Wide Range Of Excitation Frequencies Research Articles

Design and implementation of tuned viscoelastic dampers for vibration control in milling

Passive means of vibration attenuation have been employed successfully and efficiently in machining systems such as turning and milling. Traditional approach to controlling vibration in a milling system is to develop control mechanisms for cutting tools or machine spindles. However, due to the nature of milling operations where the cutting tools rotate at high speed, the passive vibration control methods find very limited application with the traditional approach. In order to utilise the potential of the passive vibration control methodology in milling applications, the milling operation should be viewed as a system comprising an elastic structure and operation parameters. Dynamics of this closed-loop system should improve with improvement in dynamics of any of the system components, especially within the elastic structure that comprises the cutting tool, the machine tool, the workholding system and the workpiece. Although the level of improvement will vary depending on which component of the elastic chain is targeted for this purpose. This paper presents the development and testing of tuned viscoelastic dampers (TVDs) for vibration control through their application on a workpiece in milling operations. This work targets workpiece held on a palletised workholding system for the control of unwanted vibration and thus deviates from the traditional approach where cutting tool and/or machine spindles are targeted for vibration control strategies. Palletised workholding systems, due to their compact design, offer an opportunity to design passive damping mechanisms that are easier to implement in the case of a milling system. The TVD developed through this research is based on a commercially available viscoelastic damping polymer. Advantage of such materials is their high damping performance over a wide range of excitation frequencies. The TVD design process has used a unique combination of analytical modelling with experimental FRF data. Modal impact testing showed that the application of the TVD reduced the amplitude of vibration acceleration by 20 dB for the target mode. Since the target mode corresponded to torsional vibration, the TVD was effective in two planar coordinates, i.e. X and Y. In addition, the TVD also significantly reduced the amplitude of a vibration mode far from the mode it was designed for. The system has been tested experimentally to demonstrate significant reduction in vibration amplitudes during a milling process. The milling tests with different combinations of cutting parameters show that multi-TVD approach is always valid regardless of the parameters being used. The only requirement for TVDs to function effectively is that the natural frequency of the system, for which the TVDs are designed, is excited during the milling process.

Vibration Suppression of Nonlinear Reciprocating System by Control of Anti-Resonance Point

Conventional dynamic vibration absorbers cannot reduce the vibration amplitude to zero over the wide frequency range. We have proposed the control method of a semi-active dynamic absorber that can suppress the amplitude of the main system subjected to a linear restoring force to zero over the wide excitation frequency range. The proposed controller estimates in real time the varying excitation frequency by adaptive filter. According to the estimated excitation frequency, the stiffness of the dynamic vibration absorber is changed so that the main system is always excited at antiresonance point. In this paper, we show that the proposed control method for the linear system can be adaptable to the main system subjected to a nonlinear restoring force. We theoretically clarify that the nonlinearity of the main system does not affect the system in the vicinity of the antiresonance point and the amplitude of the main system even with nonlinear stiffness can be suppressed to zero over the wide excitation frequency range. Furthermore, the performance to the nonlinear system of the proposed control method is experimentally discussed.

Vibration isolation using buckled or pre-bent columns—Part 2: Three-dimensional motions of horizontal rigid plate

This is a continuation of previous work to investigate the use of pairs of pre-bent columns, bonded with a viscoelastic filler, as vibration isolators. In this paper, four of these devices support the corners of a square, rigid plate. When the system is in equilibrium, small harmonic vibrations are applied vertically to the base of the isolators, and the steady-state response of the system is determined. First, the system is analyzed for the fully symmetric case, i.e., the center of mass of the plate coincides with the geometric center. Then, the system is analyzed for various cases in which the center of mass has some eccentricity. The eccentric weight introduces rotational motions of the plate. The governing equations are formulated and then numerically solved in Mathematica using a shooting method. The displacement transmissibility is plotted over a range of excitation frequencies, and the mode shapes are shown for the first few resonant frequencies. Free vibration of the system is also considered. For this three-dimensional system, the pre-bent columns can be effective at isolating vibrations for a wide range of excitation frequencies.

Matrix Variate Distributions for Probabilistic Structural Dynamics

Matrix variate distributions are proposed to quantify uncertainty in the mass, stiffness, and damping matrices arising in linear structural dynamics. The proposed approach is based on the so-called Wishart random matrices. It is assumed that the mean of the system matrices are known. A new optimal Wishart distribution is proposed to model the random system matrices. The optimal Wishart distribution is such that the mean of the matrix and its inverse produce minimum deviations from their respective deterministic values. The method proposed here gives a simple nonparametric approach for uncertainty quantification and propagation for complex aerospace structural systems. The new method is illustrated using a numerical example. It is shown that Wishart random matrices can be used to model uncertainty across a wide range of excitation frequencies.

