Showing papers on "Natural frequency published in 2004"

Vibration suppression capabilities of magnetorheological materials based adaptive structures

Abstract: This paper discusses the investigation of vibration suppression capabilities of magnetorheological (MR) materials in adaptive structures. Homogeneous three-layered adaptive beams with MR materials sandwiched between two elastic layers were considered. By varying the externally applied magnetic field level over the MR layer, the stiffness and damping properties of the adaptive beam can be varied. These variations in the damping and stiffness properties can be used to tune the vibration characteristics of the adaptive beams such as natural frequencies, vibration amplitudes, mode shapes and loss factors. In this study, theoretical investigation of the MR adaptive beams vibration behavior based on the energy approach is accomplished. Experiments were performed to observe the theoretically predicted vibration responses in real time. From both studies, vibration suppression capabilities of MR adaptive beams were observed in the forms of shifts in natural frequency values, variations in loss factors, and vibration amplitudes.

Free Vibration Analysis of Rotating Blades With Uniform Tapers

Abstract: A spectral finite element method (SFEM) is proposed to develop a low-degree-of-freedom model for dynamic analysis of rotating tapered beams. The method exploits semi-analytical progressive wave solutions of the governing partial differential equations. Only one single spectral finite element is needed to obtain any modal frequency or mode shape, which is as accurate or better than other approaches reported in the literature for straight or uniformly tapered beams. The minimum number of such spectral finite elements corresponds to the number of substructures, that is, beam sections with different uniform tapers, in a rotating beam to capture the complete system dynamic characteristics. The element assembly procedure is accomplished in the same fashion as the conventional finite element approach. Results are for a number of examples such as a straight beam and beams with uniform taper or compound tapers. Overall, for a rotating blade system, our SFEM provides highly accurate predictions for any modal frequency using a single element or very few elements corresponding to the number of uniform taper changes in the blade system. Nomenclature EI (x) = beam bending flexural stiffness EI 0 = reference beam bending flexural stiffness L = beam length M(x) = beam bending moment m(x) = beam mass per unit length m0 = reference beam mass per unit length R =o ffset length between beam and rotating hub T (x) = beam axial force due to centrifugal stiffening V (x) = beam shear force W(x) = beam bending mode shape function w(x, t) = beam transverse displacement α = beam mass per unit length constant βi = beam bending flexural stiffness constant, i = 1, 4 η = nondimensional axial force µ = nondimensional natural frequency � = beam rotation speed ω =e xcitation frequency

Natural sway frequencies and damping ratios of trees: concepts, review and synthesis of previous studies

Abstract: Previous studies that measured the natural frequencies and damping ratios of conifer trees were reviewed and results synthesized. Analysis of natural frequency measurements from 602 trees, belonging to eight different species, showed that natural frequency was strongly and linearly related to the ratio of diameter at breast height to total tree height squared (i.e., DBH/H2). After accounting for their size, pines (Pinus spp.) were found to have a significantly lower natural frequency than both spruce (Picea spp.) and Douglas-fir (Pseudotsuga spp.). Natural sway frequencies of de-branched trees were significantly higher than those of the same trees with the branches intact, and the difference increased with an increasing ratio of DBH/H2. Damping mechanisms were discussed and methods for measuring damping ratio were presented. Analysis of available data suggested that internal damping ratios were typically less than 0.05 and were not related to tree diameter. External damping was mainly due to aerodynamic drag on the foliage and contact between the crowns of adjacent trees. Analysis of data from previous wind-tunnel studies indicated that damping due to aerodynamic drag is a nonlinear function of velocity. Damping due to crown contact has been suggested by a previous author to be a function of both the distance to and the size of adjacent trees. Therefore, in uniformly spaced stands it may be possible to model crown contact damping as a function of stand density index (SDI), a common forestry measure which incorporates both of these variables.

Identification of Natural Frequencies and Dampings of In Situ Tall Buildings Using Ambient Wind Vibration Data

Abstract: An accurate prediction for the response of tall buildings subject to strong wind gusts or earthquakes requires the information of in situ dynamic properties of the building, including natural frequencies and damping ratios. This paper presents a method of identifying natural frequencies and damping ratios of in situ tall buildings using ambient wind vibration data. Our approach is based on the empirical mode decomposition (EMD) method, the random decrement technique (RDT), and the Hilbert–Huang transform. Our method requires only one acceleration sensor. The noisy measurement of the building acceleration is first processed through the EMD method to determine the response of each mode. Then, RDT is used to obtain the free vibration modal response. Finally, the Hilbert transform is applied to each free vibration modal response to identify natural frequencies and damping ratios of in situ tall buildings. The application of the proposed methodology is demonstrated in detail using simulated response data of a ...

