Models for rotating rigid discs excited by contact elements have been developed for the study of break noise and vibration. More recently, models for clutch squeal/eek noise have been developed as well. Such phenomenological representations, even though simple, are of great help for designers given that many physical features can be included, such as the circulatory and gyroscopic effects. Instability or self-excited vibrations are represented by wobbling motions. In this study, a device is included as a disc connected to the primary system by a set of spring and damping elements. A complex coordinate notation was helpful to make a concise physical description of the in-phase and out-of-phase wobbling motions between the bodies. If its properties are properly adjusted, all modes interact (indicating veering or crossings between the eigenvalue loci), and the system is stabilized.

A successful application of statistical energy analysis for analyzing energy exchanges between weakly coupled subsystems theoretically requires a diffuse vibrational field in all subsystems. So as to verify the conditions of establishment of the diffuse field in practice, full-field vibration measurements were conducted with a high-speed camera on a simply supported rectangular plate excited by a wide band random force. The results constitute an experimental investigation of the diffuse field region in the frequency-structural damping domain and a validation of previously obtained numerical results. The domain of the diffuse field is confined to high frequencies and low damping, with limits than can be easily defined. However, it is shown that the vibrational field is not fully spatially homogeneous due to enhancement of response induced by the effect of coherence of rays. Theoretical values of the enhancement factor obtained using an image source analysis are confirmed by measurement results.

Significant handle vibrations often occur during mowing operation even with anti-vibration type brush cutters. This is often caused by combined-bending natural mode of the main pipe and driveshaft which is mainly excited by cutting head rotational force. In this study, we focused on the placement span of the rubber bushings that support the driveshaft to suppress this kind of resonance. More specifically, we have designed a new component, called a span-tuning dynamic vibration absorber (ST-DVA), which utilizes the bending mode of the driveshaft that is determined by the placement span of rubber bushings. Analysis results of the finite element method (FEM) showed that the ST-DVA generated anti-resonance at a specific point on the main pipe under the first-order inertial force of the cutting head. We also succeeded in controlling anti-resonance frequency under the excitation. In actual measurements at the target frequency, handle vibration of the first-order component of the cutting head could be reduced by 51% and overall handle vibration could be reduced by 49% compared with those produced via equal-span rubber bushing placement. Hence, our study provides a design method that makes it possible to utilize the driveshaft, which a primary brush cutter component, as a dynamic vibration absorber by altering the placement span of the rubber bushings.

This paper explores the addition of small stubs with anechoic terminations (termed herein “anechoic stubs”) as a means of damping and/or removing vibration modes from planar frame structures. Due to the difficulties associated with representing anechoic boundary conditions in more traditional analysis approaches (e.g., analytical, finite element, finite difference, and finite volume), the paper employs and further develops an exact wave-based approach, incorporating Timoshenko beams, in which ideal and non-ideal anechoic terminations are simply represented by a reflection matrix. Several numerically evaluated examples are presented documenting novel effects anechoic stubs have on the vibration modes of a two-story frame, such as eliminated, inserted, and exchanged mode shapes. Modal damping ratios are also computed as a function of the location and number of anechoic stubs, illustrating optimal locations and optimal reflection ratios as a function of mode number. Forced vibration studies are then carried out, demonstrating reduced, eliminated, and inserted resonance response.

Aiming at preventing stick-slip oscillations in drilling systems for oil and gas explorations, a reduced-order model is proposed to capture the nonlinear torsional dynamics of drilling operations. In this model, the drill string structure is simplified as a single-degree-of-freedom (DOF) system suffering from dry frictions at the drill bit, while the electromechanical boundary generated by the top drive system is modeled as another tunable DOF used for stick-slip suppression. To simplify and parameterize the problems, a normalized 2DOF system with negative damping and tunable parameters is deduced via nondimensionalization and linearization. Based on this system, stability criteria are obtained analytically in the five-dimensional parametric space. Stable regions and the optimized boundary parameters are found analytically. The results suggest that the system can be stabilized by an optimally tuned boundary when and only when the magnitude of the negative damping is no greater than 2 . It also reveals that the stability deteriorates if the inertia on the top is huge and nonadjustable, which is the commonest scenario for commercial drilling rigs nowadays. Finally, applications of the tuned boundary in a typical drilling system for stick-slip mitigation are conducted and verified numerically. The results indicate that the control performance can be potentially enhanced by three to five times, via an additional virtual negative inertia generated by the top drive motor. This research provides an alternative approach to fully optimize the top boundary for curing stick-slip vibrations in drilling systems.

