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Two different methods of analysis were developed in order to clarify the phenomenon of paper flutter. One of these is a flutter simulation using a Navier–Stokes code (N–S simulation). N–S simulation was used to determine the unsteady lift force, the amplitude of flutter, and the air-flow around a paper sheet, by means of a time-marching scheme. The other form of analysis is based on a potential-flow analysis of an oscillating thin airfoil via an eigenvalue analysis for determining stability. The flutter speeds and flutter modes obtained by each method are consistent. Aspects of the behavior of paper flutter that had not been clarified in the experimental analysis were clarified by potential flow analysis. From the results of this study, it was shown that potential flow analysis is very convenient and adequate for a parametric study of this problem.

Fluidelastic instability is a key issue in steam generator tube arrays subjected in two-phase flow. Lots of experimental analyses were conducted on fluidelastic instability of a tube array subjected to air-water cross-flow. However, there is seldom theoretical analysis to calculate the critical velocity. Therefore, considering the effect of two-phase flow, the fluidelastic instability of a rotated triangular tube array was studied in this paper. A mathematical model of a tube array with unsteady fluid force model was set up. A program based on the model was written, and an experiment was carried out to verify the correctness of the program. The results of this program were in good agreement with the experimental data. Using this program, the critical velocity of fluid-elastic instability considering the effect of two-phase flow was determined by the eigenvalue analysis. This paper investigated the critical velocities of fluid-elastic instability for void fraction ranging from 0% to 90% with five tube natural frequencies, respectively. The results show that void fraction and tube natural frequency are the key factors in fluidelastic instability, which have an obvious effect on the critical velocity of fluidelastic instability.

The present study investigates the effect of multiple dynamic absorbers on chatter generated in the end milling operations by performing stability analysis and a cutting test. The dynamic absorbers proposed in the present paper are attached to a collet chuck in order to suppress tool chatter caused by the bending vibration of the tool and spindle system. The dynamic milling model is considered to have two orthogonal degrees of freedom. The dynamic absorbers, which have identical mass, damping ratio, and natural frequency, are assumed to have a single degree of freedom that rotates with a tool and spindle system. In the present paper, stability analyses are performed by means of complex eigenvalue analysis for each angular immersion of the cutting edge in order to investigate the effect of the dynamic absorbers on the stability of the dynamic milling model. The optimal natural frequency and damping ratio of the dynamic absorbers to maximize the chatter-free axial depth of cut are shown to vary with spindle speed. Furthermore, the effect of the dynamic absorbers on chatter is validated by a cutting test, and the experimental results are confirmed to agree qualitatively with the analytical results.

In this paper a novel supplementary subsynchronous damping controller (SSDC) is proposed for the STATic synchronous COMpensator (STATCOM) which is capable of damping out subsynchronous oscillations in power system with series compensated transmission lines. An auxiliary subsynchronous damping controller (SSDC) for a STATCOM using the generator rotor speed deviation signal as the stabilizing signal has been designed to damp subsynchronous oscillations. Eigenvalue analysis and transient simulations of detailed nonlinear system are considered to investigate the performance of the controller. Robustness of the controller has been analyzed by facing the system with disturbances leading to significant changes in generator operating point. This paper deals with a cascaded multilevel converter model, which is a 48-pulse (three levels) source converter. The IEEE Second Benchmark (SBM) model is considered for the analysis and the complete digital simulation of the STATCOM within the power system is performed in the MATLAB/Simulink environment.

This paper proposes a method for PSS parameter tuning. The proposed method is based on the system identification using a Kalman filter. To eliminate the influence of inaccuracies of the mathematical model due to incomplete data of the system parameters, this paper proposes a procedure for identifying system parameters based on a Kalman filter. The identified system is the basis for determining the eigenvalue sensitivity function. PSS tuning is carried out based on the eigenvalue sensitivity analysis of changes of PSS parameters. In order to obtain the eigenvalue sensitivity function on the PSS parameter in a wider range of parameter values, it has been proposed to determine eigenvalues on the basis of the Bairstow method for solving polynomial equations. The entire procedure can be applied on-line, so the PSS structure and settings can be adaptive. Experimental tests carried out on a synchronous generator connected to an AC system demonstrate the effectiveness of the proposed method. Performance of the PSS tuned by using the proposed method was compared with the performance of the PSS tuned by using eigenvalue sensitivity.

