Abstract
The current paper investigates the dynamical property of a pendulum attached to a rotating rigid frame with a constant angular velocity about the vertical axis passing to the pivot point of the pendulum. He’s homotopy perturbation method is used to obtain the analytic solution of the governing nonlinear differential equation of motion. The fourth-order Runge-Kutta method (RKM) and He’s frequency formulation are used to verify the high accuracy of the obtained solution. The stability condition of the motion is examined and discussed. Some plots of the time histories of the gained solutions are portrayed graphically to reveal the impact of the distinct parameters on the dynamical motion.
Highlights
It is known that many engineering problems can be formulated by nonlinear ordinary or partial differential equations
Asymptotic solutions have shed the interest of many scientists to deal with various nonlinear equations, such as the averaging method and the small parameter method for some weak nonlinear problems [1,2,3,4]
The multiple scales (MS) method and the Lindstedt-Poincaré (LP) method have great advantages in obtaining the solutions of vibratory systems [5,6]. These methods depend on a small parameter, and improper selection of this parameter leads to wrong solutions
Summary
It is known that many engineering problems can be formulated by nonlinear ordinary or partial differential equations. In [10], the solution of the dynamical motion of a vibrating system was obtained using HPM. This system consists of two masses, one of them attached with a fixed spring and it moves horizontally. The approximate solution was obtained applying the HPM and Laplace transform in which the stability conditions were obtained. This problem was studied previously in [12] using the method of variational approach, the comparison shows that HMP is very accurate, and it is easy to use. Where prims denote the derivative with respect to time τ
Sign-in/Register to view highlights & summary 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.
