Formulation of the Eigenvalue Problem for an Unconstrained Circular Bar

1 Many eminent mathematicians and applied mechanicists have been interested in the vibration problems of naturally curved and twisted bars These equations are solved for some cases, such as an elastic solid full toroid [1, 2, 5], whereas for an incomplete circular bar the solution, because of tedious calculations, has been left in a closed form Derivations of the Eigenvalue Problem The homogenous elastic circular bar of constant cross section is referred to a fixed system of orthogonal Cartesian coordinates (Q, T = \ f {r;t).(r;t)pdu ) + a(e\t) For the in-plane motion (that is, the displacement of the center line of the circular bar is predominantly in the plane containing the undeformed center line), the position vector r in terms of the unit vectors may be expressed a

Nonlinear forced vibrations of curved microbeam resting on nonlinear foundation using the modified strain gradient theory

The nonlinear forced vibrations of a curved micro- beam resting on the nonlinear foundation are examined. The equations of motion are derived using the Hamilton's principle and the modified strain gradient theory which is capable to examine the size effects in the microstructures. The nonlinear partial differential equations of motion are reduced to a time-dependent ordinary differential equation containing quadratic and cubic nonlinear terms. A frequency response of the curved microbeam for the primary resonance is determined using multiple time scales perturbation method. From the application point of view, the frequency response curves may be useful to select the optimum values of design parameters. The effects of geometry parameters and foundation moduli on the vibration behavior of the curved microbeam are illustrated.Розглянуто нелінійні змушені коливання викривленої мікробалки, яка лежить на нелінійній основі.Рівняння руху отримані на основі принципу Гамільтона і модифікованої теорії градієнтів деформації. що дає змогу вивчити ефекти розміру в мікроструктурі. Нелінійні рівняння руху з частинними похідними зведено до залежного від часу рівняння, яке містить квадратично і кубічно нелінійні члени. Визначено частотну характеристику викривленої балки для першого резонансу, для чого використано метод багатомасштабних у часі збурень. З прикладної точки зору, криві частотної характеристики можуть бути корисними для вибору оптимальних значень параметрів при проектуванні. Проілюстровано вплив геометричних параметрів модулів основи на коливання викривленої мікробалки

A cyber-kill-chain based taxonomy of crypto-ransomware features

In spite of being just a few years old, ransomware is quickly becoming a serious threat to our digital infrastructures, data and services. Majority of ransomware families are requesting for a ransom payment to restore a custodian access or decrypt data which were encrypted by the ransomware earlier. Although the ransomware attack strategy seems to be simple, security specialists ranked ransomware as a sophisticated attack vector with many variations and families. Wide range of features which are available in different families and versions of ransomware further complicates their detection and analysis. Though the existing body of research provides significant discussions about ransomware details and capabilities, the all research body is fragmented. Therefore, a ransomware feature taxonomy would advance cyber defenders’ understanding of associated risks of ransomware. In this paper we provide, to the best of our knowledge, the first scientific taxonomy of ransomware features, aligned with Lockheed Martin Cyber Kill Chain (CKC) model. CKC is a well-established model in industry that describes stages of cyber intrusion attempts. To ease the challenge of applying our taxonomy in real world, we also provide the corresponding ransomware defence taxonomy aligned with Courses of Action matrix (an intelligence-driven defence model). We believe that this research study is of high value for the cyber security research community, as it provides the researchers with a means of assessing the vulnerabilities and attack vectors towards the intended victims

Compliant Leg Architectures and a Linear Control Strategy for the Stable Running of Planar Biped Robots

