Design and mathematical modelling of the kinetic sculpture Blade
Thesis DisciplineMechanical Engineering
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
Christchurch born artist Len Lye (1901- 1980) built the kinetic sculpture, Blade (1965), as a prototype for what he perceived to be a much larger work. This thesis presents a study, which predicts the vibratory response of Blade and develops a design for the sculpture to be built at the largest practical economic size. Len Lye's aesthetic requirements stipulate that the vibratory blade form of the scaled sculpture must be geometrically similar to the original work and that static similarity should exist between the original and the scaled blades. Dimensionless formulae are derived and used to study the influence of design parameters and increasing size on structural properties such as natural frequencies, blade forces and moments, and system power requirements. For a solid metal blade of rectangular cross section it is found that the size, which Blade may be scaled, is limited by the magnitude of the bending stresses in the blade material. Len Lye's specification imposes a set of requirements and constraints on the design, which in addition to economic constraints leads to a variational study which maximises the number of performances per dollar expended on blade materials with increasing size. As a result of this study a titanium alloy 6AI/4V is selected for the scaled blade with a nominal blade length is 3.355m. To test the validity of the design, frequencies and mode shapes were calculated and a numerical simulation performed. The exact solution for the natural bending frequencies and mode shapes for the blade and the wand are obtained using simple beam theory. The Rayleigh Ritz method is used to calculate the plate frequencies and mode shapes for the blade. The calculated frequencies and mode shapes include the effects of the longitudinal gravitational loading. In this study they are the second and third blade bending frequencies and the third plate mode Len Lye described as the desirable vibrating single and double harmonic blade forms and the shimmering frequency respectively. For the simulation a mathematical model is developed to describe the dynamics of the interaction of the blade and the wand. The model predicted a swinging phenomenon, which Lye observed in the performance of Blade at the prototype size and regarded as undesirable. A system configuration for the scaled Blade involving a lighter more flexible wand and modified ground motion characteristics predicted a significant reduction of this swinging phenomenon and is incorporated in the design. Features in the design of the mechanism for the original sculpture were found to be unsatisfactory so a new improved mechanism concept was developed. The complete design was produced and the system was manufactured and built. The performance of the scaled Blade is found to be consistent with the prediction from the mathematical model.