Transverse Vibrations in Beams Supported by a Piece-Wise Homogeneous Visco- Elastic Foundation

Transversal vibrations induced by a load moving uniformly along an infinite beam resting on a piece-wise homogeneous visco-elastic foundation are studied. Special attention is paid to the additional vibrations, conventionally referred to as transition radiations, which arise as the point load traverses the place of foundation discontinuity. The governing equations of the problem are solved by the normalmode analysis. The solution is expressed in a form of infinite sum of orthogonal natural modes multiplied by the generalized coordinate of displacement. The natural frequencies are obtained numerically exploiting the concept of the global dynamic stiffness matrix. This ensures that the frequencies obtained are exact. The methodology has restrictions neither on velocity nor on damping. The approach looks simple, though, the numerical expression of the results is not straightforward. A general procedure for numerical implementation is presented and verified. To illustrate the utility of the methodology parametric optimization is presented and influence of the load mass is studied. The results obtained have direct application in analysis of railway track vibrations induced by high-speed trains when passing regions with significantly different foundation stiffness.

Optimal choice between even- and uneven-aged forestry: the case of non-industrial private forest owners

An infinite-horizon discrete time model with multiple size-class structures using a transition matrix is built to assess optimal harvesting schedules in the context of Non-Industrial Private Forest (NIPF) owners. Three model specifications accounting for forest income, financial return on an asset and amenity valuations are considered. Numerical simulations suggest uneven-aged forest management where a rational forest owner adapts her or his forest policy by influencing the regeneration of trees or adjusting consumption dynamics depending on subjective time preference and market return rate dynamics on the financial asset. Moreover she or he does not value significantly non-market benefits captured by amenity valuations relatively to forest income.