This paper presents the analysis of a new class of differential continuum system with a solution of traveling waves containing coupled spatial and temporal variables. Herein, we derive the analytical solution of the damped vibration response of a longitudinally moving wire with damping, subject to an oscillating boundary condition. The vibration response is the outcome of combining four traveling waves, induced by a wave initiating from the oscillating boundary, and traveling between the two boundaries. The four different traveling waves are the independent bases of the vibration responses that span the solution space of vibration of such continuum system. The combination, or the interference, of these traveling waves in the undamped condition produces nodal points in the vibration response, which can be formulated through the analytical solution. The impacts of wire speed, oscillating frequency at the boundary and damping factors on the vibration response are investigated. Furthermore, the vibration induced by the oscillating motion of the boundary has a profound impact on the effectiveness of slicing ingots with rocking motion of oscillating wire guides in wiresaw manufacturing processes.

This work investigates the effect of elastic support stiffness on the accuracy of moving load identification of Euler–Bernoulli beams. It uses the angular velocity response in solving the ill-posed inverse vibration problem and Tikhonov regularization in the load identification process of two moving loads. The effects from moving loads’ traveling direction, measurement location arrangements, number of participant measurements, and damping ratios are considered in the studies under noisy disturbance conditions. Results show that the stiffness of the translational rotational springs at the boundaries can impact the accuracy of identified moving loads considerably. Angular velocities presented much better results than accelerations under low stiffness conditions when vertical elastic supports were used. However, acceleration showed better performance when a very soft translational spring was used at one end and a much stiffer translational spring at the other end, as well as when rotational springs with large stiffness were used with simply supported beam conditions. The combination of angular velocities and accelerations provided a balanced solution for a wide range of elastic supports with different stiffnesses.

The development of reduced-order models remains an active research area, despite advances in computational resources. The present work develops a novel order-reduction approach that is designed to incorporate isolated regions that contain, for example, nonlinearitites or accumulating damage. The approach is designed to use global modes of the overall system response, which are then naturally coupled to the response in the isolated region of interest. Two examples are provided to demonstrate both the accuracy and the computational efficiency of the proposed approach. The performance of this approach is compared to the exact response corresponding to a finite element simulation for the chosen problems. In addition, the accuracy and computational efficiency are shown relative to a standard Galerkin reduction based on the linear normal modes. It is found that the proposed reduction offer computational efficiency comparable to a Galerkin reduction, but more accurately represents the response of the system when both are compared to the finite element simulation.

The Floquet theory has been classically used to study the stability characteristics of linear dynamic systems with periodic coefficients and is commonly applied to Mathieu’s equation, which has parametric stiffness. The focus of this article is to study the response characteristics of a linear oscillator for which the damping coefficient varies periodically in time. The Floquet theory is used to determine the effects of mean plus cyclic damping on the Floquet multipliers. An approximate Floquet solution, which includes an exponential part and a periodic part that is represented by a truncated Fourier series, is then applied to the oscillator. Based on the periodic part, the harmonic balance method is used to obtain the Fourier coefficients and Floquet exponents, which are then used to generate the response to the initial conditions, the boundaries of instability, and the characteristics of the free response solution of the system. The coexistence phenomenon, in which the instability wedges disappear and the transition curves overlap, is recovered by this approach, and its features and robustness are examined.

Reduced order models (ROMs) can be simulated with lower computational cost while being more amenable to theoretical analysis. Here, we examine the performance of the proper orthogonal decomposition (POD), a data-driven model reduction technique. We show that the accuracy of ROMs obtained using POD depends on the type of data used and, more crucially, on the criterion used to select the number of proper orthogonal modes (POMs) used for the model. Simulations of a simply supported Euler–Bernoulli beam subjected to periodic impulsive loads are used to generate ROMs via POD, which are then simulated for comparison with the full system. We assess the accuracy of ROMs obtained using steady-state displacement, velocity, and strain fields, tuning the spatiotemporal localization of applied impulses to control the number of excited modes in, and hence the dimensionality of, the system’s response. We show that conventional variance-based mode selection leads to inaccurate models for sufficiently impulsive loading and that this poor performance is explained by the energy imbalance on the reduced subspace. Specifically, the subspace of POMs capturing a fixed amount (say, 99.9%) of the total variance underestimates the energy input and dissipated in the ROM, yielding inaccurate reduced-order simulations. This problem becomes more acute as the loading becomes more spatio-temporally localized (more impulsive). Thus, energy closure analysis provides an improved method for generating ROMs with energetics that properly reflect that of the full system, resulting in simulations that accurately represent the system’s true behavior.