In this paper, we determine periodicity of quantum walks defined by mixed paths and mixed cycles. By the spectral mapping theorem of quantum walks, consideration of periodicity is reduced to eigenvalue analysis of $\eta$-Hermitian adjacency matrices. First, we investigate coefficients of the characteristic polynomials of $\eta$-Hermitian adjacency matrices. We show that the characteristic polynomials of mixed trees and their underlying graphs are same. We also define $n+1$ types of mixed cycles and show that every mixed cycle is switching equivalent to one of them. We use these results to discuss periodicity. We show that the mixed paths are periodic for any $\eta$. In addition, we provide a necessary and sufficient condition for a mixed cycle to be periodic and determine their periods., Comment: 22 pages, 12 figures

This paper studies influence of control system dynamics on the small-signal stability of modular multilevel converter (MMC) based multi-terminal DC (MTDC) transmission system. The small signal model is derived based on the state–space model of an MMC-based MTDC. Eigenvalue analysis and participation factor analysis are applied to study the inherent oscillatory modes of MMC-based MTDC transmission systems. The impacts of control system parameters on small-signal stability of the system are investigated through sensitivity analysis. The study shows that the control systems strongly affected the small signal stability of the MMC-based MTDC and the d-axis proportional gains in d–q decoupling main controllers have great impact on system stability, which needs to be properly selected for stability enhancement.

In this paper, an extensive numerical study is performed with the aim to investigate the elastic buckling behavior of simply supported cylindrically curved steel panels subjected to a pure shear load. The main objective is to understand the influence of geometrical parameters, such as curvature and aspect ratio, but also of the edge in-plane constraints. Finally, a new formula is proposed, which allows simple and accurate estimation of the critical shear stress of unstiffened curved panels with three different types of edge constraints, for various curvatures (1

This paper presents a comprehensive small-signal stability analysis for synchronous generator (SG)-based microgrids (MGs) considering the control type of SGs and wide range of loading condition. The original aim is to evaluate the effect of loading conditions on the small-signal stability of droop-controlled and PQ-controlled SGs which has not been adequately addressed in the literature. To this purpose, complete state–space small-signal model of a typical medium voltage AC MG involving both droop-controlled and PQ-controlled SGs is developed. This facilitates stability studies by means of eigenvalue analysis. Results show that the small-signal stability behavior of droop-controlled SGs is different from that of PQ-controlled SGs. It is found that droop-controlled SGs show weaker stability or even instability in light loading condition. It is found that operation of PQ-controlled SGs in the presence of droop-controlled SGs can result in better stability of SG-based MG at light loading conditions. Effect of reference powers of PQ-controlled SGs on small-signal stability is also investigated. Moreover, the effect of Power System Stabilizer (PSS) on the damping of the weak stability or instability observed in low loading conditions of droop-controlled SG-based MGs is investigated. Time-domain simulations are used in order to verify the proposed theoretical analysis.

In this paper, a new two-sided looped-functional is introduced for stability analysis of sampled-data systems. The functional fully utilizes the information on both the intervals x ( t ) to x ( t k ) and x ( t ) to x ( t k + 1 ) . Based on the two-sided functional, an improved stability condition is derived in the form of linear matrix inequality (LMI). Numerical examples show that the result computed by the presented condition approximates nearly the theoretical bound (bound obtained by eigenvalue analysis) and outperforms substantially others in the existing literature.

This paper presents a study on amplitude death in nonlinear coupled oscillators containing fractional derivatives. Analytical criterion for amplitude death region is obtained by eigenvalue analysis and verified by numerical results. It is found that amplitude death regions can be enlarged to a large extent by fractional derivatives. For this reason, amplitude death can be detected in fractional Stuart–Landau systems with weak coupling strength and low frequency, whereas it never appears in integer-order systems. Interestingly, the widening of amplitude death region induced by fractional derivative is shared by a variety of oscillators with different types of coupling mechanisms. An interpretation for the underlying mechanism of this phenomenon is briefly addressed, based on which we further suggest a coupling organization leading to amplitude death only in fractional oscillators.