This paper investigates two fundamental structures for biped robots and a control strategy to achieve stable biped running. The first biped structure contains straight legs with telescopic springs, and the second one contains knees with compliant elements in parallel with the motors. With both configurations we can use a standard linear discrete-time state-feedback control strategy to achieve an active periodic stable biped running gait, using the Poincare map of one complete step to produce the discrete-time model. In this case, the Poincare map describes an open-loop system with an unstable equilibrium, requiring a closed loop control for tabilization. The discretization contains a stance phase, a flight phase and a touch-down. In the first approach, the control signals remain constant during each phase, while in the second approach both phases are discretized into a number of constant-torque intervals, so that its formulation can be applied easily to stabilize any active biped running gait. Simulation results with both the straight-legged and the kneed biped model demonstrate stable gaits on both horizontal and inclined surfaces

New family of iterative methods with high order of convergence for solving nonlinear systems

In this paper we present and analyze a set of predictor-corrector iterative methods with increasing order of convergence, for solving systems of nonlinear equations. Our aim is to achieve high order of convergence with few Jacobian and/or functional evaluations. On the other hand, by applying the pseudocomposition technique on each proposed scheme we get to increase their order of convergence, obtaining new high-order and efficient methods. We use the classical efficiency index in order to compare the obtained schemes and make some numerical test.This research was supported by Ministerio de Ciencia y Tecnología MTM2011-28636-C02-02 and by FONDOCYT 2011-1-B1-33, República Dominicana.Cordero Barbero, A.; Torregrosa Sánchez, JR.; Penkova Vassileva, M. (2013). New family of iterative methods with high order of convergence for solving nonlinear systems. En Numerical Analysis and Its Applications. Springer Verlag. 222-230. https://doi.org/10.1007/978-3-642-41515-9_23S222230Cordero, A., Hueso, J.L., Martínez, E., Torregrosa, J.R.: A modified Newton-Jarratt’s composition. Numer. Algor. 55, 87–99 (2010)Cordero, A., Hueso, J.L., Martínez, E., Torregrosa, J.R.: Efficient high-order methods based on golden ratio for nonlinear systems. Applied Mathematics and Computation 217(9), 4548–4556 (2011)Cordero, A., Torregrosa, J.R.: Variants of Newton’s Method using fifth-order quadrature formulas. Applied Mathematics and Computation 190, 686–698 (2007)Cordero, A., Torregrosa, J.R.: On interpolation variants of Newton’s method for functions of several variables. Journal of Computational and Applied Mathematics 234, 34–43 (2010)Cordero, A., Torregrosa, J.R., Vassileva, M.P.: Pseudocomposition: a technique to design predictor-corrector methods for systms of nonlinear equtaions. Applied Mathematics and Computation 218(23), 11496–11504 (2012)Nikkhah-Bahrami, M., Oftadeh, R.: An effective iterative method for computing real and complex roots of systems of nonlinear equations. Applied Mathematics and Computation 215, 1813–1820 (2009)Ostrowski, A.M.: Solutions of equations and systems of equations. Academic Press, New York (1966)Shin, B.-C., Darvishi, M.T., Kim, C.-H.: A comparison of the Newton-Krylov method with high order Newton-like methods to solve nonlinear systems. Applied Mathematics and Computation 217, 3190–3198 (2010

A hierarchical key pre-distribution scheme for fog networks

Security in fog computing is multi-faceted, and one particular challenge is establishing a secure communication channel between fog nodes and end devices. This emphasizes the importance of designing efficient and secret key distribution scheme to facilitate fog nodes and end devices to establish secure communication channels. Existing secure key distribution schemes designed for hierarchical networks may be deployable in fog computing, but they incur high computational and communication overheads and thus consume significant memory. In this paper, we propose a novel hierarchical key pre-distribution scheme based on “Residual Design” for fog networks. The proposed key distribution scheme is designed to minimize storage overhead and memory consumption, while increasing network scalability. The scheme is also designed to be secure against node capture attacks. We demonstrate that in an equal-size network, our scheme achieves around 84% improvement in terms of node storage overhead, and around 96% improvement in terms of network scalability. Our research paves the way for building an efficient key management framework for secure communication within the hierarchical network of fog nodes and end devices. KEYWORDS: Fog Computing, Key distribution, Hierarchical Networks