Mems inertial power generators for biomedical applications

An inertial vibration scavenging micro-generator is described which is suitable for biomedical applications. MEMS fabrication techniques have been used to construct a variable capacitor having one moving plate on which a proof mass is attached. Energy is extracted when the plates separate at constant charge. This device is non-resonant, so can operate over a wide range of excitation frequencies and amplitudes. The energy extracted per cycle, 120 nJ, is well above previous reports. The fabrication techniques employed are described, and test data are given and compared to modeling results, showing good agreement.

Broad-band Viscoelastic Rotational Vibration Control for Remote Sensing Applications

The ability to eliminate, or effectively control, vibration in remote sensing applications is critical. Any perturbations of an imaging system are greatly magnified over the hundreds of kilometers from the orbiting space platform to the Earth's surface. Space platforms, such as the International Space Station, are not as predictable or stable as many other spacecraft. Therefore, an effective vibration isolation and/or absorber system is needed that operates over a wide range of excitation frequencies. A passive system is also preferred to reduce the resources required, as well as to provide a reliable and self-contained system. To accomplish these goals, a vibration amplitude limiting system has been developed that uses both vibration isolation and absorber components. Viscoelastic structural elements that act as both a spring and a damper in a single element are implemented in the design. This configuration also demonstrates a favorable frequencydependent response and produces a system with improved dynamic behavior compared to conventional spring and damper designs. This rotation limiting vibration system has been designed and analyzed for use in digital remote sensing imaging. The transmissibility and the ground jitter associated with the system are determined. A summary of these results will be presented along with a comparison to a more conventional vibration isolation/absorber system.

Dynamic stability of stiffened plates with cutout subjected to harmonic in-plane partial edge loading

The dynamic instability characteristics of eccentrically stiffened plates with cutout subjected to harmonic in-plane partial edge loadings at the plate boundaries are studied using finite element method. The instability regions are determined for a wide range of excitation frequencies with different boundary condition, partial edge loading at different locations, cutout ratios and various parameters of stiffeners using Bolotin's method and Hill's infinite determinants by varying the number, size and location of the stiffeners. In the structural modeling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained.

The damping performance of a single particle impact damper

This paper presents results from computer simulations used to investigate 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. Measurements of the damping performance, particle flight times, and structure contact times are presented. Performance at both the structure's undamped natural frequency and off-resonant conditions are studied in depth. Maximum damping at a fixed oscillation frequency occurs at an optimal lid height that increases with increasing mass ratio, increasing structural damping ratio, but decreases with coefficient of restitution. The corresponding maximum degree of damping increases with increasing mass ratio and coefficient of restitution, but decreases with increasing structural damping ratio. Field plots of the damping ratio are also presented as functions of oscillation amplitude and frequency to demonstrate the damper performance over a range of design parameters and operating conditions.

Dynamical theory of spectroscopy with pulse excitation in strong laser fields

A non-perturbative theory of spectroscopy with pulsed laser excitation is presented with approximations that make calculation with long pulses as accessible as for short pulses. We apply it to continuum Raman scattering with a strong field and show that: (a) for a pulse shorter than the molecular dissociation time the range of excitation frequencies giving fluorescence-like emissions is greater than in a weak field, and (b) for a pulse that is longer than the molecular dissociation time, Raman-like emissions are dominant, with vibrational progressions over a wider range of excitation frequencies than in a weak field.

Strouhal numbers for flow past a combined circular–rectangular prism

Unsteady loading frequencies due to cross-flow on a novel drop wire design are investigated with results presented in terms of the Reynolds number, the Strouhal number and the angle of attack. The wire model has a cross section which is composed of a circle and attached rectangle. Comparison is made to results in the literature for flow over circular and square cylinders. The study shows that wires of this design combining both rounded and square edged surfaces may be particularly susceptible to flow induced vibrations due to vortex shedding, due to the wider range of excitation frequencies (Strouhal numbers) they experience.

CONVERGENCE ANALYSIS OF VOLTERRA SERIES RESPONSE OF NONLINEAR SYSTEMS SUBJECTED TO HARMONIC EXCITATION

Volterra series provides a strong platform for non-linear analysis and higher order frequency response functions. However, limited convergence is an inherent difficulty associated with the series and needs to be addressed rigorously, prior to its application to a physical system. The power series representation of the response of non-linear systems, subjected to harmonic excitation is investigated in this study. The problem of convergence is addressed in terms of the convergence of individual frequency harmonics of the non-linear response. Though the procedure is applicable to general polynomial form non-linearity, it is illustrated for a Duffing oscillator subjected to harmonic excitation. A general and structured series expression is obtained for amplitudes of all the response harmonics and convergence is investigated in terms of a non-dimensional non-linear parameter. Critical values of this parameter, representing the upper limit of excitation level for the convergence, are defined for a wide range of excitation frequencies. Zones of convergence and divergence of the response series are presented graphically, for a range of the non-dimensional non-linear parameter and the number of terms included in the approximation of a response harmonic. An algorithm based on ratio test is presented to compute the critical value of the non-dimensional non-linear parameter. Results obtained from the suggested algorithm are found to be in close agreement with the exact values. The method gives better results compared to previous methods and has wider application in terms of excitation frequency. The procedure is also investigated for a two-degree-of-freedom system.