Small signal stability of permanent magnet synchronous generator (PMSG)-based wind turbines connected to the power grid should be studied properly in order to facilitate damping strategy design. In this paper, unified small-signal models for different types of PMSGs are developed to study their small-signal stability. The models are composed of mechanical systems, electrical systems and control systems. A two-mass shaft model for the mechanical system is provided to analyze the dynamic and steady-state behaviors of the wind turbine and generator rotor. Meanwhile, PMSG, converter system and transmission line are separately modeled to build unified small-signal models for three PMSG-based wind turbine generator systems (WTGS). Then, based on unified small-signal models, eigenvalue analysis is conducted to determine the relation between different oscillation modes and state variables through calculating participation factors. With modal analysis, the developed small signal models are able to find out all types of oscillation modes for PMSGs connected to the power grid, which are subsynchronous oscillation (SSO), subsynchronous control interaction (SSCI) and low-frequency oscillation, including frequency and damping of each oscillation mode. Different initial values of the small signal models can influence both frequencies and damping ratios of oscillation modes, which lay basis for further damping strategy study.

In this paper, we propose to analyze stable and unstable modes of black-box image denoisers through nonlinear eigenvalue analysis. We aim to find input images for which the denoiser output is proportional to the input. We treat this as a generalized nonlinear eigenproblem. Potential implications are wide, as most image processing algorithms can be viewed as black-box operators. We introduce a generalized nonlinear power-method to solve eigenproblems for such operators. This allows us to reveal stable modes of the denoiser: optimal inputs, achieving superior PSNR in noise removal. Analogously to the linear case, such stable modes show coarse structures and correspond to large eigenvalues. We also provide a method to generate unstable modes, which the denoiser suppresses strongly, which are textural with small eigenvalues. We validate the method using total-variation (TV) and demonstrate it on the EPLL (Zoran–Weiss) and the Non-local means denoisers. Finally, we suggest an encryption–decryption application.

This paper presents a finite-element (FE) investigation on the axial compressive capacity of aluminium alloy circular hollow sections (CHSs) with circular holes. The geometrical and material non-linearities were considered in the finite-element analysis (FEA). Two consecutive steps including an eigenvalue analysis and a load-displacement non-linear analysis were performed in the FEA. The FE models were validated against the test results reported by the first author in a previous study. The validated FE models were used to conduct an extensive parametric study comprising 300 FE models, to investigate the effects of five geometrical parameters on axial compressive capacity: the wall thickness, overall length, the diameter, and the quantity and location of the circular through-holes. In addition, a comparison was performed between the FEA strengths and design strengths calculated using the design formulae of American Design Manual (AA), European Code (EC9), Australian/New Zealand Standard (AS/NZS), Chinese Code for imperforated members, and North American Specification (NAS). Moreover, the FEA strengths were compared against the design strengths calculated from the proposed design guidelines of Dhanalakshmi and Shanmugam, Shanmugam et al., Shanmugam and Dhanalakshmi, and Moen and Schafer for cold-formed steel (CFS) sections with holes. The comparison of design strengths against FEA results showed that the current design formulae for CFS perforated sections are not suitable for aluminium alloy CHSs with circular holes. Therefore, new design equations were proposed based on the current design formulae that use effective area method (EAM) by considering the influences of key geometrical parameters.

In this paper, we consider a generalized indefinite block triangular preconditioner for the generalized saddle point problems. The eigenvalue analysis of the preconditioned matrix is given, which generalizes the existing results in the literature. Some corrections to the theoretical or numerical results in the previously published works are also presented. Numerical experiments are provided to confirm the bounds for the eigenvalues of the preconditioned matrix, and illustrate the efficiency of the preconditioned GMRES.

