Oscillations of a Multi-String Pendulum

摘要

The mathematical pendulum is one of the most widely studied problems in engineering physics. This is, however, primarily limited to the classical pendulum with a single bar and mass configuration. Extensions to this include multi-degree of freedom systems, but many of the classical assumptions, such as a single bar per mass, are preserved. Several designs used in practice utilize multiple or trapezoidal configurations to enhance stability. Such designs have not been studied in great detail and there is a need for additional work to fully analyze their response characteristics. The two-string pendulum design characteristics are initially investigated, both in terms of oscillation characteristics and string tension. Analytical and numerical methodologies are applied to predict the response of the two-string pendulum in free and forced oscillations. Validation of the results is performed by comparisons to simulations conducted with a standard commercial software package. A preliminary optimization study is conducted for a driven two-string pendulum. Finally, it is shown how to apply the results of the analysis and optimization studies developed in this work in a typical design case.