Vibration characteristic of trees during cutting operation

Vibration is not good for cutting operation. It leads to premature failure. Two major failure modes in trees during cutting are trunk and root failure. Trunk failure happens on the part of the trunk loaded above ground. It includes breakage of the trunk above the root collar, even if the root collar and lower trunk are below ground. The main goal of this study is to provide analytical tools to investigate vibration characteristics of trees during cutting operation. Tree stability and failure are very important issues in urban areas where there can be risks of damage to people and property and in forests where damage may cause economic loss. Tree failure may cause severe damages to nearby properties, vehicles and houses. In addition, trees standing next to highways, school yards, picnic grounds or homes are of particular concern. They may also cause fire and/or power outage. Damping of trees is categorized into internaland external damping. Internal damping is because of energy dissipation in the stem-ground connection system and internal friction within the wood material of the stem and the branch system. External damping is as a result of aerodynamic drag of the crown and due to collision with neighbouring trees. Defining a damping model for a natural system like a tree is complex and difficult, as the dissipation mechanisms are not completely understood. Therefore, damping coefficient is simply assumed to be proportional to the velocity, so called viscous damping. This study presents analytical tool and model to simulate the motion of the cut piece and calculate induced forces to the tree top during cutting process. The outputs of the model are force function and displacement of tree top during cutting process. MATLAB is used to numerically solve the equations of motion. The dynamic models are among the first attempts to use analytical tools to find the forces induced to the tree during cutting process. This study is very rare in the case of the variety of the topics it covers from modelling falling piece motion to studying dynamic properties of tree trunk, and finite element modelling. Obtain a spectrum by running the proposed model for hundreds of cases with different geometric and material properties. Proposed model can be run for large number of trees and in each case the natural frequency of vibrations of tree and maximum displacement of tree top or maximum axial strain near tree bottom must be calculated. The data from these analyses can be used to make a spectrum which indicates maximum displacement of tree top or maximum axial strain near tree bottom versus frequency. The spectrum provides a powerful tool for the arborist to predict the ultimate displacement and strains generated during cutting process.