Contact between a curved viscoelastic beam and a rigid plane

Abstract

The following problem has been analysed by the theory of small deflections of bending. A circularly curved beam of Maxwell material is pressed against a rigid horizontal plane by two constant and concentrated forces P, each acting on one end of the beam. Before loading there is contact only at the mid-point of the beam. As load is applied the Maxwellian beam behaves like a Hookean beam. If the load P is below a critical value Pc, there is contact only at the mid-point, but if the load exceeds this value, linear contact is formed along a certain length 2λ° of the beam. At the time t the beam will rise from the support over a distance of 2λ° ( t) if the load P exceeds Pc, while if P is less than Pc there will be a similar deflection only after a critical time tc. The contact pressure is two concentrated forces, acting on each contact point. Expressions for the deflections w(O, t) and w( L, t) of the centre and the ends of the beam are also derived and are compared with corresponding expressions for a Hookean beam. The paper shows that essential differences can exist between contact problems with similar viscoelastic or elastic bodies.