Showing papers on "Natural frequency published in 2005"
TL;DR: In this article, the stiffness and damping properties of carbon nanotube-epoxy composites are examined for use in structural vibration applications, and it is observed that enhancement in damping ratio is more dominant than enhancement in stiffness by using carbon Nanotube reinforcement.
215 citations
TL;DR: In this paper, the authors present the results of a dynamic finite element analysis of a planar fully parallel robot with flexible links, which leads to a set of linear ordinary differential equations of motion.
193 citations
TL;DR: In this paper, an analytical, as well as experimental approach to the crack detection in cantilever beams by vibration analysis is established, which is based on measured frequencies and mode shapes of the beam.
192 citations
TL;DR: In this paper, the incremental harmonic balance (IHB) method is formulated for the nonlinear vibration analysis of axially moving beams, and the Galerkin method is used to discretize the governing equations.
150 citations
143 citations
TL;DR: In this article, a general asymptotic format is presented for the effect on the modal vibrations of a transverse damper close to the end of a cable, and it is demonstrated that the maximum attainable damping is a certain fraction of the relative frequency increase, depending on the type of damping device.
Abstract: A general asymptotic format is presented for the effect on the modal vibrations of a transverse damper close to the end of a cable. Complete locking of the damper leads to an increase of the natural frequencies, and it is demonstrated that the maximum attainable damping is a certain fraction of the relative frequency increase, depending on the type of damping device. The asymptotic format only includes a real and a complex nondimensional parameter, and it is demonstrated how these parameters can be determined from the frequency increase by locking and from an energy balance on the undamped natural vibration modes. It is shown how the asymptotic format can incorporate sag of the cable, and specific results are presented for viscous damping, the effect of stiffness and mass, fractional viscous damping, and a nonlinear viscous damper. The relation of the stiffness component to active and semiactive damping is discussed.
120 citations
TL;DR: In this article, a voice coil motor is used as the actuator in an active dynamic vibration absorber which can be regulated for different conditions by using the root-locus theorem.
Abstract: A dynamic vibration absorber reduces the influence of a force whose excitation frequency nearly coincides with the natural frequency of a rotating machine. However, the performance of this type of passive absorber can be affected by changes in the environment. In this paper, we describe a voice coil motor (VCM) that can serve as the actuator in an active dynamic vibration absorber which can be regulated for different conditions. With a VCM, suitable controllers can be designed for periodic excitation force rejection by using the characteristics of the notch filter in combination with the root-locus theorem. We have evaluated the performance of the active vibration absorber by both simulations and experiments.
112 citations
TL;DR: In this article, the authors measured the natural frequency and damping ratio of nine plantation-grown Douglas-fir (Pseudotsuga menziesii Mirb. Franco) trees from the Oregon Coast Range under different levels of crown removal.
Abstract: Natural frequency and damping ratio were measured for nine plantation-grown Douglas-fir (Pseudotsuga menziesii Mirb. Franco) trees from the Oregon Coast Range under different levels of crown removal. Natural frequency of trees, in both their unpruned and completely de-branched states, was linearly related to the ratio of diameter at breast height to total tree height squared (i.e., DBH/H2), as expected from the theory governing the oscillation of a cantilever beam. Pruning resulted in an increase in natural frequency; however, at least 80% of the crown mass needed to be removed before this increase was noticeable. A single equation was developed that enabled the natural frequency of a tree of given size and pruning intensity to be predicted. Damping ratios of unpruned trees varied considerably from 8% to almost critical, while those for completely de-branched trees ranged from 1% to 8%. Two different trends in damping ratio were observed during pruning. Some trees exhibited an increase in damping ratio with initial crown removal, followed by a sharp decrease when the uppermost portion of the crown was removed. Others showed little or no change in damping ratio followed by a sharp reduction upon removal of the uppermost portion of the crown. Damping was mainly due to aerodynamic drag and preventing interference with neighbouring trees had little effect. Theoretical analysis using the finite element method indicated that changes in natural frequency as a result of pruning are not due to changes in damping ratio, but rather changes in mass distribution. This analysis also suggested that treating branches as lumped masses rather than individual cantilevers attached to the main stem may not be appropriate.
110 citations
TL;DR: In this paper, the authors demonstrated that the theoretical performance of the resonant microcantilever chemical sensor is essentially due to the resonance value and not due to mode order.