Resonance frequency of microbubbles: Effect of viscosity

Abstract: The transmitted frequency at which a gas bubble of millimeter or submillimeter size oscillates resonantly in a low-viscosity liquid is approximately equal to the undamped natural frequency (referred to as the Minnaert frequency if surface tension effects are disregarded). Based on a theoretical analysis of bubble oscillation, this paper shows that such an approximation cannot be validated for microbubbles used in contrast-enhanced ultrasound imaging. The contrast-agent microbubbles represent either encapsulated bubbles of size less than 10 microm or free (nonencapsulated) bubbles of submicron size. The resonance frequency of the microbubbles deviates significantly from the undamped natural frequency over the whole range of microbubble sizes due to the increased viscous damping coefficient. The difference between these two frequencies is shown to have a tremendous impact on the resonant backscatter by the microbubbles. In particular, the first and second harmonics of the backscattered signal from the microbubbles are characterized by their own resonance frequencies, equal to neither the microbubble resonance frequency nor the undamped natural frequency.

Micromachined silicon Generator for Harvesting Power from Vibrations

Abstract: This paper describes the design, simulation and fabrication of an electromagnetic device for generating electrical energy from vibrations. A range of dimensions has been simulated using ANSYS in order to determine natural frequencies and material stresses. A 300µm wide paddle beam gives a natural frequency of 6.4 kHz for the mode of operation and induced stresses at maximum amplitudes are well within material limits. Ansoft's Maxwell 2D has been used to predict the voltages generated and an integrated electroplated coil of 71 turns produces 0.38V with no load. Devices are currently being fabricated and the process is described.

The natural frequencies of the arterial system and their relation to the heart rate

Abstract: We assume the major function of the arterial system is transporting energy via its transverse vibration to facilitate the blood flowing all the way down to the microcirculation. A highly efficient system is related to maintaining a large pressure pulse along the artery for a given ventricular power. The arterial system is described as a composition of many infinitesimal Windkessels. The strong tethering in the longitudinal direction connects all the Windkessels together and makes them vibrate in coupled modes. It was assumed that at rest condition, the arterial system is in a steady distributed oscillatory state, which is the superposition of many harmonic modes of the transverse vibration in the arterial wall and the adherent blood. Every vibration mode has its own characteristic frequency, which depends on the geometry, the mass density, the elasticity, and the tethering of the arterial system. If the heart rate is near the fundamental natural frequency, the system is in a good resonance condition, we call this "frequency matching". In this condition, the pulsatile pressure wave is maximized. A pressure wave equation derived previously was used to predict this fundamental frequency. The theoretical result gave that heart rate is proportional to the average high-frequency phase velocity of the pressure wave and the inverse of the animal body length dimension. The area compliance related to the efficiency of the circulatory system is also mentioned.

Wave Power Generator

Abstract: An object is to provide a wave power generator which can convert wave energy to electric energy with high efficiency and supply electric power of a large capacity at low cost and has a simple structure and is low in construction cost. The wave power generator includes a heavy body 3 elastically supported by air springs 4 as elastic members in an enclosing wall 2 on a floating body 1 and an electromagnetic damper as a generating means 7 provided between the heavy body 3 and the floating body 1 . The spring constant of the air springs 4 is adjustable by providing auxiliary tanks in the piston 6 and the floating body 1 so that the undamped natural frequency of the air spring is equal to or close to the frequency of waves within a predetermined frequency ratio ω/ω 0 . Thus, the frequency of the spring system resonates with the frequency of waves, so that the relative movement of the power generating means 7 increases to a maximum and power generation is carried out with maximum efficiency.

Transient energy exchange between a primary structure and a set of oscillators: return time and apparent damping.

