Abstract
In this paper, a new method to approach the free response of the second order partial differential system with time periodic coefficient is presented with a special form of a trigonometric series with mode functions, and it can be expressed in a closed-form solution. As a result that the partial differential equation with time periodic coefficient can be transformed into a linear algebra equations, from which a characteristic equation can be obtained. Then, complex oscillation frequency and all harmonic coefficients can be computed. All arbitrary constants in a general solution can be obtained with initial conditions. Investigations show that the proposed approach not only computes free vibration with multiple modes with higher accuracy, but also it is suitable to analyze vibration instability. So this study is valuable for vibration analysis in an elastic continuum with time periodic coefficient.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