Abstract: By measuring shifts in the resonant frequency of a silicon microcantilever coated with a sensitive layer, it is possible to obtain a competitive chemical microsensor. In fact, the sensitivity of such a microsensor is improved when used in high resonant frequency device. Usually, to increase the resonant frequency, smaller microcantilevers are used. The limitation on increasing the natural frequency by reducing the microstructure size is often due to the limitation of the deflection measurement principle. Furthermore, it could also be difficult to obtain reproducible sensitive coatings on very small surfaces. In order to achieve high sensitivities corresponding to high frequencies without decreasing the microstructure size, high-order flexural modes can be considered. In this paper, it is demonstrated that the theoretical performance of the resonant microcantilever chemical sensor is essentially due to the resonant frequency value and not due to the mode order. The advantages of increasing the resonant frequency by using high-order modes is also confirmed experimentally.
108 citations
TL;DR: In this article, a global linear stability analysis (LSA) for the combined flow and oscillator was carried out for a cylinder with low non-dimensional mass and was found that vortex shedding and self-excited vibrations of the cylinder are possible for Re as low as 20.
Abstract: Flow past a stationary cylinder becomes unstable at Re. Flow-induced vibrations of an elastically mounted cylinder, of low non-dimensional mass, is investigated at subcritical Reynolds numbers. A stabilized finite-element formulation is used to solve the incompressible flow equations and the cylinder motion in two dimensions. The cylinder is free to vibrate in both the transverse and in-line directions. It is found that, for certain natural frequencies of the spring–mass system, vortex shedding and self-excited vibrations of the cylinder are possible for Re as low as 20. Lock-in is observed in all cases. However, the mass of the oscillator plays a major role in determining the proximity of the vortex-shedding frequency to the natural frequency of the oscillator. A global linear stability analysis (LSA) for the combined flow and oscillator is carried out. The results from the LSA are in good agreement with the two-dimensional direct numerical simulations.
104 citations
TL;DR: In this paper, the average radiation efficiency of point-excited rectangular plates, including those with a very large aspect ratio (strips), was investigated by using a modal summation method based on the farfield sound intensity.
TL;DR: In this article, the first cantilever of the Second Severn Crossing cable-stayed bridge was monitored for dynamic effects during construction and the contribution of aerodynamic and structural damping were separated, and the magnitude of the components was discussed.
TL;DR: In this article, a first electrode, a second electrode, and a mobile element are coupled to a first voltage source and an oscillating voltage difference between the second electrode and the third electrode at the scanning frequency of the application is used to oscillate the mobile element.
Abstract: In one embodiment of the invention, a MEMS structure includes a first electrode, a second electrode, and a mobile element. The first electrode is coupled to a first voltage source. The second electrode is coupled to a second voltage source. The mobile element includes a third electrode coupled to a third voltage source. A steady voltage difference between the first electrode and the third electrode is used to tune the natural frequency of the structure to a scanning frequency of an application. An oscillating voltage difference between the second electrode and the third electrode at the scanning frequency of the application is used to oscillate the mobile element. In one embodiment, the mobile unit is a mirror.
TL;DR: In this article, the frequency dependence of damping in symmetric, three-layered, laminated, micromechanical Euler-Bernoulli beams using an analytical framework developed by Bishop and Kinra was investigated.
Abstract: Minimization of structural damping is an essential requirement in the design of multifunctional composite micromachined resonators used for sensing and communications applications. Here, we study thermoelastic damping in symmetric, three-layered, laminated, micromechanical Euler–Bernoulli beams using an analytical framework developed by Bishop and Kinra in 1997. The frequency dependence of damping in two representative sets of structures—metallized ceramic beams and ceramic/ceramic laminates—is investigated in detail. The effects of material properties and relative volume fractions are numerically evaluated. The results indicate that metallization of Si and SiC beams using Al, Cu, Ag or Au leads to a considerable increase in damping over a broad frequency range. Similarly, coating silicon with SiC leads to a monotonic increase of the peak damping value as a function of the volume fraction of silicon carbide but, remarkably, there exists a range of frequencies at which the damping in the composite is less than that of bare silicon. Implications for the design of metallized ceramic beams, and for the simultaneous optimization of natural frequency and damping, are discussed.
TL;DR: In this paper, a two-dimensional nonlinear random sloshing problem is analyzed by the fully nonlinear wave velocity potential theory based on the finite element method, where wave elevation and hydrodynamic force are obtained.
