Due to the long-term problem of electricity and potable water in most developing and undeveloped countries, predominantly rural areas, a novelty of the pendulum water pump, which uses a vertically excited parametric pendulum with variable-length using a sinusoidal excitation as a vibrating machine, is presented. With this, more oscillations can be achieved, reducing human effort further and having high output than the existing pendulum water pump with the conventional pendulum. The pendulum, lever, and piston assembly are modeled by a separate dynamical system and then joined into the many degrees-of-freedom dynamical systems. The present work includes friction while studying the system dynamics and then simulated to verify the system’s harmonic response. The study showed the effect of the pendulum length variability on the whole system’s performance. The vertically excited parametric pendulum with variable length in the system is established, giving faster and longer oscillations than the pendulum with constant length. Hence, more and richer dynamics are achieved. A quasi-periodicity behavior is noticed in the system even after 50 s of simulation time; this can be compensated when a regular external forcing is applied. Furthermore, the lever and piston oscillations show a transient behavior before it finally reaches a stable behavior.
A comprehensive review of variable-length pendulums is presented. An attempt at a unique evaluation of current trends in this field is carried out in accordance with mathematical modeling, dynamical analysis, and original computer simulations. Perspectives of future trends are also noted on the basis of various concepts and possible theoretical and engineering applications. Some important physical concepts are verified using dedicated numerical procedures and assessed based on dynamical analysis. At the end of the review, it is concluded that many variable-length pendulums are very demanding in the modeling and analysis of parametric dynamical systems, but basic knowledge about constant-length pendulums can be used as a good starting point in providing much accurate mathematical description of physical processes. Finally, an extended model for a variable-length pendulum’s mechanical application being derived from the Swinging Atwood Machine is proposed. The extended SAM presents a novel SAM concept being derived from a variable-length double pendulum with a suspension between the two pendulums. The results of original numerical simulations show that the extended SAM’s nonlinear dynamics presented in the current work can be thoroughly studied, and more modifications can be achieved. The new technique can reduce residual vibrations through damping when the desired level of the crane is reached. It can also be applied in simple mechatronic and robotic systems.
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