EFFICIENT COMPUTATION OF FREQUENCY RESPONSE OF MULTI-DEGREE OF FREEDOM NON-LINEAR VIBRATIONAL SYSTEM
Open Access
- Author:
- Pradeep Kumar, Arjun
- Graduate Program:
- Mechanical Engineering
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- May 03, 2017
- Committee Members:
- Alok Sinha, Thesis Advisor/Co-Advisor
Qian Wang, Committee Member
Karen Ann Thole, Committee Member - Keywords:
- frequency sweep
interpolation
Padé’s interpolation technique
nonlinear systems
structural acoustics
structural dynamics
finite element method - Abstract:
- Frequency sweep problems occur in several applications of structural dynamics, acoustics and structural acoustics. In general, the evaluation of a frequency response function involves finding solution to a large-scale system of coupled equations defining a vast system. Hence finding solutions to frequency response functions for a large range of frequencies is computationally exhaustive. However, the established method of interpolation techniques can be implemented to reduce the cost of computation. So far, several techniques of interpolation techniques have been successfully implemented in systems involving large-scale coupled linear equations. This thesis proposes implementation of Padé’s interpolation technique in a large-scale nonlinear system. More specifically, this thesis focuses on the additional computational efforts required in finding solution to frequency sweep problems of large nonlinear systems when compared with large linear systems. The accuracy and computational efficiency of the mentioned approach are demonstrated with solutions to frequency sweep problems for a single and two degrees of freedom of nonlinear systems. Further this thesis has discussed methods to approach solution of frequency response problem of a multi-degree of freedom nonlinear system using finite element method.