The Simultaneous Metric Dimension of Families Composed by Lexicographic Product Graphs

Let ${\mathcal G}$ be a graph family defined on a common (labeled) vertex set $V$. A set $S\subseteq V$ is said to be a simultaneous metric generator for ${\cal G}$ if for every $G\in {\cal G}$ and every pair of different vertices $u,v\in V$ there exists $s\in S$ such that $d_{G}(s,u)\ne d_{G}(s,v)$, where $d_{G}$ denotes the geodesic distance. A simultaneous adjacency generator for ${\cal G}$ is a simultaneous metric generator under the metric $d_{G,2}(x,y)=\min\{d_{G}(x,y),2\}$. A minimum cardinality simultaneous metric (adjacency) generator for ${\cal G}$ is a simultaneous metric (adjacency) basis, and its cardinality the simultaneous metric (adjacency) dimension of ${\cal G}$. Based on the simultaneous adjacency dimension, we study the simultaneous metric dimension of families composed by lexicographic product graphs

Dynamical analysis of a duolever suspension system

The authors investigate the dynamical behaviour of a Duolever type of suspension on a standard sports motorcycle. The paper contains the modelling aspects of it, as well as the optimization process followed in order to obtain the suspension parameters and geometry arrangements. Head angle, wheelbase and normal trail are studied as indicators of the handling properties of the suspension system. Matlab optimization toolbox was used to design a mathematical model of a duolever front suspension system which keeps its normal trail constant during the full suspension travel. By using VehicleSim software, non-linear simulations were performed on motorcycle model that includes a duolever suspension. By a quasi-static variation of the forward speed of the motorcycle, the time histories of the system's states were obtained. The corresponded root locus to the linearized model were plotted and compared to those of the original motorcycle model without duolever system. A modal analysis was performed in order to get a deeper understanding of the different modes of oscillation and how the duolever system affects them. The results show that whilst a satisfactory anti-dive effect is achieved with this suspension system, it has a destabilizing effect on pitch and wobble modes

Effects of interconnected suspension systems on the dynamics of sport motorcycles

The effects of interconnected front and rear suspension systems on the in-plane dynamics of sport motorcycle is investigated. The interconnected suspension mathematical description is presented and included in a high-fidelity motorcycle model. The suspension behaviour under road step bump inputs is studied for different values of stiffness and damping interconnection coefficients. Optimal values of interconnection coefficients are proposed for the current motorcycle model. Finally, the oscillating dynanlics of the motorcycle at straight rurrning conditions is studied through its normal modes