The simulation of the coupling between components modeled by finite elements (FEs) plays an important role for the prediction of the forced response of the assembly in terms of resonant frequencies, vibration amplitudes, and damping. This is particularly critical when the time-varying stress distribution must be limited for vibrating components with thin thickness coupled with large contacts. Typical examples can be found in aeronautical structures (plates, panels, and bladed disk components) assembled with bolted flanges, riveted lap joints, or joints without hole discontinuities like rail-hook joints, lace wire sealings, and strip dampers. In this paper, a new test rig is introduced for the experimental validation of a reduced-order model (ROM) based on the Gram–Schmidt Interface (GSI) modes applied to a friction contact whose dimensions are not negligible with respect to the size of the substructures. In this case, classical approaches like Craig–Bampton technique might be not effective in reducing the size of the problem when many contact nodes subjected to nonlinear contact loads cannot be omitted. The technique is implemented in a solution scheme in the frequency domain using penalty contact elements and the harmonic balance method. The preload on the joint is produced by permanent magnets to enhance the friction contact without introducing uncertainties due to bolting. Measurements are compared with the ROM simulations and with standard time-domain integration of the full FE model. The advantage of using the GSI technique is shown in terms of time computation and accuracy of the simulation.

In this paper, acoustic vibration of hexagonal nanoparticles is investigated. In terms of the spherical system of vector functions, the first-order differential equation with constant coefficients for a layered sphere is obtained via variable transformation and mass conservation. The propagation matrix method is then used to obtain the vibration equation in the multilayered system. Further utilizing a new root-searching algorithm, the present solution is first compared to the existing solution for a uniform and isotropic sphere. It is shown that, by increasing the sublayer number, the present solution approaches the exact one. After validating the formulation and program, we investigate the acoustic vibration characteristics in nanoparticles. These include the effects of material anisotropy, damping, and core–shell imperfect interface on the vibration frequency and modal shapes of the displacements and tractions.

It is well-known that nonlinear dry friction damping has the potential to bound the otherwise unboundedly growing vibrations of self-excited structures. An important technical example are the flutter-induced friction-damped limit cycle oscillations of turbomachinery blade rows. Due to symmetries, natural frequencies are inevitably closely spaced, and they can generally be multiples of each other. Not much is known on the nonlinear dynamics of self-excited friction-damped systems in the presence of such internal resonances. In this work, we analyze this situation numerically by regarding a two degrees-of-freedom system. We demonstrate that in the case of closely-spaced natural frequencies, the self-excitation of the lower-frequency mode gives rise to non-periodic oscillations, and the occurrence of unbounded behavior well before reaching the maximum friction damping value. If the system is close to a 1:3 internal resonance, limit cycles associated with much higher frictional damping appear, however, most of these are unstable. If more than one mode is subjected to self-excitation, the maximum resistance against self-excitation is at least given by the damping capacity of the most weakly friction-damped mode. These results are of high technical relevance, as the prevailing practice is to analyze only periodic limit states and argue the stability solely by the slope of the damping-amplitude curve. Our results demonstrate that this practice leads to considerable mis- and overestimation of the resistance against self-excitation, and a more rigorous stability analysis is required.

Air damper dynamic vibration absorber (DVA) is modeled using Maxwell transformed element and coulomb element. This damper serves to minimize vibration at resonant and operation of constant speed machine. Its stiffness and damping factor are transformed from Maxwell to Voigt arrangement. Meanwhile, viscous equivalent Coulomb damping is expressed by absolute relative motion. System transmissibility contours are plotted by min–max approach. Its optimal parameters are determined using this approach. Contour operation minimization is obtained from minimum system transmissibility. Moreover, exact solution of fixed points and optimal natural frequency ratio are obtained by a modified fixed point theory. Optimal design curve is derived by Coulomb damping derivative and maximum condition. Operational vibration level is minimized by 7% at the operation minimization using minimum condition. On the experimental side, test platform of the air damper is constructed using linear slide block system. Computational model of the air damper is established by its physical details and experimental data. Linear relationship is obtained between viscous and Coulomb damping angles. Modified fixed points are validated by frequency response function resonant peaks. Experimental vibration level is minimized by 5%, which being close to the minimization result. The model is validated within 5% accuracy by its optimal experimental curve.

