On vibrational stabilizability of nonlinear systems

Conditions of vibrational stabilizability for trivial solutions of nonlinear systems are derived. Several examples based on the classical equations of the theory of oscillations are given.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45223/1/10957_2004_Article_BF00939147.pd

Progress in Classical and Quantum Variational Principles

We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original Maupertuis (Euler-Lagrange) principle constrains the energy at every point along the trajectory. The generalized Maupertuis principle is equivalent to Hamilton's principle. Reciprocal principles are also derived for both the generalized Maupertuis and the Hamilton principles. The Reciprocal Maupertuis Principle is the classical limit of Schr\"{o}dinger's variational principle of wave mechanics, and is also very useful to solve practical problems in both classical and semiclassical mechanics, in complete analogy with the quantum Rayleigh-Ritz method. Classical, semiclassical and quantum variational calculations are carried out for a number of systems, and the results are compared. Pedagogical as well as research problems are used as examples, which include nonconservative as well as relativistic systems

Self-adaptive approach for optimisation of passive control systems for seismic resistant buildings

The concept of passive control of the seismic response of structures was introduced to improve the performance of structures by increasing their energy dissipation and reduce or eliminate damage in the structural elements. The key task in the design of passive systems is to determine the forces in the control devices (yield/slip or post-tensioning) at each floor, that will result in best performance (e.g. minimum inter-storey drift). This can be achieved by large parametric studies in which both the maximum control force (e.g. at ground level) and the distribution of forces along the height of the structure are varied. Alternatively, optimum forces in the devices can be achieved by semi-active control, where the structure self-adapts to the earthquake. Both solutions are expensive: the first requires hundreds of non-linear response simulations in the design stage; the second needs a system of sensors, controllers and electromechanical devices. Presented here is a new Self Adaptive Optimisation Approach (SAOA) in which the self-optimisation of a semi-active system is used in the design stage and the resulting distribution of control forces is adopted as a passive system. The new approach was evaluated through comparing the simulated dynamic responses of two relatively simple benchmark structures (braced and post-tensioned) with three sets of control forces: (1) passive system with forces obtained in parametric study, (2) semi-active system with self-adapting control forces, and (3) passive system with SAOA-optimized forces. The results show good performance of the SAOA systems, indicating that SAOA offers a simple and effective solution that can replace the existing optimisation approaches for the design of passively controlled earthquake resistant structures. This study presents a novel idea of using the semi-active control as a tool for optimising a passive control system. The passive control systems can be further improved by a larger study in which the semi-active control algorithms are also optimised

Investment in Tourism Market: A Dynamic Model of Differentiated Oligopoly

We present a theoretical model in tourism economics, assuming that the market for tourism is an oligopoly with differentiated products. Destinations (i.e., countries, regions, sites or even firms) can invest in order to improve their carrying capacity that can be interpreted as the stock of physical, natural or cultural resources. Tourism flows yield current revenues, but they are usually detrimental for the cultural or natural resource stock over time. We find the solution of the dynamic model, and in particular we find the open-loop Nash equilibrium of the game among the destinations, under alternative settings, depending on whether the arrivals are exogenous or endogenous, and depending on whether the degree of differentiation among destinations is exogenous or endogenous. The model is rather general, and it can provide answers to different specific questions, like the choice between mass- vs. elite-tourism development strategies; the effect of the number of competing products upon profits; the optimal degree of product differentiation