In this paper, a modified eigen-buckling algorithm based on eigenvalue analysis was presented for evaluating the in-plane buckling strength of parabolic steel arch bridges. The buckling strength of parabolic arches under uniformly distributed vertical loads was studied. The slenderness parameter was modified to unify the buckling curves. Parametric analysis was carried out to study the applicability of the new algorithm. Finally, a case study regarding the bearing capacity of a steel arch bridge was performed to verify the proposed method. The results showed that the influences of geometric imperfections, rise-to-span ratio, and material yield strength of parabolic arches were taken into account by modifying the slenderness parameter. The buckling strength results of the arches using the modified dimensionless slenderness agreed very well with the straight column buckling curves in the specifications. The modified eigen-buckling algorithm provided very high accuracy in buckling strength assessment for parabolic steel arch bridges when the span was less than 200 m. The modified eigen-buckling algorithm predicted the load-bearing capacities of the arch bridge very well. Hence, the proposed method can be used for preliminary buckling strength evaluations in the bridge design stage.

This paper presents an investigation on the mechanical performance of parallel bamboo strand lumber (PBSL) columns under axial compression. Experimental test and numerical analysis were performed for 40 PBSL columns with various slenderness ratios. Failure modes, ultimate capacity and load-strain response are reported and evaluated. Compressive failure is the typical failure mode of columns with small slenderness ratios, however, buckling failure is commonly observed for longer columns. Elastic eigenvalue analysis is found effective to predict critical buckling load of long columns, as buckling occurs within elastic range. However inelastic behavior has significant effect on critical load when the buckling stress exceeds proportional limit of the material. As a result, inelastic approaches provide more accurate prediction of critical load for columns with a slenderness ratio lower than the elastic threshold (λy). The presented experimental results and numerical analysis validated the feasibility of the elastic/inelastic buckling analysis approaches on determination of ultimate capacity of axial loaded PBSL columns.

Due to the crucial importance of the FACTS based damping controllers in mitigation the deteriorative impacts of the power system low frequency oscillations, particularly the inter-area modes, improving the system stability margins seems indispensible. This paper proposes an optimization approach to effectively carry out the multi-machine based stabilization function of the Gate-Controlled Series Capacitor (GCSC) in providing a robust damping to the power system low frequency oscillations. It is aimed to provide a reliable damping framework by means of an optimized GCSC based supplementary damping controller. Thus, to attain the most efficient set of the damping controller parameters, Particle Swarm Optimization algorithm as a proficient optimum hunter is employed to explore for the global stabilization solution in accordance to a vast range of power system operating conditions. Moreover, as a weighty assessment, the eigenvalue analysis is taken into account as the cornerstone of the performed studies in order to investigate the damping methodology in which the unstable or lightly damped inter-area modes are scheduled to effectively shift to some predominant stability zones in the s-plane. Meanwhile, derived results through the nonlinear time domain simulation as well as two dynamic performance evaluators manifestly demonstrate the impressiveness and verify the robustness of the proposed GCSC based damping scheme in enhancing the power system stability, especially regarding to the inter-area modes.

Facts devices are increasingly being applied to increase the damping of the power system. Uncoordinated design of these devices with power system stabilizers (PSSs), however, may have a detriment effect on the system performance. This paper presents seeker optimization algorithm (SOA) to design the parameters of PSS and STATCOM coordinately to improve more stability of power system. The SOA is used to achieve the best optimal results to minimize the objective function of the optimization problem. Simulations are carried out on a two-area Kundur and 39-bus New England power systems, and simulation results confirm the efficiency of the proposed method to stabilize power system oscillations. Comparing SOA with other intelligent method (GA) shows that a better performance is achieved. In addition, the effectiveness of the coordinated design using the proposed method is confirmed through eigenvalue analysis.