It has been shown that shunting electromagnetic devices with electrical networks can be used to damp vibrations. These absorbers have however limitations that restrict the control performance, i.e., the total damping of the system and robustness versus parameter variations. On the other hand, the electromagnetic devices are widely used in active control techniques as an actuator. The major difficulty that arises in practical implementation of these techniques is the power consumption required for conditioners and control units. In this study, robust hybrid control system is designed to combine the passive electromagnetic shunt damper with an active control in order to improve the performance with low power consumption. Two different active control laws, based on an active voltage source and an active current source, are proposed and compared. The control law of the active voltage source is the direct velocity feedback. However, the control law of the active current source is a revisited direct velocity feedback. The method of maximum damping, i.e., maximizing the exponential time-decay rate of the response subjected to the external impulse forcing function, is employed to optimize the parameters of the passive and the hybrid control systems. The advantage of using the hybrid control configuration in comparison with purely active control system is also investigated in terms of the power consumption. Besides these assets, it is demonstrated that the hybrid control system can tolerate a much higher level of uncertainty than the purely passive control systems.

In this technical brief, the experimental study and model validations for the damping mechanisms of cable-harnessed beam structures are presented. The structure consists of cables wrapped around a host beam in a periodic zigzag pattern. A special case of cable attached along the beam length over its centerline is also considered. First, material damping in the cables is characterized using dynamic tests and the relevant cable damping factors are calculated for both the Kelvin–Voigt and hysteretic damping models. Experimental modal testing is then performed on the fabricated cable-harnessed beams to obtain the frequency response functions (FRFs). Finally, the experimental FRFs are compared with the damped analytical models. The test and model results are shown to be in very good agreements in predicting the structural damping induced by the cables.

Dynamic vibration absorber (DVA) is a practical tool used for sound and vibration suppression in the specific frequency band. The parameters of DVAs should be optimally tuned to obtain the best sound and vibration suppression application effects. When the DVAs are used for structural vibration reduction, DVAs’ two parameters which are the optimal frequency ratio and damping ratio have simple analytical expressions. However, the concise analytical expressions of the DVAs that are used for suppressing the structural sound radiations have not been reported. First, this paper investigates the characteristics of DVAs in suppressing sound radiation from thin plates. Second, the fixed points’ phenomenon of the sound radiations of the plate carrying DVAs is revealed. In addition, the classical fixed points’ theory is extended into the optimization process of the DVAs that are used for sound radiation control of the plate. The analytical expression of the optimal frequency ratio, as well as the damping ratio optimization method of the DVA, is simultaneously proposed. Third, the installation position of DVAs is also presented to obtain a better acoustic radiation effect. Finally, the numerical simulations are performed to verify the availability of the method. It is showed that the best sound radiation control effect could be obtained by adopting the optimization means proposed in this paper.

Recent developments in the aerospace industry have driven focus toward accurately modeling the effects of the cables and electronic cords on space structures. In the past, researchers have modeled the mass and stiffness effects of these cables but primarily overlooked their damping effects through careful analytical model developments. The objective of the current work is to present analytical models for cable-harnessed structures that also include the damping effects in their vibration response. Obtaining simple, low-order and high-fidelity models are highly advantageous in designing robust vibration real-time control algorithms for structures. Additionally, the analytical models are useful tools in providing insight into and better understanding of the dynamics of space structures as they are often difficult to be tested prior to launch due to their large size and at best only a few components may be tested. Motivated by the space applications, this work considers beam structures wrapped with cables which are modeled using beam and string theory assumptions. Two different damping models namely Kelvin–Voigt and hysteretic damping are considered. The homogenization approach is used as a starting point for structures of periodic wrapping patterns. Using the variational principle, the governing partial differential equation for the transverse coordinate of vibrations is found for three cable patterns and the results are compared to those from the distributed transfer function method (DTFM). Finally, the effects of several structural parameters are studied on the overall system damping.

The multi-degrees-of-freedom (MDOF) tuned mass damper (TMD) has proven its ability to suppress multiple modes of interest, and it possesses less mounting space than multiple single degree-of-freedom TMDs of equal damping mass. However, it is challenging to implement the exact design of MDOF TMDs having expected vibration modes. The conceptual design of MDOF TMD containing visualized DOFs is first presented by the graphical approach, and the visualization of the quantitative relationship between the freedoms and constraints of TMD is attained. Then, dynamics modeling is analytically formulated by incorporating experimental data, and optimization of MDOF TMD considering background modes is performed. Two scenarios of MDOF TMD (i.e., 2DOFs TMD and 3DOFs TMD) are simulated. Vibration suppression of single dominant mode and multiple modes are achieved, corresponding to the case when the primary structure is subjected to wide and narrow band harmonic excitations, respectively. Afterward, a TMD with one rotational and two translational (1R2 T) DOFs is designed by embodying the geometric constraint patterns by flexible beams, and changeable elastic elements are incorporated. Experiments show that the first, second, and third bending modes of the cantilever beam are suppressed by 80.0%, 67.5%, and 61.2%, respectively, by the 3DOFs TMD for multiple modes suppression.