to the inlet pipe. For swirl numbers of order 1 the resulting flow is highly complex with significant inner and outer recirculation regions. The RNG and standard k-epsilon models are used to model the flow for both swirling and non-swirling entry jets and the results compared with experimental data [2]. Near wall viscous effects are accounted for in both models via the standard wall function formulation [3]. For the RNG model, additional computations with grid placement extending well inside the near wall viscous-affected sublayer are performed in order to assess the low Reynolds number capabilities of the model.

Nonradial directional performance measurement with undesirable outputs: An application to OECD and Non-OECD countries

The objective of this paper is to provide a more comprehensive e±ciency measure to estimate the performance of OECD and non-OECD countries. A Russell directional distance function that appropriately credits the decision-making unit not only for increase in desirable outputs but also for the decrease of undesirable outputs is derived from the proposed weighted Russell directional distance model. The method was applied to a panel of 116 countries from 1992 to 2010. This framework also decomposes the comprehensive efficiency measure into individual input/ output components' inefficiency scores that are useful for policy making. The results reveal that the OECD countries perform better than the non-OECD countries in overall, goods,labor and capital efficiencies, but worse in bad and energy efficiencies.

Korteweg-De Vries Equation for Non-Linear Ion-Acoustic Waves in a Plasma with Negative Ions

The theoretical analysis, based on the perturbation technique, of ion-acoustic waves in the vicinity of a Korteweg-de Vries (K-dV) equation derived in a plasma with some negative ions has been made. The investigation shows that the negative ions in plasma with isothermal electrons introduced a critical concentration at which the ion-acoustic wave plays an important role of wave-breaking and forming a precursor while the plasma with non-isothermal electrons has no such singular behaviour of the wave. These two distinct features of ion waves lead to an overall different approach of present study of ion-waves. A distinct feature of non-uniform transition from the nonisothermal case to isothermal case has been shown. Few particular plasma models have been chosen to show the characteristics behaviour of the ion-waves existing in different cases

Reinventing Nordic Openness : Transparency and State Information in Finland

The study explores new ideational changes in the information strategy of the Finnish state between 1998 and 2007, after a juncture in Finnish governing in the early 1990s. The study scrutinizes the economic reframing of institutional openness in Finland that comes with significant and often unintended institutional consequences of transparency. Most notably, the constitutional principle of publicity (julkisuusperiaate), a Nordic institutional peculiarity allowing public access to state information, is now becoming an instrument of economic performance and accountability through results. Finland has a long institutional history in the publicity of government information, acknowledged by law since 1951. Nevertheless, access to government information became a policy concern in the mid-1990s, involving a historical narrative of openness as a Nordic tradition of Finnish governing Nordic openness (pohjoismainen avoimuus). International interest in transparency of governance has also marked an opening for institutional re-descriptions in Nordic context. The essential added value, or contradictory term, that transparency has on the Finnish conceptualisation of governing is the innovation that public acts of governing can be economically efficient. This is most apparent in the new attempts at providing standardised information on government and expressing it in numbers. In Finland, the publicity of government information has been a concept of democratic connotations, but new internationally diffusing ideas of performance and national economic competitiveness are discussed under the notion of transparency and its peer concepts openness and public (sector) information, which are also newcomers to Finnish vocabulary of governing. The above concepts often conflict with one another, paving the way to unintended consequences for the reforms conducted in their name. Moreover, the study argues that the policy concerns over openness and public sector information are linked to the new drive for transparency. Drawing on theories of new institutionalism, political economy, and conceptual history, the study argues for a reinvention of Nordic openness in two senses. First, in referring to institutional history, the policy discourse of Nordic openness discovers an administrative tradition in response to new dilemmas of public governance. Moreover, this normatively appealing discourse also legitimizes the new ideational changes. Second, a former mechanism of democratic accountability is being reframed with market and performance ideas, mostly originating from the sphere of transnational governance and governance indices. Mobilizing different research techniques and data (public documents of the Finnish government and international organizations, some 30 interviews of Finnish civil servants, and statistical time series), the study asks how the above ideational changes have been possible, pointing to the importance of nationalistically appealing historical narratives and normative concepts of governing. Concerning institutional developments, the study analyses the ideational changes in central steering mechanisms (political, normative and financial steering) and the introduction of budget transparency and performance management in two cases: census data (Population Register Centre) and foreign political information (Ministry for Foreign Affairs). The new policy domain of governance indices is also explored as a type of transparency. The study further asks what institutional transformations are to be observed in the above cases and in the accountability system. The study concludes that while the information rights of citizens have been reinforced and recalibrated during the period under scrutiny, there has also been a conversion of institutional practices towards economic performance. As the discourse of Nordic openness has been rather unquestioned, the new internationally circulating ideas of transparency and the knowledge economy have entered this discourse without public notice. Since the mid 1990s, state registry data has been perceived as an exploitable economic resource in Finland and in the EU public sector information. This is a parallel development to the new drive for budget transparency in organisations as vital to the state as the Population Register Centre, which has led to marketization of census data in Finland, an international exceptionality. In the Finnish Ministry for Foreign Affairs, the post-Cold War rhetorical shift from secrecy to performance-driven openness marked a conversion in institutional practices that now see information services with high regards. But this has not necessarily led to the increased publicity of foreign political information. In this context, openness is also defined as sharing information with select actors, as a trust based non-public activity, deemed necessary amid the global economic competition. Regarding accountability system, deliberation and performance now overlap, making it increasingly difficult to identify to whom and for what the public administration is accountable. These evolving institutional practices are characterised by unintended consequences and paradoxes. History is a paradoxical component in the above institutional change, as long-term institutional developments now justify short-term reforms.