Dynamic performance of UV photodetectors based on polycrystalline diamond

Dynamic behavior of photogenerated carriers in diamond-based UV photodetectors is investigated over a wide excitation frequency range, enabling an analysis of the influence of film morphology and impurity content on device response times. Under pulsed light excitation, short time detector photoresponse varies from 2.5 to 10 ns, whereas carrier lifetimes estimated under steady-state illumination lie in the 0.1-1 ns range, exhibiting a small dependence on the film microstructure. Conversely, very long response times, strongly dependent on film characteristics, are detected by decreasing the excitation frequency. Such results are discussed in terms of carrier recombination at defect- and impurity-related centers, trapping at localized states close to the band edges, and dispersive transport. It is suggested that device response times are mainly related to charge trapping either into discrete or continuously distributed energy levels, rather than to recombination of carriers at midgap defect states.

Near-wake of a perturbed, horizontal cylinder at a free-surface

A horizontal cylinder intersecting a free surface is subjected to controlled vertical perturbations, and the consequent vortex formation is characterized by high-image-density particle image velocimetry, which leads to instantaneous patterns of velocity, vorticity, and streamlines. For the limiting case of the stationary cylinder, the near wake does not exhibit rapid formation of organized vortical structures in a manner similar to Kármán vortices. Application of perturbations, however, generates phase-locked vortex formation over a wide range of excitation frequencies, even at relatively low amplitudes, indicating that the near wake in presence of a free surface is convectively, rather than absolutely, unstable. At a sufficiently high value of excitation frequency, the formation of the initial vortex undergoes an abrupt change in timing, which is analogous to that occurring for Kármán vortex formation from a completely submerged cylinder. All of these features of the near wake are interpreted in terms of foci, saddle points, and reattachment points of the streamwise topology.

Vibration of Foundations on Incompressible Soils with No Elastic Region

The dynamic response of rigid foundations supported on a homogeneously nonlinear elastoplastic half‐space is investigated in the context of nonlinear finite‐element (FE) analysis. The constitutive equation for the half‐space is described by a bounding surface plasticity model with a vanishing elastic region. This model is based on a total stress formulation in which the plastic modulus is determined from an interpolated exponential hardening rule. The incompressibility constraint is handled via the mean dilatational formulation of the B‐method. The computational problem associated with the disparity between the longitudinal and shear wave velocities is addressed in the context of radiation boundary condition. The relative significance on the foundation response of the more rapidly propagating P waves, as they reflect spuriously from the FE boundaries, is investigated. It is shown that the reflected P waves have no significant influence on the dynamic response of finite‐size foundations; nor do they have any significant effect on the response of strip foundations vibrating in the rocking mode. Furthermore, it is shown that nonlinear effects can have a significant influence on the dynamic response of vibrating foundations over a wider range of excitation frequencies than originally thought. The numerical simulations presented in this paper are performed using data on real soils determined from resonant column, cyclic triaxial, and other one‐dimensional “radial” loading tests.

Response of submerged finite-length cylindrical shells with internals to an impulse load

A finite-length, submerged cylindrical shell with elastic endcaps containing internal substructures is excited by a short-duration load. A recently developed modal-based analysis method is used to generate the responses on the shell surface and in the near and far fields. The method was developed specifically for analyzing the acoustic effects of substructures in an efficient manner. Nearly all of the computational effort is in determining the impedance relations between the pressure and the velocity along the shell surface. This analysis requires the evaluation of a twofold integral over the shell surface for each pair of pressure and velocity shape functions [Ginsberg etal. (1986)]. Once the impedance relations are determined, the analysis of the radiation problem for a given set of internal substructures and applied loads is solved with relatively little computational effort. The efficiency of the method stems from the fact that the same set of impedance relations can be used for any configuration of internal substructures and applied loads. In addition, the method can be combined with a frequency window method when analyzing responses for a wide range of excitation frequencies. Such analysis is useful when going into the time domain using the fast Fourier transform. The study shows that substructures interact with the in-plane and flexural waves propagating in the shell, causing wave conversion and subsequent radiation into the surrounding fluid. [Work supported by ONR.]