To ensure the small-signal stability of a power system, power system stabilizers (PSSs) are extensively applied for damping low frequency power oscillations through modulating the excitation supplied to synchronous machines, and increasing interest has been focused on developing different PSS schemes to tackle the threat of damping oscillations to power system stability. This paper examines four different PSS models and investigates their performances on damping power system dynamics using both small-signal eigenvalue analysis and large-signal dynamic simulations. The four kinds of PSSs examined include the Conventional PSS (CPSS), Single Neuron based PSS (SNPSS), Adaptive PSS (APSS) and Multi-band PSS (MBPSS). A steep descent parameter optimization algorithm is employed to seek the optimal PSS design parameters. To evaluate the effects of these PSSs on improving power system dynamic behaviors, case studies are carried out on an 8-unit 24-bus power system through both small-signal eigenvalue analysis and large-signal time-domain simulations.

Semi-analytical elastic methods for stiffened plate analysis are computationally very efficient. In addition to eigenvalue analysis, such methods may also offer a viable approach for the prediction of ultimate strength limits (USLs) of the plates when combined with appropriate strength criteria. In this paper, existing strength criteria are discussed, and extended criteria proposed for plates with various stiffener arrangements and boundary conditions such as full out-of-plane supports along all edges or plates with a free or partially stiffened edge. The extended criteria reflect in a simplified manner the effect of redistribution of stresses due to the formation of local plastic regions at stiffeners, supporting edges and in the plate interior. The equilibrium path is traced using large deflection theory and the Rayleigh–Ritz approach on an incremental form. The approach is able to account for the reserve strength of slender plates in the postbuckling region. With the considered criteria included, good agreement is obtained with results from fully nonlinear finite element analyses for different support conditions and for a variety of plate and stiffener dimensions.

One of the most important aims of potential field geophysicists is delineate the edges of subsurface structures. There are many methods based on horizontal and vertical derivative of potential field data for edge detection and enhancement. The structure tensor technique one of the image processing techniques is used to edge detection studies in many scientific areas. In this paper, the technique was applied to potential field data and detected edges of the subsurface lineaments using its eigenvalue analysis. Based on noise-free and noisy synthetic data sets, the technique was tested and satisfactory results were obtained. The proposed method was applied on two real potential field data which are gravity data of Konya region and magnetic data of Eastern Anatolia Region in Turkey. These examples demonstrate that the technique provides beneficial information to geoscientists for determining the horizontal location of subsurface structures such as contacts, faults or various source bodies.

The engineering response of metamaterials has a dramatic impact on the physics, optics and engineering communities, because they offer electromagnetic properties that are difficult or impossible to achieve with conventional materials. In this paper, an asymptotic analysis of the electromagnetic fields at multi-material wedges composed of metamaterials is proposed. This is made possible by removing the assumption of positive electric permittivities and magnetic permeabilities, an hypothesis which usually applies to conventional materials. Exploring the whole range of variability of these electromagnetic properties, it is shown that, in addition to the classical real eigenvalues 0⩽λ

The tuning of the PSS parameters for a multi-machine power system is usually formulated as an objective function with constraints consisting of the damping factor and damping ratio. A novel mixed-integer ant direction hybrid differential evolution algorithm, called MIADHDE, is proposed to solve this kind of problem. The MIADHDE is improved from ADHDE by the addition of accelerated phase and real variables. The performances of three different objective functions are compared to the MIADHDE in this paper. Both local and remote feedback signals of machine speed deviation measurements can be selected as input signals to the PSS controllers in the proposed objective function. The New England 10-unit 39-bus standard power system, under various system configurations and loading conditions, is employed to illustrate the performance of the proposed method with the three different objective functions. Eigenvalue analysis and nonlinear time domain simulation results demonstrate the effectiveness of the proposed algorithm and the objective function with a remote signal.

This paper analyzes the frequency dynamic behavior in a power system with a high wind power penetration. To this end, wind farms equipped with squirrel cage and doubly fed induction generators are compared. Aspects of the modeling of the different kinds of wind generation and power systems are cited. Then, it is shown, through an eigenvalue analysis, that wind farms equipped by doubly fed induction machines, adequately controlled, can contribute to improve the frequency dynamics. Simulations are presented which verify the theoretical results.

