Turbine engine rotor blade with tip shelf

An apparatus for a turbine engine, comprising:

• a turbine blade comprising an airfoil;
• the airfoil extending longitudinally between a leading edge and a trailing edge, the airfoil extending laterally between a pressure side and a suction side, the airfoil extending spanwise from a base to a tip, and the airfoil including a body section, a tip section and a channel;
• the body section extending spanwise from the base to a shelf, the body section extending laterally from the pressure side to the suction side, and the body section comprising one or more cooling apertures formed in the shelf;
• the tip section connected to the body section, the tip section extending spanwise from the shelf to the tip, and the tip section extending laterally from the suction side to a sidewall;
• and
• the channel projecting spanwise into the airfoil from the tip to the shelf, and the channel projecting laterally into the airfoil from the pressure side to the sidewall;
• wherein a density of at least a portion of the tip section varies longitudinally and/or spanwise along the channel.