Showing papers on "Natural frequency published in 2000"
TL;DR: In this paper, a solution of the problem of vibrations of a taut cable equipped with a concentrated viscous damper is presented, expressed in terms of damped complex-valued modes, leading to a transcendental equation for the complex eigenfrequencies.
Abstract: A solution is presented of the problem of vibrations of a taut cable equipped with a concentrated viscous damper. The solution is expressed in terms of damped complex-valued modes, leading to a transcendental equation for the complex eigenfrequencies. A simple iterative solution of the frequency equation for all complex eigenfrequencies is proposed. The damping ratio of the vibration modes, determined from the argument of the complex eigenfrequency, are typically determined to within one percent in two iterations. An accurate asymptotic approximation of the damping ratio of the lower modes is obtained. This formula permits explicit determination of the optimal location of the viscous damper, depending on its damping parameter.
283 citations
TL;DR: In this paper, the dynamic response of a helicopter planetary gear system is examined over a wide range of operating speeds and torques using a unique, semianalytical finite element formulation that admits precise representation of the tooth geometry and contact forces.
Abstract: The dynamic response of a helicopter planetary gear system is examined over a wide range of operating speeds and torques. The analysis tool is a unique, semianalytical finite element formulation that admits precise representation of the tooth geometry and contact forces that are crucial in gear dynamics. Importantly, no a priori specification of static transmission error excitation or mesh frequency variation is required; the dynamic contact forces are evaluated internally at each time step. The calculated response shows classical resonances when a harmonic of mesh frequency coincides with a natural frequency. However, peculiar behavior occurs where resonances expected to be excited at a given speed are absent. This absence of particular modes is explained by analytical relationships that depend on the planetary configuration and mesh frequency harmonic. The torque sensitivity of the dynamic response is examined and compared to static analyses. Rotational mode response is shown to be more sensitive to input torque than translational mode response.
256 citations
TL;DR: In this article, the effect of planet phasing to suppress planetary gear vibration in certain harmonics of the mesh frequency is examined based on the physical forces acting at the sun-planet and ring-planet meshes.
182 citations
TL;DR: In this article, a single-degree-of-freedom (SDOF) structure, rigidly supporting a tuned liquid damper (TLD) and subjected to both real and artificially generated earthquake ground motions, is shown to significantly reduce the structure's response to these motions.
Abstract: Numerical simulations of a single-degree-of-freedom (SDOF) structure, rigidly supporting a tuned liquid damper (TLD) and subjected to both real and artificially generated earthquake ground motions, show that a properly designed TLD can significantly reduce the structure's response to these motions. The TLD is a rigid, rectangular tank with shallow water in it. Its fundamental linear sloshing frequency is tuned to the structure's natural frequency. The TLD is more effective in reducing structural response as the ground excitation level increases. This is because it then dissipates more energy due to sloshing and wave breaking. A larger water-depth to tank-length ratio than previous studies suggested, which still falls within the constraint of shallow water theory, is shown to be more suitable for excitation levels expected in strong earthquake motions. A larger water-mass to structure-mass ratio is shown to be required for a TLD to remain equally effective as structural damping increases. Furthermore, the reduction in response is seen to be fairly insensitive to the bandwidth of the ground motion but is dependent on the structure's natural frequency relative to the significant ground frequencies. Finally, a practical approach is suggested for the design of a TLD to control earthquake response. Copyright © 2000 John Wiley & Sons, Ltd.
156 citations
TL;DR: In this article, the predicted natural frequency based on the measured added mass was approximately equal to the measured mean oscillation frequency, and the added mass coefficient was found to be weakly influenced by the external harmonic disturbance.
152 citations
TL;DR: In this paper, an exact method for solving the vibration of a double-beam system subject to harmonic excitation is presented, which involves a simple change of variables and modal analysis to decouple and to solve the governing differential equations respectively.
151 citations
TL;DR: In this paper, a marine engine-mount system for vibration control is designed to minimize the vertical force transmitted from the engine to the floor to control the structure-borne noise in order to avoid possible system resonance.
102 citations
TL;DR: In this paper, a set of fundamental dynamic equations of a two-dimensional, higher-order theory for thick rectangular plates subjected to in-plane stresses is derived through Hamilton's principle, and convergence properties of the minimum natural frequency and the buckling stress are examined in detail.