Low-frequency oscillations have been observed on trunk transmission systems in Japan, and have been the subject for studies in fields of operation, control, and devices by the many power system utilities. Power system stabilizers (PSSs) are very effective controllers in enhancing the damping of low-frequency oscillations, since the controllers can increase damping torque for inter area modes by introducing additional signals into the excitation controllers already equipped with generators. In this paper, allocation of PSSs in an interconnected power system with inter area modes has been determined by an eigenvalue analysis, and PSSs for the allocated generators have been designed by a frequency response method. The designed PSSs have been verified in a Japanese power system standard model. This test system is created as a standard model based on the trunk transmission systems in the eastern area of Japan, and reflects characteristic features of the real power systems; therefore, realistic allocation and design for enhancement of the stability of low-frequency oscillations have been verified.

A research programme into both the static and dynamic performance of ground anchorage systems, with an emphasis on resin bonded rock bolts, started at the University of Aberdeen in the early 1980s. The work involved measurements on active construction sites which was underpinned by laboratory and computer modelling and led to the development of a new method for the non-destructive testing of anchorages. Part of the research programme was focused on assessing how changes in the load influence the dynamic responses of an anchorage. This in turn produced a new testing method able to determine the variation in frequency response of the anchorage with changes in load. The development of a lumped parameter model able to simulate the response of anchorages to changes in static load and an applied impulse load was a further step forward in the research programme. The achievements of the lumped parameter model revealed the head of the anchorage to be the most influential component of the anchorage system in determining dynamic response. The results obtained from the numerical model when laboratory anchorages were simulated are shown to be in agreement with the results obtained from the actual laboratory tests. Based on the successful results obtained to date regarding laboratory rock bolt anchorages, a further step was made in order to employ the numerical model for the first time to observe the influence of load on the frequency response of rock bolt anchorages installed in the field. This paper describes the application of the model to such field anchorages and highlights some of the detailed modelling aspects required to replicate real anchorage behaviour.

The main objective of this paper is to present the tuning and performance evaluation of a damping controller recently proposed for a STATCOM. A detailed eigenvalue analysis is carried out to study the effectiveness of the control law and the location of the damping controller. With the objective of damping tie line oscillations two methods (Method-1 and -2) are proposed for tuning the controller parameters. The performance of the controller is evaluated for these methods of tuning by carrying out the simulation of a four-machine system for small and large disturbances. Case study shows that tie line oscillations are better damped when controller is tuned by Method-1 and is located at the sending end of the tie line.

In this paper a power flow controller is designed for a 48-step static synchronous series compensator (SSSC). Torsional characteristics of an SSSC compensated power system are studied and compared to a fixed capacitor compensated power system. The effects of dc link capacitor of the SSSC on torsional modes are studied. An integral state feedback controller is proposed to improve the torsional characteristics of the SSSC. The torsional characteristics are studied through eigenvalue analysis and the results are validated through PSCAD/EMTDC simulation studies.

Let K be a closed convex cone in a Hilbert space (H,〈·,·〉), and let K+ be its positive dual cone. The K-eigenvalues of a continuous linear mapping A:H→H are defined via the complementarity system: x∈K, Ax−λx∈K+, 〈x,Ax−λx〉=0. This paper explores two issues related to this concept: existence results, and upper bounds for the number of K-eigenvalues when the cone K is finitely generated. Special attention is devoted to the case of a Pareto cone in a finite dimensional space.

In this paper, the phenomenon of limit cycle due to load–tap changer interaction is investigated. The role of OLTC deadband in creating a limit cycle phenomenon is addressed. The impact of tap dynamics modelling on system/voltage behaviour is carefully considered. Analytical insights into observed behaviour of power systems with different tap models are given using eigenvalue analysis, the describing function method and time simulation. The conditions for occurrence of limit cycles and the identification of key parameters influencing their characteristics are another important aspect of this investigation.