TL;DR: In this paper, the damping performance of a single particle vertical impact damper over a wide range of excitation frequencies and amplitudes, particle-to-structure mass ratios, lid clearance ratios, structural damping ratios, and coefficients of restitution were investigated.
TL;DR: In this article, the free vibration of composite beams with two overlapping delaminations has been solved analytically without resorting to numerical approximation, and the influence of the longer delamination on the natural frequencies and mode shapes of the cantilever and clamped-clamped beams are investigated.
Abstract: The free vibration of composite beams with two overlapping delaminations have been solved analytically without resorting to numerical approximation. The delaminated beam is analyzed as seven interconnected Euler–Bernoulli beams using the delaminations as their boundaries. The continuity and equilibrium conditions are satisfied between the adjoining regions of the beams. Lower and upper bounds of the natural frequencies of the delaminated beams are identified by assuming totally ‘free’ and totally ‘constrained’ deformations of the delaminated layers, respectively. The influence of the delaminations on the natural frequencies and mode shapes of the cantilever and clamped–clamped beams are investigated. Results show the dominating influence of the longer delamination on the natural frequency of the beam. Similar trends are observed for the second mode frequency and mode shape of the cantilever beam and the fundamental frequency and mode shape of the clamped–clamped beam. Comparison with analytical and experimental results reported in the literature verifies the validity of the present solution.
TL;DR: In this article, a fully nonlinear 2-D σ -transformed finite difference solver was developed based on inviscid flow equations in rectangular tanks, where the fluid equations were coupled to a linear elastic support structure.
TL;DR: In this paper, the authors presented a methodology to analyze the influence of the foundation or supporting structure on the rotor-bearings system performance, using the Finite Elements Method (FEM) to model the rotor.
TL;DR: In this article, an analytical solution for the static deformation and steady-state vibration of simply supported hybrid cylindrical shells consisting of fiber-reinforced layers with embedded piezoelectric shear sensors and actuators is presented.
Abstract: An analytical solution is presented for the static deformation and steady-state vibration of simply supported hybrid cylindrical shells consisting of fiber-reinforced layers with embedded piezoelectric shear sensors and actuators. The piezoelectric shear actuator, which is poled in the circumferential direction, will induce transverse shear deformation of the hybrid shell when it is subjected to an electric field in the radial direction. Suitable displacement and electric potential functions that identically satisfy the boundary conditions at the simply supported edges are used to reduce the governing equations of static deformation and steady-state vibrations of the hybrid laminate to a set of coupled ordinary differential equations in the radial coordinate, which are solved by employing the Frobenius method. Natural frequencies, mode shapes, displacements, electric potential, and stresses are presented for four-layer hybrid laminates consisting of a piezoelectric shear sensor and actuator sandwiched between fiber-reinforced composite layers. Active vibration damping is implemented using a positive position feedback controller. Frequency response curves for different controller frequencies, controller damping ratio, and feedback gain demonstrate that the embedded shear actuator can be used for active damping of the fundamental flexural mode. In addition, it is demonstrated that vibration suppression of thickness modes is also feasible using the piezoelectric shear actuator.
Patent•
14 Mar 2005
TL;DR: In this paper, a method for driving a droplet ejection device having an actuator, including applying a multipulse waveform that includes two or more drive pulses to the actuator to eject a single droplet of a fluid, wherein a frequency of the drive pulses is greater than a natural frequency, fj, of the device.
Abstract: In general, in one aspect, the invention features a method for driving a droplet ejection device having an actuator, including applying a multipulse waveform that includes two or more drive pulses to the actuator to cause the droplet ejection device to eject a single droplet of a fluid, wherein a frequency of the drive pulses is greater than a natural frequency, fj, of the droplet ejection device.
TL;DR: In this article, a theoretical analysis of the flexural vibration of a beam with a control system which implements direct velocity feedback using either an ideal collocated force actuator or a closely located piezoelectric patch actuator is presented.
01 Jan 2005
TL;DR: In this paper, the stiffness and damping coefficients of a bump-type gas foil bearing were derived from the recorded periodic load and bearing motions at the system natural frequency, i.e. null damping.