Abstract: Natural frequencies and buckling stresses of a thick isotropic plate on two-parameter elastic foundations are analyzed by taking into account the effect of shear deformation, thickness change, and rotatory inertia. Using the method of power series expansion of the displacement components, a set of fundamental dynamic equations of a two-dimensional, higher-order theory for thick rectangular plates subjected to in-plane stresses is derived through Hamilton's principle. Several sets of truncated approximate theories are used to solve the eigenvalue problems of a simply supported thick elastic plate. To assure the accuracy of the present theory, convergence properties of the minimum natural frequency and the buckling stress are examined in detail. The distribution of modal transverse stresses are obtained by integrating the three-dimensional equations of motion in the thickness direction. The present approximate theories can accurately predict the natural frequencies and buckling stresses of thick plates on elastic foundations as compared with Mindlin plate theory and classical plate theory.
93 citations
TL;DR: In this article, the authors presented a new analysis method for identifying synchronous resonance engine order using two tip-timing vibration measurements, made at different locations on the turbomachinery casing using a minimum of two probes.
Abstract: Non-contact measurement of vibration at turbomachinery rotor blade tips using blade tip-timing has become an industry-standard procedure Current research focuses on analysis methods for interpretation of the measured vibration data from a limited number of probes The methods are classified by the form of the vibration they can identify Identification of asynchronous response amplitude and frequency is well documented Whilst a method for identifying maximum synchronous resonance amplitude has existed since the early 1970s, there is no published evidence of a method for directly identifying frequency or engine order using a small number of probes This paper presents a new analysis method for identifying synchronous resonance engine order using two tip-timing vibration measurements The measurements are made at different locations on the turbomachinery casing using a minimum of two probes A detailed description of the method and results from its practical application are given The potential of the method to identify the amplitude and frequency of close modes, not possible with current methods, is demonstrated The effect of blade mistuning on the accuracy of the method is investigated Existing synchronous response analysis methods and the new method presented here give the response amplitude and frequency after the resonance has been traversed Real-time identification of synchronous response amplitude and frequency would allow tip-timing to be used as a safety monitor of all blades Real-time methods, their limitations and practical application are discussed The future use of tip-timing as the dominant vibration measurement system is discussed with reference to experience on measurements made solely with tip-timing on assemblies with undefined vibration characteristics
91 citations
TL;DR: In this paper, the authors proposed a systematic procedure for finding the optimal damper positioning to minimize the dynamic compliance of a planar building frame, which is expressed in terms of the transfer function amplitudes of the interstorey drifts evaluated at the undamped fundamental natural frequency.
Abstract: A systematic procedure is proposed for finding the optimal damper positioning to minimize the dynamic compliance of a planar building frame. The dynamic compliance is expressed in terms of the transfer function amplitudes of the interstorey drifts evaluated at the undamped fundamental natural frequency. The dynamic compliance is minimized subject to a constraint on the sum of the damping coefficients of added viscous dampers. Optimality criteria are derived and the optimal damper positioning is determined based on a proposed steepest direction search algorithm. This algorithm allows one to find an optimal damper positioning sequentially for gradually increasing total damper capacity levels. Numerical results including comparison with the corresponding uniform damper placement demonstrate the usefulness and validity of this procedure.
77 citations
TL;DR: In this article, the transverse vibrations of highly tensioned pipes with vanishing flexural stiffness and conveying fluid with time-dependent velocity are investigated, and the stability boundaries are determined analytically.
TL;DR: In this paper, a theoretical study on how to use saturation phenomena to design nonlinear vibration absorbers and how to improve their stability and effective frequency bandwidth is presented, and guidelines for designing nonlinear vibrational absorbers are derived.
TL;DR: In this paper, the lock-on phenomenon has been detected and its effect on the thermal field has been determined, and the results show that the lockon phenomenon occurs within a band of frequency near the natural frequency and the heat transfer coefficient has shown appreciable increase in the lock on frequency range.
TL;DR: In this article, the authors investigated spatial modulation of the doublet modes, particularly those retaining repeated natural frequencies for which modulation is most acute, and proposed an algebraic relation and a diagrammatic method with a view towards predicting the wavenumbers present in modulated eigenfunctions.