Nonlinear Lateral, Rocking, and Torsional Vibration of Rigid Foundations

Two‐ and three‐dimensional finite element (FE) analyses are performed to investigate the influence of nonlinear soil behavior on the dynamic response of harmonically excited rigid foundations. Lateral, rocking, and torsional vibration modes are considered. An elastoviscoplastic constitutive model with kinematic hardening is assumed for the foundation soil, and computations are done implicitly in the time domain. The foundation responses for lateral, rocking, and torsional modes are characterized by increased vibrational amplitudes due to material stiffness degradation. Furthermore, resonance frequencies are created that resemble those observed for vertically oscillating finite‐size foundations. Nonlinear soil effects are shown to be dominant over a wide range of excitation frequencies for foundations vibrating in torsional and lateral modes. In contrast, nonlinear soil effects are shown to be dominant over a much narrower range of excitation frequencies for the rocking mode. The methodology presented in this paper is useful for nonlinear vibration and transient soil‐structure interaction (SSI) analysis.

Oscillatory measurement of linear viscoelasticity: Dynamic moduli revisited

The current technique for the measurement of linear viscoelastic dynamic moduli is reconsidered. The transfer function analysis reveals the existence of nonlinear components in the response of the sample in a wide range of excitation frequencies around the reasonances of the measuring system. This analysis permits the disclosure of the components of the response which behave in accordance to linear viscoelastic theory and separates the undesirable nonlinear components. This results in partial corrections of the anomalous behavior of the calculated dynamic moduli through the standard technique.

Parametric studies on the measurements of damping quantities

Damping is a property of a structure or specimen which describes how rapidly a mode of vibration decays once it is excited. The energy dissipation due to damping mechanism in the system or specimen is a complex phenomenon which depends on many parameters. There is usually significant variation in the measured damping quantity. The parametric studes were performed to investigate the effect of sensitive parameters on the measured damping quantities; air and water, temperature, frequency and boundary conditions. The type of excitation used was random noise. A flat plate configuration was used to minimize extraneous energy losses (i.e. joints) associated with built-up structure. The wide range of excitation frequencies is considered to understand the frequency-dependent damping characteristics in both air and water media. As a results of investigation, the sensitivities of damping quantities were tabulated and discussed.

Preliminary results of vibrator-aided experiments in non-linear seismology conducted at Uetze, F.R.G.

Following acoustics and largely thanks to the pioneering work of a group of Soviet geophysicists, the study of non-linear elastic properties and their effects is becoming an active field of research in geophysics. The research so far has produced a substantial body of evidence indicating that earth materials, from soils to crystalline rocks, are much more non-linear than is commonly believed and certainly far more non-linear than the materials usually used and studied in acoustics. But although most of the evidence comes from vibrator-aided experiments, apparently best suited for investigating the non-linearity of the geophysical medium owing to the ability of modern vibrators to generate seismic signals of prescribed form, the absence of a standard experimental technique makes it difficult to estimate and compare the various results, particularly in view of the considerable non-linearity of the source (vibrator-ground system) itself. The aim of the present vibrator-aided experiments was to try to confirm certain results in non-linear seismology, particularly the effects of harmonic generation and non-linear interaction in vibrator-induced sinusoidal seismic waves, by using an experimental method designed to enable one to discriminate between source, near-field and far-field non-linear effects. In the experiments, two identical prospecting vibrators, installed on the ground surface some 16 m apart, were driven in the harmonic regime separately and simultaneously (tests on non-linear evolution and interaction), a wide range of excitation frequencies and amplitudes being covered, and the resulting ground-surface motion was picked up by an array consisting of 48 groups of 12 vertical geophones-velocimeters and recorded, in multiplex form, by a prospecting seismic station. Tests were made first for short and intermediate source-receiver distances (near field, distance range covered 0–200 m, 5-m spacing of geophone groups), then for large distances (far field, range 1.5–3.5 km, 50-m spacing). A preliminary examination of the field data, available at present for analysis in the form of traces or Fourier spectra, both without amplitude information, indicates the effects of harmonic generation (both in the near and far fields) and non-linear interference (only in the near field) as well as the phenomenon of modulational instability (only in the near field and for very low excitation levels). It seems that, whereas the near field was dominated by surface Rayleigh waves, the far field was dominated by body waves propagated through the water-saturated layer. Lastly, as expected, the baseplate-accelerometer signal, recorded for one of the vibrators, typically contains a large amount of harmonic distortion, usually decreasing with increasing excitation frequency, but somewhat startingly, sometimes decreasing with increasing excitation level.

Static and dynamic stability of variable thickness annular plates

The static and dynamic stability of variable thickness annular plates subject to periodic in-plane forces is studied. For this purpose a sector finite element model with the wave propagation technique of cyclic symmetry is developed. Plate thickness is both increased and decreased in the outward radial direction by the equations h = h max( r r o ) +λ or h = h max( r r i ) −λ respectively. The Mindlin plate finite element model is used to handle both the thick and thin plates. The instability regions are determined for a wide range of excitation frequencies with different boundary conditions by using Bolotin's method with the effect of static forces taken into account.