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Formulas for natural frequency and mode shape
01 Jan 1979-
About: The article was published on 1979-01-01 and is currently open access. It has received 2002 citations till now. The article focuses on the topics: Natural frequency & Normal mode.
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TL;DR: In this article, the authors present a comprehensive review of the principles and operating strategies for increasing the operating frequency range of vibration-based micro-generators presented in the literature to date.
Abstract: This paper reviews possible strategies to increase the operational frequency range of vibration-based micro-generators. Most vibration-based micro-generators are spring-mass-damper systems which generate maximum power when the resonant frequency of the generator matches the frequency of the ambient vibration. Any difference between these two frequencies can result in a significant decrease in generated power. This is a fundamental limitation of resonant vibration generators which restricts their capability in real applications. Possible solutions include the periodic tuning of the resonant frequency of the generator so that it matches the frequency of the ambient vibration at all times or widening the bandwidth of the generator. Periodic tuning can be achieved using mechanical or electrical methods. Bandwidth widening can be achieved using a generator array, a mechanical stopper, non-linear (e.g. magnetic) springs or bi-stable structures. Tuning methods can be classified into intermittent tuning (power is consumed periodically to tune the device) and continuous tuning (the tuning mechanism is continuously powered). This paper presents a comprehensive review of the principles and operating strategies for increasing the operating frequency range of vibration-based micro-generators presented in the literature to date. The advantages and disadvantages of each strategy are evaluated and conclusions are drawn regarding the relevant merits of each approach.
588 citations
Cites methods from "Formulas for natural frequency and ..."
...For a cantilever with a mass at the free end (figure 3), the resonant frequency is given by [10]...
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01 Sep 2001
TL;DR: In this article, the authors developed and verified a six degree of freedom, non-linear simulation model for the REMUS vehicle, the first such model for this platform, and the simulator output is then checked against vehicle dynamics data collected in experiments performed at sea.
Abstract: Improving the performance of modular, low-cost autonomous underwater vehicles (AUVs) in such applications as long-range oceanographic survey, autonomous docking, and shallow-water mine countermeasures requires improving the vehicles' maneuvering precision and battery life. These goals can be achieved through the improvement of the vehicle control system. A vehicle dynamics model based on a combination of theory and empirical data would provide an efficient platform for vehicle control system development, and an alternative to the typical trial-and-error method of vehicle control system field tuning. As there exists no standard procedure for vehicle modeling in industry, the simulation of each vehicle system represents a new challenge. Developed by von Alt and associates at the Woods Hole Oceanographic Institute, the REMUS AUV is a small, low-cost platform serving in a range of oceanographic applications. This thesis describes the development and verification of a six degree of freedom, non-linear simulation model for the REMUS vehicle, the first such model for this platform. In this model, the external forces and moments resulting from hydrostatics, hydrodynamic lift and drag, added mass, and the control inputs of the vehicle propeller and fins are all defined in terms of vehicle coefficients. This thesis describes the derivation of these coefficients in detail. The equations determining the coefficients, as well as those describing the vehicle rigid-body dynamics, are left in non-linear form to better simulate the inherently non-linear behavior of the vehicle. Simulation of the vehicle motion is achieved through numeric integration of the equations of motion. The simulator output is then checked against vehicle dynamics data collected in experiments performed at sea. The simulator is shown to accurately model the motion of the vehicle. Thesis Supervisor: Jerome Milgram Title: Professor of Ocean Engineering, MIT Thesis Supervisor: Kamal Youcef-Toumi Title: Professor of Mechanical Engineering, MIT Thesis Supervisor: Christopher von Alt Title: Principal Engineer, WHOI Candide had been wounded by some splinters of stone; he was stretched out in the street and covered with debris. He said to Pangloss: "Alas, get me a little wine and oil, I am dying." "This earthquake is not a new thing," replied Pangloss. "The town of Lima suffered the same shocks in America last year; same causes, same effects; there is certainly a vein of sulfur underground from Lima to Lisbon." "Nothing is more probable," said Candide, "but for the love of God, a little oil and wine." "What do you mean, probable?" replied the philosopher. "I maintain that the matter is proved." Candide lost consciousness.
535 citations
TL;DR: In this paper, a review of the literature related to the vibratory behavior of carbon nanotubes and their composites is presented, along with key conclusions and recommendations from these studies.
502 citations
TL;DR: In this article, a new class of vibration energy harvester based on magnetostrictive material (MsM), Metglas 2605SC, is designed, developed and tested.
Abstract: A new class of vibration energy harvester based on magnetostrictive material (MsM), Metglas 2605SC, is designed, developed and tested. It contains two submodules: an MsM harvesting device and an energy harvesting circuit. Compared to piezoelectric materials, the Metglas 2605SC offers advantages including higher energy conversion efficiency, longer life cycles, lack of depolarization and higher flexibility to survive in strong ambient vibrations. To enhance the energy conversion efficiency and alleviate the need of a bias magnetic field, Metglas ribbons are transversely annealed by a strong magnetic field along their width direction. To analyze the MsM harvesting device a generalized electromechanical circuit model is derived from Hamilton’s principle in conjunction with the normal mode superposition method based on Euler‐Bernoulli beam theory. The MsM harvesting device is equivalent to an electromechanical gyrator in series with an inductor. In addition, the proposed model can be readily extended to a more practical case of a cantilever beam element with a tip mass. The energy harvesting circuit, which interfaces with a wireless sensor and accumulates the harvested energy into an ultracapacitor, is designed on a printed circuit board (PCB) with plane dimension 25 mm × 35 mm. It mainly consists of a voltage quadrupler, a 3 F ultracapacitor and a smart regulator. The output DC voltage from the PCB can be adjusted within 2.0‐5.5 V. In experiments, the maximum output power and power density on the resistor can reach 200 μW and 900 μ Wc m −3 , respectively, at a low frequency of 58 Hz. For a working prototype under a vibration with resonance frequency of 1.1 kHz and peak acceleration of 8.06 m s −2 (0.82 g), the average power and power density during charging the ultracapacitor can achieve 576 μ Wa nd 606 μ Wc m −3 , respectively, which compete favorably with piezoelectric vibration energy harvesters. (Some figures in this article are in colour only in the electronic version)
441 citations
Cites background or methods from "Formulas for natural frequency and ..."
...By taking the mode shape function of equation (28) and using integral formulae containing φi from the handbook [22], the closed-form of modal matrices can be further simplified as...
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...Table 2 lists the mode shape constants of λi and ηi for a cantilever beam from the handbook [22]....
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TL;DR: Graphene oxide films' ability to withstand high in-plane tension as well as their high Q-values reveals that film integrity is enhanced by platelet-platelet bonding unavailable in pure graphite.
Abstract: We report a process to form large-area, few-monolayer graphene oxide films and then recover the outstanding mechanical properties found in graphene to fabricate high Young’s modulus ( ) 185 GPa), low-density nanomechanical resonators. Wafer-scale films as thin as 4 nm are sufficiently robust that they can be delaminated intact and resuspended on a bed of pillars or field of holes. From these films, we demonstrate radio frequency resonators with quality factors (up to 4000) and figures of merit (f × Q >1 0 11 ) well exceeding those of pure graphene resonators reported to date. These films’ ability to withstand high in-plane tension (up to 5 N/m) as well as their high Q-values reveals that film integrity is enhanced by platelet-platelet bonding unavailable in pure graphite. Nanoelectromechanical systems (NEMS) are an exciting frontier 1 for the next generation devices in both sensing 2-4 and computing. 5 As NEMS resonators shrink below 100 nm they begin to achieve high operating frequencies (up to 10 9
424 citations