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Purpose: The design of a new meta-structure with quasi-zero stiffness (QZS) characteristics based on human body structure not only expands the diversity of quasi-zero stiffness structures but also demonstrates excellent performance in the field of low-frequency vibration damping. Methods: Firstly, a quasi-zero stiffness unit structure combining a horizontal cosine beam and vertical cosine beam is designed based on the human body structure, and multiple unit structures are combined into one meta-structure; secondly, according to the material-structural properties of the unit, a functional relationship is established for the positive stiffness structure using the segmental function method, which is combined with the functional relationship of the negative stiffness structure to obtain the theoretical model of the unit structure and then derives the mechanics of the whole meta-structure behavior of the whole meta-structure. Then, the unit structure model and the meta-structure model are designed and simulated, the static properties of the meta-structure are investigated, and photosensitive resin is chosen as the material in the simulation process. Finally, the transmittance comparison between the meta-structure and the linear vibration isolation structure with different damping coefficients is analyzed by theory, and the vibration isolation performance of the meta-structure is simulated. Results: The static simulation analysis of the meta-structure verifies the theoretical solution of the meta-structure very well. According to the theoretical formulation, different parameters can be input to obtain the quasi-zero stiffness properties of the structure. The quasi-zero stiffness properties of the structure are independent of the inherent material properties. Due to the nonlinear nature of the quasi-zero stiffness unit structure, it not only has a lower peak transmittance, but also a lower resonant frequency and a wider isolation range compared with the linear vibration isolator. Conclusions: The designed quasi-zero stiffness meta-structure is suitable for low-frequency vibration isolation of precision instruments, which can be realized by different materials, and more complex meta-structures can be designed on this basis in the future, which has great potential for application in engineering practice. [ABSTRACT FROM AUTHOR]

Purpose: For fixed or hinged single cables, the vibration equation is well developed. However, the form of boundary constraints between fixed and hinged is used extensively for the single cable in practical engineering, such as the restraint of struts between multi-span cables. As the struts with different lengths and stiffness are placed in the single cable, the mode shape of the multi-span cables is affected significantly. Moreover, with the decrease in the aspect ratio of single-span cable, the effect of the cable bending stiffness cannot be overlooked. The above effects in single and multi-span cables are studied in the proposed model. Methods: The vibration equation of the multi-span cable is developed in two steps. To establish the vibration equation of the single cable with general elastic constraint, the constraints at the ends of the strut are simplified as the compression springs that can bear the pressure. The bending springs that can consider the bending stiffness are also set at both ends simultaneously, then the vibration equation of the single cable with a general elastic constraint can be derived. For a multi-span cable structure, the strut is simplified into the elastic constraints of a single-span cable. By combining the aforementioned vibration equations of single-span cables which have general constraints, the vibration equation of multi-span cables can be established. Results: The vibration frequency equations of m span multi-span cable with constraint stiffness are established, and the objective function optimization algorithm is validated. Conclusion: The analytical solution of the multi-span cable vibration equation in this paper is then validated by the comparison with the multi-span cable vibration model established by the finite element method. The comparison demonstrated that the proposed method is valid and practical. [ABSTRACT FROM AUTHOR]

Purpose: To suppress the low-frequency vibration of dynamic systems such as underwater vehicles, this research proposes a novel geometrically nonlinear vibration isolator using hybrid nonlinear inertial and negative stiffness element. Methods: A spring and an inerter are integrated together into a 4-rod linkage structure to form geometric nonlinearity. The performance of isolator under force or base-motion excitation is analysed. The performance of the proposed isolator in a flexible base structure simulating vibration isolation in ships is also considered. The transmissibilities and vibrational energy transfer are used to evaluate the effectiveness of isolation. Results: The results demonstrate better performance in low-frequency vibration isolation comparing to conventional linear isolator. The combined use of spring and inerter in the linkage mechanism can create a frequency band of ultra-low transmissibility and energy flow at low frequencies. Conclusion: Structural parameters of the proposed hybrid nonlinear element can be designed to alter the dynamic characteristic of the nonlinear isolator to attenuate low-frequency vibration transmission. The proposed nonlinear isolator demonstrates a strong potential for application in naval architecture. [ABSTRACT FROM AUTHOR]

Purpose: This article demonstrates the possibility of energy harvesting by mistuned pendulums with torsional coupling. Two pendulums of different lengths with coils and magnets at the pivots are used as electromagnetic harvesters. The ambient energy source to the system is considered in the form of harmonic base excitations. Torsional coupling is achieved by connecting the pendulums with a torsional spring. The non-linearity of the underlying dynamics arises due to mechanical coupling and forcing amplitude. Numerical results are presented to analyze the performance of the pendulum energy harvester under different torsional coupling values. Method: The mathematical model of the electro-mechanical system with torsionally coupled pendulums under harmonic excitation is developed. The mistuning is introduced by two pendulums with different lengths l1 and l2. The coupling between them is achieved by a torsional spring of stiffness kc. These pendulums are connected to the shafts of the electromagnetic generators with a magnet attached to the pendulum as a rotor and coil as stator. Current i is generated due to electromagnetic induction whenever pendulum oscillates. The numerical and harmonic balance method analysis were carried out. Runge-Kutta integration was used for numerical analysis. The analysis was carried out to determine the effect of coupling, length and resistive coefficient. The bifurcation diagram and Poincare plots were used for dynamic analysis and cross recurrence plots for analysis of relations between pendulum harvesters. Results: The effect of coupling on harvester performance was carried out, the variation of maximum power and frequency band with coupling can be categorized into 3 zones. The ranges for Zone-I, II and III of maximum power are [0-0.059], [0.06-0.11] and above 0.11 respectively. In Zone-I total power and the total band are dominating over pendulum-1 and pendulum-2. In Zone-II, the performance of pendulum-2 is comparable with the total performance. In contrast, the performance of pendulum-1 is low. Saturation of maximum power and bandwidth can be observed in zone-III. Uncoupled pendulum-1 and 2 exhibits a periodic oscillation. A low amplitude quasi-periodic response of pendulum-1 and high amplitude quasiperiodic response of pendulum-2 can be observed for coupling of β = 0.04. Both pendulums exhibit high amplitude chaotic response at β = 0.07. The introduction of coupling induced nonlinearity in both pendulums. the amplitude and velocity also increased due to the quasi-periodicity and chaos induced in pendulums due to the coupling and better energy harvesting capabilities can be expected. The harmonic balance analysis indicates that there is a possibility of obtaining a high amplitude current at lower frequencies provided proper initial conditions are chosen. Conclusion: A twin electromagnetic pendulum energy harvester with torsional coupling is analyzed in order to optimize the efficient energy harvesting and study the energy harvester dynamics. The paper categorized the three distinct zones based on the coupling ratio β and length ratio α2. One can select parameters from these zones based on need. Zones-II and III are the most promising zones. If one wants to harvest broader energy Zone-II is preferable with harvesting only from the energy harvester with a low resonant frequency which in turn saves material cost. To harvest peak power one can, select Zone-III and harvest from both energy harvesters. The performance in the respective zones can be further enhanced by using optimal initial conditions to obtain high energy orbits at lower frequencies. The probability of obtaining high energy orbits decreases with an increase in the coupling ratio. The effect synchronization with coupling on energy harvesting plays an important role form magnitude and bandwidth point of view. The analytical results obtained by the Harmonic Balance Method are in good agreement with numerical results. [ABSTRACT FROM AUTHOR]