Abstract: When a structure deviates from axisymmetry because of circumferentially varying model features, significant changes can occur to its natural frequencies and modes, particularly for the doublet modes that have non-zero nodal diameters and repeated natural frequencies in the limit of axisymmetry. Of technical interest are configurations in which inertia, dissipation, stiffness, or domain features are evenly distributed around the structure. Aside from the well-studied phenomenon of eigenvalue splitting, whereby the natural frequencies of certain doublets split into distinct values, modes of the axisymmetric structure that are precisely harmonic become contaminated with certain additional wavenumbers. From analytical, numerical, and experimental perspectives, this paper investigates spatial modulation of the doublet modes, particularly those retaining repeated natural frequencies for which modulation is most acute. In some cases, modulation can be sufficiently severe that a mode shape will beat' spatially as harmonics with commensurate wavenumbers combine, just as the superposition of time records having nearly equal frequencies leads to classic temporal beating. An algebraic relation and a diagrammatic method are discussed with a view towards predicting the wavenumbers present in modulated eigenfunctions given the number of nodal diameters in the base mode and the number of equally spaced model features.
TL;DR: In this article, the lock-on phenomenon is found to occur within a band of frequency encompassing the natural frequency, however, becomes wider as the amplitude of oscillation increases, and its effect on the flow hydrodynamics has been determined.
Abstract: The characteristics of the flow in the wake of a circular cylinder performing rotational oscillation about its own axis and placed horizontally in a cross-stream is investigated. The governing equations based on stream function-vorticity formulation are solved numerically to determine the flow field structure. The parameters dominating flow structure are Reynolds number, Re, amplitude of oscillation, Θ A and frequency ratio F R =S/S 0 where S is the forcing frequency and S 0 is the natural frequency of vortex shedding. The ranges considered for these parameters are 40≤Re≤200, 0≤Θ A ≤π and 0≤F R ≤2. The lock-on phenomenon has been predicted and its effect on the flow hydrodynamics has been determined. The lock-on phenomenon is found to occur within a band of frequency encompassing the natural frequency. This band, however, becomes wider as the amplitude of oscillation increases
TL;DR: In this paper, an experimental investigation was carried out on the damping behavior of laminated honeycomb cantilever beams with fine solder balls enclosed in the cells as dampers.
TL;DR: In this paper, the motion of a Bernoulli-Euler cantilever beam clamped on a moving cart and carrying an intermediate lumped mass is considered, and the equations of motion of the beam-mass-cart system are analyzed through unconstrained modal analysis and a unified characteristic equation for calculating the natural frequencies of the system is established.
01 Jan 2000
TL;DR: In this paper, the authors presented a new way of plotting the MAC such that both the mode shape correlation as well as the natural frequency comparisons can be viewed simultaneously, and the new plot method is naturally extended to the correlation of frequency response functions (FRFs) using the Frequency Domain Assurance Criterion (FDAC).
Abstract: The Modal Assurance Criterion (MAC) has been used for numerous years as a measure of correlation between test and analytical mode shapes. The fact that the MAC considers only mode shapes usually means that a separate frequency comparison must be used in conjunction with the MAC values to determine the correlated mode pairs The mode shape correlation has generally been displayed as the MAC matrix tabulated or plotted versus experimental mode number on the x axis and analytical mode number on the y axis. The natural frequency correspondence is usually displayed with a separate plot such as the experimental natural frequency versus the analytical natural frequency. Together, the two plots are used to determine the overall correlation/correspondence of the modes. This paper presents a new way of plotting the MAC such that both the mode shape correlation as well as the natural frequency comparisons can be viewed simultaneously. Further, the new plot method is naturally extended to the correlation of frequency response functions (FRFs) using the Frequency Domain Assurance Criterion (FDAC) and a new technique called the Modal FRF Assurance Criterion (MFAC). Two case studies of real structures are presented to illustrate the advantages of the new methods.
TL;DR: In this article, a simple analytical expression is presented, that relates the effective natural frequencies of the beam to the intensity of harmonic excitation, and experiments performed with a laboratory beam confirm the general tendency of this prediction, though there are discrepancies that cannot be explained in the linear Galerkin-discretized beam model.