The design of local preconditioners to accelerate the convergence to a steady state for the compressible Euler equations has so far been solely based on eigenvalue analysis. However, numerical evidence exists that the eigenvector structure also has an influence on the performance of preconditioners and should therefore be included in the design process. In this paper, we present the mathematical framework for the eigenvector analysis of local preconditioners for the multi-dimensional Euler equations. The non-normality of the preconditioned system is crucial in determining the potential for transient amplification of perturbations. Several existing local preconditioners are shown to possess a highly non-normal structure for low Mach numbers. This non-normality leads to significant robustness problems at stagnation points. A modification to these preconditioners which eliminates the non-normality is suggested, and numerical results are presented showing the marked improvement in robustness.

A simplified h -version of the adaptive boundary elements is proposed for the eigenvalue analysis of the Helmholtz equation. The new scheme considers the effect of each local boundary element refinement, not on the eigenvalue but on the eigenvector, which is devised for possible application of the conventional adaptive mesh construction strategy for boundary value problems. In this paper, for improvement of computational efficiency, the local reanalysis for obtaining the eigenvector is employed. The error indicator of the eigenvector in place of that of the eigenvalue, the global value, decides selectively the boundary elements to be refined. Utility of the proposed method is compared, through some examples, with those previously developed.

The dual reciprocity method (DRM) is a general technique for taking domain integrals to the boundary in BEM analysis. In this paper it is applied to the eigenvalue analysis of Helmholtz problems. A solution procedure is presented which avoids the complex eigenvalues usually associated with the non-symmetric BEM matrices and which is at the same time easy to implement. Characteristics numerical examples are used to illustrate the proposed method.

This paper describes techniques developed to evaluate the small-signal stability of large power systems. The method developed is diakoptics-based and the system stability is calculated using eigenvalue and frequency response techniques. The method is applied to a typically large power system and the results obtained compare very well with those obtained using the Ontario Hydro multimachine eigenvalue program.

A generalized formulation for the analysis of doubly curved shell structures using the finite element method has been described in a previous paper. The results of the eigenvalue analysis performed for an isotropic shell element have been presented to show proper inclusion of six rigid body modes. One paraboloid of revolution shell problem using this formulation has been solved with three different mesh sizes and taking three different values of Poisson's ratio. A comparative study of the results with those of earlier investigators, along with the effects of Poisson's ratio on the values of the shell actions, has been made.

This paper utilizes the eigenvalue analysis in identifying model parameters and selecting their appropriate values to obtain a stable system response in the production-stock problem of Coyle. The model is first assumed to be in steady-state equilibrium. This obviates the need for the delays in physical flows and the smoothing levels in the information flows, and helps in converting an eight-order model into a second-order model. Applying the eigenvalue analysis to select appropriate parameter values, it is shown that the initial policy set, which was rejected by Coyle because it produced undesirable, explosive oscillations, can result in extremely good model behaviour. The model behaviour so obtained has been found to be superior even to that obtained with the final policy of Coyle.

Frequently in the analysis of the steady state stability of a power system large portions of the system remain unchanged while parameters in one or a few machines and their associated control systems are altered and the effect on the total system examined. The section of the system in which the parameters are to be altered can be designated as the study system while the remainder of the system can be designated as the external system. This paper describes a procedure to form a low order mathematical equivalent of the external system which can be simply linked to a complete model of the study system. Stability can then be determined by an eigenvalue analysis of the resulting lower order system.

The paper presents an initial post buckling analysis for the rotationally symmetric branching of a cylindrical shell with a free edge following the linear eigenvalue analysis of Ashwell. The shell is supposed to be infinitely long and a closed form solution is obtained for the initial curvature of the post buckling path. This curvature is seen to be negative and more severe than that of the corresponding classical solution. The solution is shown to be relevant to the buckling of a cracked concrete shell such as a cooling tower.

Because of the very large matrices arising in dynamic analyses problems treated by the finite element method, approximate methods have to be used for eigenvalue determinations. In this paper a method for obtaining accurate error bounds for eigenvalue analysis by elimination of variables is described. The method is based on theorems of Kato and Temple. It has been applied to a large scale problem: namely a delta wing for which both numerical and experimental analyses are available. The results showed that loss of accuracy for the lower modes was negligible.