Transient response of non-linear spring-mass systems

• Main Author: Ergin, Erdem I.
• Format: Others
• Published: 1954
• Online Access: https://thesis.library.caltech.edu/4730/1/Ergin_ei_1954.pdf; Ergin, Erdem I. (1954) Transient response of non-linear spring-mass systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/0528-K973. https://resolver.caltech.edu/CaltechETD:etd-12032003-092544 <https://resolver.caltech.edu/CaltechETD:etd-12032003-092544>

The purpose of this thesis is: 1) To investigate the applicability and to compare the accuracy of existing perturbation methods of non-linear mechanics for the solution of transient response problems, and 2) To describe a new analytical approximate method for the solution of certain types of non-linear problems involving pulse excitation. This new method combines the advantages of engineering accuracy with ease of applicability. In the course of this study it is found that the solution of homogeneous non-linear equations can be obtained readily and with sufficient accuracy by the perturbation methods of Kryloff and Bogoliuboff or Lindstedt, even for large nonlinearities. Greater accuracy can be attained by the use of the newly developed bi-linear approximation. The advantage of the bi-linear method becomes more pronounced when the step function or the single pulse response of the system is investigated. It is shown that the bi-linear method is the only convenient analytical approximate method available for the solution of general pulse excitation problems involving non-linear spring-mass systems.