Abstract: According to theoretical predictions one can change the effective stiffness or natural frequency of an elastic structure by employing harmonic excitation of very high frequency. Here we examine this effect for a hinged-hinged beam subjected to longitudinal harmonic excitation. A simple analytical expression is presented, that relates the effective natural frequencies of the beam to the intensity of harmonic excitation. Experiments performed with a laboratory beam confirm the general tendency of this prediction, though there are discrepancies that cannot be explained in the framework of the linear Galerkin-discretized beam model.
TL;DR: In this paper, the authors developed a continuous linear-elastic one-dimensional analytic model that should accurately represent a vertically tethered system subject to surface excitation, which can accurately predict: (a) the transfer function between the motion of the ship and cage, (b) the transferred function between ship motion and tension in the tether and (c) the natural frequency and its harmonics of the ROPOS deep-sea ROV system for depths between 0 and 1765 m up to moderately rough sea conditions.
TL;DR: In this paper, the authors investigated the effect of sloshing with an elastic annular plate structure attached to a cylindrical sidewall on the natural frequency of free liquid surface.
TL;DR: In this article, the Rayleigh-Plesset equation was used to compute bubble dynamics on the micro-scale using the Lagrangian finite volume calculus and implicit adaptive time marching.
Abstract: Bubbly cavitating flow generated by the normal oscillation of a wall bounding a semi-infinite domain of fluid is computed using a continuum two-phase flow model. Bubble dynamics are computed, on the microscale, using the Rayleigh-Plesset equation. A Lagrangian finite volume
scheme and implicit adaptive time marching are employed to accurately resolve bubbly shock waves and other steep gradients in the flow. The one-dimensional, unsteady computations show that when the wall oscillation frequency is much smaller than the bubble natural frequency, the power radiated away from the wall is limited by an acoustic saturation effect (the radiated power becomes
independent of the amplitude of vibration), which is similar to that found in a pure gas. That is, for large enough vibration amplitude, nonlinear steepening of the generated waves leads to shocking of the wave train, and the dissipation associated with the jump conditions across each shock limits the radiated power. In the model, damping of the bubble volume oscillations is restricted to a simple "effective" viscosity. For wall oscillation frequency less than the bubble natural frequency, the saturation amplitude of the radiated field is nearly independent of any specific damping mechanism. Finally, implications for noise radiation from cavitating flows are discussed.
TL;DR: In this paper, the potential of the piecewise linear vibration absorber in a system subject to narrow band harmonic loading is explored and the absorber parameters needed to produce good designs have been determined and the quality of realized suppression zone is discussed.
Abstract: This paper explores the potential of the piecewise linear vibration absorber in a system subject to narrow band harmonic loading. Such a spring is chosen because the design of linear springs is common knowledge among engineers. The two-degrees-of-freedom system is solved by using the Incremental Harmonic Balance method, and response aspects such as stiffness crossing frequency and jump behaviour are discussed. The effects of mass, stiffness, natural frequency ratios, and stiffness crossing positions on the suppression zone are probed. It is shown that a hardening absorber can deliver a wider bandwidth than a linear one over a range of frequencies. The absorber parameters needed to produce good designs have been determined and the quality of the realized suppression zone is discussed. Design guidelines are formulated to aid the parameter selection process.
TL;DR: In this paper, a theoretical and experimental investigation into the modeling and design of piezoelectric flap actuators is described, and a companion experimental parametric study is executed in which ten identical piezo flaps with varying piezo patch sizes are fabricated in the Dynamics and Controls Laboratory at the University of Florida.
Abstract: A theoretical and experimental investigation into the modeling and design of piezoelectric flap actuators is described. The motivation for this study is to develop design tools for piezoelectric actuators in active flow control systems. In line with this goal, structural dynamic models of varying complexity must first be assessed. Theoretical modeling of the flaps is carried out using finite element analysis. For comparison, a companion experimental parametric study is executed in which ten otherwise identical piezo flaps with varying piezo patch sizes are fabricated in the Dynamics and Controls Laboratory at the University of Florida. The flaps are characterized using a laser displacement sensor and a scanning laser vibrometer to obtain the frequency response functions between the input voltage signal and the tip displacement and velocity of the flaps. The DC response and natural frequency of the flaps are extracted from the frequency response functions, and these are compared with the theoretical values.