Abstract: In this paper we examine the conditions that influence the return time, the time it takes before energy returns from a set of satellite oscillators attached to a primary structure. Two methods are presented to estimate the return time. One estimate is based on an analysis of the reaction force on a rigid base by a finite number of oscillators as compared with an infinite number of continuously distributed oscillators. The result gives a lower-bound estimate for the return time. A more accurate estimation results from considering the dynamic behavior of a set of oscillators as waves in a waveguide. Such an analogy explains energy flow between a primary structure and the oscillators in terms of pseudowaves and shows that a nonlinear frequency distribution of the oscillators leads to pseudodispersive waves. The resulting approximate expressions show the influence of the natural frequency distribution within the set of oscillators, and of their number, on the return time as compared with the asymptotic case of a continuous set with infinite oscillators. In the paper we also introduce a new method based on a Hilbert envelope to estimate the apparent damping loss factor of the primary structure during the return time considering transient energy flow from the primary structure before any energy reflects back from the attached oscillators. The expressions developed for return time and damping factor show close agreement with direct numerical simulations. The paper concludes with a discussion of the return time and its relation to apparent damping and optimum frequency distribution within a set of oscillators that maximize these quantities.

Parametric resonance and nonlinear string vibrations

Abstract: Periodic changes in the tension of a taut string parametrically excite transverse motion in the string when the driving frequency is close to twice the natural frequency of any transverse normal mode of the string. The literature on this phenomenon is synthesized and extended to include the effects of damping as well as nonlinearity. It is shown that it is nonlinearity rather than damping that limits the growth of a resonantly excited mode, although damping is needed for steady-state oscillations to occur. The validity of the usual approximation that the string tension depends only on time and not on space is checked by modeling a string as point masses joined by massless linear springs. It is found that although this approximation is likely to be violated in practice, the violation does not have a significant effect on the results. The source of the disagreement in the literature for the speed of longitudinal waves in a stretched string is identified.

Estimation of power system parameters

Abstract: This paper describes the use of a system identification technique to estimate the parameters of a low-order, dynamic model for a power system. The basic technique is to obtain an ARIMAX model by applying a prediction error method to data consisting of 1-s samples of the system frequency and the power output of the Dinorwig fast-response pumped-storage station. From this model the natural frequency, damping factor and stiffness (or "beta") of the power system are obtained. The paper first establishes an appropriate order for the ARIMAX model. Simulation is used to validate the model and ensure that the results are not an artefact of either the input, the identification method or the model structure. It is shown that the precision of the parameter estimates is limited by unknown load disturbances. An example of the use of the technique to analyze the daily variation of parameters is given.

Testing of tuned liquid damper with screens and development of equivalent TMD model

Abstract: The tuned liquid damper (TLD) is increasingly being used as an economical and effective vibration absorber. It consists of a water tank having the fundamental sloshing fluid frequency tuned to the natural frequency of the structure. In order to perform efficiently, the TLD must possess a certain amount of inherent damping. This can be achieved by placing screens inside the tank. The current study experimentally investigates the behaviour of a TLD equipped with damping screens. A series of shake table tests are conducted in order to assess the effect of the screens on the free surface motion, the base shear forces and the amount of energy dissipated. The variation of these parameters with the level of excitation is also studied. Finally, an amplitude dependent equivalent tuned mass damper (TMD), representing the TLD, is determined based on the experimental results. The dynamic characteristics of this equivalent TMD, in terms of mass, stiffness and damping parameters are determined by energy equivalence. The above parameters are expressed in terms of the base excitation amplitude. The parameters are compared to those obtained using linear small amplitude wave theory. The validity of this nonlinear model is examined in the companion paper.

Image reader for use in image forming apparatus

Abstract: An image reader of the present invention comprises a fluctuation detector that can be connected to the external equipment by means of an image data input-output section, and can subject image data, continuous in a first direction and outputted as image information on a test chart is photoelectrically converted by means of a CCD sensor when a mirror set or the test chart is moved in the first direction, to Fourier conversion, thereby obtaining the frequency of a fluctuation of the obtained image data and a maximum value of the amplitude thereof. If the obtained maximum value of the fluctuation amplitude is greater than a given value, the fluctuation detector is used to compare the frequency of the fluctuation and the natural frequency of a drive motor for generating driving force for moving the mirror set or the image. If the fluctuation frequency and the natural frequency are not equal, the value of current supplied to the drive motor is increased.