This paper presents a distributed parameter model to study the effects of the harnessing cables on the dynamics of a host structure motivated by space structures applications. The structure is modeled using both Euler–Bernoulli and Timoshenko beam theories (TBT). The presented model studies the effects of coupling between various coordinates of vibrations due to the addition of the cable. The effects of the cable's offset position, pretension, and radius are studied on the natural frequencies of the system. Strain and kinetic energy expressions using linear displacement field assumptions and Green–Lagrange strain tensor are developed. The governing coupled partial differential equations for the cable-harnessed beam that includes the effects of the cable pretension are found using Hamilton's principle. The natural frequencies from the coupled Euler, Bernoulli, Timoshenko and decoupled analytical models are found and compared to the results of the finite element analysis (FEA).

The experimental study and model validations for the coupled dynamics of a cable-harnessed beam structure are presented. The system under consideration consists of multiple pretensioned cables attached along the length of the host beam structure positioned at an offset distance from the beam centerline. Analytical model presented by the coupled partial differential equations (PDEs) for various coordinates of vibrations is found, and the displacement frequency response functions (FRFs) obtained for both Euler–Bernoulli and Timoshenko-based models are compared to those from the experiments for validation. The results are shown to be in very good agreement with the experiments.

We propose utilization of the nonlinear coupling between the roll and pitch motions of wave energy harvesting vessels to increase their power generation by orders of magnitude. Unlike linear vessels that exhibit unidirectional motion, our vessel undergoes both pitch and roll motions in response to frontal waves. This significantly magnifies the motion of the vessel and thus improves the power production by several orders of magnitude. The ocean waves result in roll and pitch motions of the vessel, which in turn causes rotation of an onboard pendulum. The pendulum is connected to an electric generator to produce power. The coupled electro-mechanical system is modeled using energy methods. This paper investigates the power generation of the vessel when the ratio between pitch and roll natural frequencies is about 2 to 1. In that case, a nonlinear energy transfer occurs between the roll and pitch motions, causing the vessel to perform coupled pitch and roll motion even though it is only excited in the pitch direction. It is shown that co-existence of pitch and roll motions significantly enhances the pendulum rotation and power generation. A method for tuning the natural frequencies of the vessel is proposed to make the energy generator robust to variations of the frequency of the incident waves. It is shown that the proposed method enhances the power output of the floating wave power generators by multiple orders of magnitude. A small-scale prototype is developed for the proof of concept. The nonlinear energy transfer and the full rotation of the pendulum in the prototype are observed in the experimental tests.

In this paper, the nonlinear response of indenter-foam dampers is characterized. Those dampers consist of indenters pressed on open-cell foams swollen with wetting liquids. Recently, the authors identified the dominant mechanism of damping in those dampers as poro-viscoelastic (PVE) relaxations as in articular cartilage, one of nature's best solutions to vibration attenuation. Those previous works by the authors included dynamic mechanical analyses of the indenter-foam dampers under small vibrations, i.e., linear regime. The current study features the dynamic response of similar dampers under larger strains to investigate the nonlinear regime. In particular, the indenter-foam dampers tested in this paper consist of an open-cell polyurethane foam swollen with castor oil. Harmonic displacements are applied on the swollen and pre-compressed foam using a flat-ended cylindrical indenter. Measured forces and corresponding hysteresis (force-displacement) loops are then analyzed to quantify damping performance (via specific damping capacity) and nonlinearities (via harmonic ratio). The effects of strain and strain rates on the damping capacity and harmonic ratio are investigated experimentally. The dominant source of the non-linearity is identified as peeling at the indenter-foam interface (and quantified via peeling index). A representative model consisting of a linear viscoelastic foam and rate-dependent adhesive interface (slider element with limiting adhesive strength) explains the observed trends in peeling and thus nonlinear dynamic response. Possible remedies to suppress those nonlinearities in future designs of indenter-foam dampers are also discussed.

This paper presents a method to utilize the pitch-roll nonlinear energy transfer phenomenon in vessels for off-shore wave power generation. This paper builds on an existing design where the power generator is a horizontal pendulum on board a vessel. The surface waves result in rocking of the ship, which in turn results in rotation of the pendulum. The pendulum is connected to a DC generator to produce power. The coupled electro-mechanical system is modeled using energy methods. The design in this paper utilizes the nonlinear coupling between the roll and pitch motions of the generator vessel. The natural frequency of the roll motion of the vessel is tuned to be twice the fundamental frequency of the pitch motion. In this specific condition when the vessel is excited in the pitch direction, the energy is nonlinearly transferred to the roll mode and the vessel oscillates in the roll direction. It is shown that the combination of the pitch as well as roll motion is far superior to the pitch motion since the combination results in full rotations of pendulum. A pendulum in full rotations generates orders of magnitude more power compared to a locally oscillating pendulum.

The dynamics of space structures is significantly impacted by the presence of power and electronic cables. Robust physical model is essential to investigate how the host structure dynamics is influenced by cable harnessing. All the developed models only considered the decoupled bending motion. Initial studies by authors point out the importance of coordinate coupling in structures with straight longitudinal cable patterns. In this article, an experimentally validated mathematical model is developed to analyze the fully coupled dynamics of beam with a more complex cable wrapping pattern which is periodic in nature. The effects of cable wrapping pattern and geometry on the system dynamics are investigated through the proposed coupled model. Homogenization-based mathematical modeling is developed to obtain an analogous solid beam that represents the cable wrapped system. The energy expressions obtained for fundamental repeating segment are transferred into the global coordinates consisting of several periodic elements. The coupled partial differential equations (PDE) are obtained for an analogous solid structure. The advantage of the proposed analytical model over the existing models to analyze the vibratory motion of beam with complex cable wrapping pattern has been shown through experimental validation.

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When there is a two to one internal resonance ratio between the natural frequencies of the pitch motion and the roll motion of a ship, a nonlinear energy transfer occurs between the modes. If the ship is excited near the pitch natural frequency and at a large enough excitation amplitude, the pitch mode transfers energy to the roll mode. We use this interesting phenomenon to develop a wave power device for off-shore purposes. In this paper, we experimentally show that we can use a horizontal pendulum and use the quadratic nonlinear coupling between the pitch and the roll mode to get full rotation of the pendulum inside the ship. A rotating pendulum will generate orders of magnitude more power than a locally oscillating one when connected to a DC generator. This article measures the angle of the pendulum at the pitch frequency excitation of the ship to experimentally confirm the expected theoretical results on this phenomenon.