TL;DR: In this article, the damping and nonlinear parameters of the first mode of a three-beam two-mass frame are characterized and quantified using perturbation techniques and spectral moments.
Abstract: Perturbation techniques and spectral moments are combined tocharacterize and quantify the damping and nonlinear parameters of thefirst mode of a three-beam two-mass frame. The frame is excitedharmonically near twice its lowest natural frequency. The response ismodeled with a second-order nonlinear equation with quadratic and cubicterms and linear and quadratic damping terms. The method of multiplescales is used to obtain a second-order approximate solution for thismodel. Bispectral analysis is used to quantify the level of couplingbetween modes and measure their phase difference. The amplitudes andphase difference between the excitation and response mode with differentfrequencies are substituted into the approximate solution to determinethe damping and nonlinear parameters.
TL;DR: In this paper, the damping coefficient of a mechanical two-degree-of-freedom system is considered under the conditions of one-to-one or two-toone internal resonance, i.e., when natural frequencies of two modes are approximately equal to each other or when one natural frequency is nearly twice as large as another natural frequency.
Abstract: Free damped vibrations of a mechanical two-degree-of-freedom system are considered under the conditions of one-to-one or two-to-one internal resonance, i.e., when natural frequencies of two modes – a mode of vertical vibrations and a mode of pendulum vibrations – are approximately equal to each other or when one natural frequency is nearly twice as large as another natural frequency. Damping features of the system are defined by the fractional derivatives with fractional parameters (the orders of the fractional derivatives) changing from zero to one. It is assumed that the amplitudes of vibrations are small but finite values, and the method of multiple scales is used as a method of solution. The model put forward allows one to obtain the damping coefficient dependent on the natural frequency of vibrations, so it has been shown that the amplitudes of vertical and pendulum vibrations attenuate by an exponential law with damping ratios which are exponential functions of the natural frequencies. Damped soliton-like solutions have been found analytically.
TL;DR: Property of the networks associated with synchronization phenomena for a discrete symmetric natural frequency distribution with three frequency components are studied based on the order parameter equations, and are shown to be in good agreement with the results of numerical simulations.
Abstract: We study associative memory based on temporal coding in which successful retrieval is realized as an entrainment in a network of simple phase oscillators with distributed natural frequencies under the influence of white noise. The memory patterns are assumed to be given by uniformly distributed random numbers on [0, 2\ensuremath{\pi}) so that the patterns encode the phase differences of the oscillators. To derive the macroscopic order parameter equations for the network with an extensive number of stored patterns, we introduce an effective transfer function by assuming a fixed-point equation of the form of the Thouless-Anderson-Palmer equation, which describes the time-averaged output as a function of the effective time-averaged local field. Properties of the networks associated with synchronization phenomena for a discrete symmetric natural frequency distribution with three frequency components are studied based on the order parameter equations, and are shown to be in good agreement with the results of numerical simulations. Two types of retrieval states are found to occur with respect to the degree of synchronization, when the size of the width of the natural frequency distribution is changed.
TL;DR: In this article, the authors considered the vibration control of a rotating Euler-Bernoulli beam with a fixed-free elastic beam attached to the servomotor, which uses PD control to achieve the desired angular rotation, at the same time, the shear force measured at the root of the beam is used as a feedback to control the beam tip vibration.
TL;DR: In this article, a mixed differential-algebraic equation (MDAE) approach is used to describe the slipping dynamics and algebraic (constraint) equations to model interfacial sticking.
Abstract: A new formulation for dynamic sliding contact problems with partial slipping is presented and used to investigate the influence of structural dynamic response on interface behavior. The mixed differential-algebraic equation (MDAE) approach uses differential equations to describe the slipping dynamics and algebraic (constraint) equations to model interfacial sticking. An efficient method for solving the case of partial interface slipping has been developed, and special consideration has been given to the changing equations of motion (at the transition from stick-to-slip and slip-to-stick). An example is presented for the case of an elastic block pressed into a rigid foundation and loaded with cyclic tangential tractions at the top of the block. The full elastodynamic transient simulations illustrate that interface slip response is a strong function of loading frequency, reaching a maximum when the external loading frequency is near the theoretical (shear-mode) natural frequency of the structure.