Vlado Gicev

The response of a shear beam as 1d medium to seismic excitations dependent on the boundary conditions

We study response of a shear beam to seismic excitations at its base. nThe research is conducted using computer simulation of the wave propagation on a numerical model. The wave equation is solved using the method of finite differences (FD) where the spatial and temporal derivatives are approximated with finite differences. We used formulation of the wave equation via the particle velocities, strains, and stresses. Integrating particle velocities in time, we obtained displacements at spatial points. The main goal in this research is to study phenomena occurring due to three different types of boundary conditions, Dirichlet, Neumann, and moving boundary when simple half-sine pulse propagates through 1D medium modeled as a shear beam.

Application of fundamental lemma of variational calculus to the problem for the brachistochrone

Variational calculus studied methods for finding maximum and minimum values of functional. It has its inception in 1696 year by Johan Bernoulli with its glorious problem for the brachistochrone: to find a curve, connecting two points A and B , which does not lie in a vertical, so that heavy point descending on this curve from position A to reach position in for at least time. In functional analysis variational calculus takes the same space, as well as theory of maxima and minimum intensity in the classic analysis . nWe will prove a theorem for functional where prove that necessary condition for extreme of functional is the variation of functional is equal to zero. We describe the solution of the equation of Euler with example of application, such as the problem of brachistochrone.