Search Results (7)

Studying nonlinear oscillations in mechanical systems is fundamental to understanding complex dynamic behavior in engineering applications. While classical analytical methods remain valuable for systems with limited complexity, they become increasingly inadequate when nonlinearities are strong and geometrically induced, as in the case of large-amplitude oscillations. This paper presents a combined numerical and experimental investigation of a mechanical system composed of two coupled pendulums, exhibiting significant nonlinear behavior due to elastic deformation throughout their motion. A mathematical model of the system was developed using the MatLab/Simulink ver.6.1 environment, considering gravitational, inertial, and nonlinear elastic restoring forces. One of the major challenges in accurately modeling such systems is accurately representing damping, particularly in the absence of dedicated dampers. In this work, damping coefficients were experimentally identified through decrement measurements and incorporated into the simulation model to improve predictive accuracy. The simulation outputs, including angular displacements, velocities, accelerations, and phase trajectories over time, were validated against experimental results obtained via high-precision inertial sensors. The comparison shows a strong correlation between numerical and experimental data, with minimal relative errors in amplitude and frequency. This research represents the first stage of a broader study aimed at analyzing forced and parametrically excited oscillations. Beyond validating the model, the study contributes to the design of a robust experimental framework suitable for further exploration of nonlinear dynamics. The findings have practical implications for the development and control of mechanical systems subject to dynamic loads, with potential applications in automation, vibration analysis, and system diagnostics. Full article

Energy harvesting from ambient vibrations has received significant attention as an alternative renewable, clean energy source for microelectronic devices in diverse applications such as wearables and environmental monitoring. However, typical vibrations in remote environments exhibit ultra-low frequencies with variations and uncertainty leading to operation away from resonance and severe underperformance in terms of power output. Pendulum-based energy harvesters offer a promising solution to these issues, particularly when designed for parametric resonant response to driven displacement of the pendulum pivot. Parametric excitation has been shown to trigger fast rotational motion of the pendulum VEH that is beneficial for energy generation and the necessary space utilization. Nevertheless, low-frequency ambient vibrations typically come at very weak amplitudes, a fact that establishes significant design barriers when traditional gravitational pendula are used for rotary energy harvesting. In this paper, we propose a novel concept that utilizes permanent magnet arrays to establish pendulum dynamics. Extensive investigation of the restoring torque of the proposed magnetic pendulum concept is conducted with analytical tools and FEA verification. The resulting oscillator exhibits frequency tuning that is decoupled from gravity and adjustable via the circularly arranged magnetic fields, leading to increased flexibility in the concurrently necessary amplitude tuning. Numerical integration of the nondimensional equation of motion is performed in the system’s parameter space to identify the impact on the regions triggering rotational response to parametric excitation. Finally, a theoretical case study is numerically investigated with the device space constrained within 20 cm³, showing a multi-fold improvement in the achieved power density of over 600 μW/cm³/g²/Hz over a broad range of frequencies and driving amplitudes as low as 1.1 Hz at 0.2 g. Full article

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. Full article

Applications of a novel time-integration technique to the non-linear and linear dynamics of mechanical structures are presented, using an extended Picard-type iteration. Explicit discrete-mechanics approximations are taken as starting guess for the iteration. Iteration and necessary symbolic operations need to be performed only before time-stepping procedure starts. In a previous investigation, we demonstrated computational advantages for free vibrations of a hanging pendulum. In the present paper, we first study forced non-linear vibrations of a tower-like mechanical structure, modeled by a standing pendulum with a non-linear restoring moment, due to harmonic excitation in primary parametric vertical resonance, and due to excitation recordings from a real earthquake. Our technique is realized in the symbolic computer languages Mathematica and Maple, and outcomes are successfully compared against the numerical time-integration tool NDSolve of Mathematica. For out method, substantially smaller computation times, smaller also than the real observation time, are found on a standard computer. We finally present the application to free vibrations of a hanging double pendulum. Excellent accuracy with respect to the exact solution is found for comparatively large observation periods. Full article

In this paper, we have investigated the dynamic response, vibration control technique, and upright stability of an inverted pendulum system in an underwater environment in view point of a conceptual future wave energy harvesting system. The pendulum system is subjected to a parametrically excited input (used as a water wave) at its pivot point in the vertical direction for stabilization purposes. For the first time, a mathematical model for investigating the underwater dynamic response of an inverted pendulum system has been developed, considering the effect of hydrodynamic forces (like the drag force and the buoyancy force) acting on the system. The mathematical model of the system has been derived by applying the standard Lagrange equation. To obtain the approximate solution of the system, the averaging technique has been utilized. An open loop parametric excitation technique has been applied to stabilize the pendulum system at its upright unstable equilibrium position. Both (like the lower and the upper) stability borders have been shown for the responses of both pendulum systems in vacuum and water (viscously damped). Furthermore, stability regions for both cases are clearly drawn and analyzed. The results are illustrated through numerical simulations. Numerical simulation results concluded that: (i) The application of the parametric excitation control method in this article successfully stabilizes the newly developed system model in an underwater environment, (ii) there is a significant increase in the excitation amplitude in the stability region for the system in water versus in vacuum, and (iii) the stability region for the system in vacuum is wider than that in water. Full article

This paper considers three dynamic systems composed of a mathematical pendulum suspended on a sliding body subjected to harmonic excitation. A comparative dynamic analysis of the studied parametric mutations of the rigid pendulum with inertial suspension point and damping was performed. The examined system with parametric mutations is solved numerically, where phase planes and Poincaré maps were used to observe the system response. Lyapunov exponents were computed in two ways to classify the dynamic behavior at relatively early stage of forced responses using two proven methods. The results show that with some parameters three systems exhibit a very similar dynamic behavior, i.e., quasi-periodic and even chaotic motions. Full article

Motivated by the dynamics of a trimaran, an investigation of the dynamic behaviour of a double forcing parametrically excited system is carried out. Initially, we provide an outline of the stability regions, both numerically and analytically, for the undamped linear, extended version of the Mathieu equation. This paper then examines the anticipated form of response of our proposed nonlinear damped double forcing system, where periodic and quasiperiodic routes to chaos are graphically demonstrated and compared with the case of the single vertically-driven pendulum. Full article