Non-linear vibrations of non-unifo with concentrated masses

Large amplitude oscillations of cantilevered beams of variable cross-section, with concentrated masses along the span, are studied in this paper. The governing non-linear ordinary differential equation is solved by an averaging technique to obtain approximate solutions. Stability boundaries of the response are also investigated.

Decoupling in non-linear systems with two degrees of freedom

The problem of decoupling a class of non-linear two degrees of freedom systems is studied. The coupled non-linear differential equations of motion of the system are shown to be equivalent to a pair of uncoupled equations. This equivalence is established through transformation techniques involving the transformation of both the dependent and independent variables. The sufficient conditions on the form of the non-linearity, for the case wherein the transformed equations are linear, are presented. Several particular cases of interest are also illustrated.

Non-linear systems with quadratic and cubic damping - an analytical approach

The possible equivalence of second-order non-linear systems having quadratic and cubic damping with third-order linear systems is studied in this paper. It is shown that this equivalence can be established through transformation techniques under certain constraints on the form of the non-linearity of the given system.

Influence of adhesive non-linearities on the performance and optimal length of adhesive bonded joints

An analytical study for the static strength of adhesive lap joints is presented. The earlier solutions of Volkersen [i], DeBruyne[2] and others were limited to linear adhesives. The influence of adhesive non-linearity was first considered by Grimes' et al[3] and Dickson et al [4]. Recently Hart-Smith[5] successfully introduced elastic-plastic behaviour of the adhesive. In the present study the problem is formulated for general non-linear adhesive behaviour and an efficient numerical algorithm is written for the solution. Bilinear and trilinear models for the nonlinearity yield closed form analytical solutions.

Application of Laplace transform technique to the solution of certain third-order non-linear systems

A number of papers have appeared on the application of operational methods and in particular the Laplace transform to problems concerning non-linear systems of one kind or other. This, however, has met with only partial success in solving a class of non-linear problems as each approach has some limitations and drawbacks. In this study the approach of Baycura has been extended to certain third-order non-linear systems subjected to non-periodic excitations, as this approximate method combines the advantages of engineering accuracy with ease of application to such problems. Under non-periodic excitations the method provides a procedure for estimating quickly the maximum response amplitude, which is important from the point of view of a designer. Limitations of such a procedure are brought out and the method is illustrated by an example taken from a physical situation.