Abstract: High performance oil-free turbomachinery implements gas foil bearings (FBs) to improve mechanical efficiency in compact units. FB design, however, is still largely empirical due to their mechanical complexity. The paper provides test results for the structural parameters in a bump-type foil bearing. The stiffness and damping (Coulomb or viscous type) coefficients characterize the bearing compliant structure. The test bearing, 38.1 mm in diameter and length, consists of a thin top foil supported on bump-foil strips. A prior investigation identified the stiffness due to static loads. Presently, the test FB is mounted on a non-rotating stiff shaft and a shaker exerts single frequency loads on the bearing. The dynamic tests are conducted at shaft surface temperatures from 25 °C to 75°C. Time and frequency domain methods are implemented to determine the FB parameters from the recorded periodic load and bearing motions. Both methods deliver identical parameters. The dry friction coefficient ranges from 0.05 to 0.20, increasing as the amplitude of load increases. The recorded motions evidence a resonance at the system natural frequency, i.e. null damping. The test derived equivalent viscous damping is inversely proportional to the motion amplitude and excitation frequency. The characteristic stick-slip of dry friction is dominant at small amplitude dynamic loads leading to a hardening effect (stiffening) of the FB structure. The operating temperature produces shaft growth generating a bearing preload. However, the temperature does not affect significantly the identified FB parameters, albeit the experimental range was too small considering the bearings intended use in industry.Copyright © 2005 by ASME
TL;DR: In this article, the authors deal with the internal resonances originated from parametric excitation of a slender pipe conveying fluid for marine applications, which corresponds to an excitation frequency that is equal to the double of the structure's first lateral natural frequency.
TL;DR: In this paper, two highly efficient fully-coupled methods of predicting the resonant forced response of turbomachinery blades have been developed with the intention of increased computational efficiency over a decoupled method.
TL;DR: In this article, a mathematical model is extended to more general cases by examining the dynamic modulus associated with damping, stiffness and mass effects, such that stiffness and damping may have infinite or zero values.
TL;DR: In this article, the authors used free-free type suspended beam arrangement coupled with circle-fit approach to determine energy dissipation in the form of damping capacity, which is based on classical vibration theory, by which the geometry and material properties of the metallic specimen are related to measured resonant frequency and structural damping.
TL;DR: In this article, a finite element formulation for active control of forced vibrations, including resonance, of thin plate/shell laminated structures with integrated piezoelectric layers, acting as sensors and actuators, based on third-order shear deformation theory, is presented.
TL;DR: In this article, a new analytical model for axially fed gas journal bearings and experimental testing of micro gas bearings to characterize and to investigate their rotordynamic behavior is presented, which is capable of dealing with all the elements of, including micro-devices, dynamic response characteristics of hydrostatic gas bearings, stiffness, natural frequency and damping, evaluation of instability boundaries, and evaluation of effects of imbalance and bearing anisotropy.
Abstract: Several years ago an effort was undertaken at MIT to develop high-speed rotating MEMS (Micro Electro-Mechanical Systems) using computer chip fabrication technology. To enable high-power density the micro-turbomachinery must be run at tip speeds of order 500 m/s, comparable to conventional scale turbomachinery. The high rotating speeds (of order 2 million rpm), the relatively low bearing aspect ratios (L/D <0.1) due to fabrication constraints, and the laminar flow regime in the bearing gap place the microbearing designs to an exotic spot in the design space for hydrostatic gas bearings. This paper presents a new analytical model for axially fed gas journal bearings and reports the experimental testing of micro gas bearings to characterize and to investigate their rotordynamic behavior. The analytical model is capable of dealing with all the elements of, (1) micro-devices, (2) dynamic response characteristics of hydrostatic gas bearings, (3) evaluation of stiffness, natural frequency and damping, (4) evaluation of instability boundaries, and (5) evaluation of effects of imbalance and bearing anisotropy. First, a newly developed analytical model for hydrostatic gas journal bearings is introduced. The model consists of two parts, a fluid dynamic model for axially fed gas journal bearings and a rotordynamic model for micro-devices. Next, the model is used to predict the natural frequency, damping ratio and the instability boundary for the test devices. Experiments are conducted using a high-resolution fiber optic sensor to measure rotor speed, and a data reduction scheme is implemented to obtain imbalance-driven whirl response curves. The model predictions are validated against experimental data and show good agreement with the measured natural frequencies and damping ratios. Last, the new model is successfully used to establish bearing operating protocols and guidelines for high-speed operation.
TL;DR: In this article, the Galerkin's method was applied to the dynamic analog of the von Karman's plate equations, and the governing equation of a cracked plate was reduced to a time-dependent Mathieu equation.