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.

Recent developments in timing belt drive for the automotive engine have seen the use of non-circular pulleys. This study presents an experimental and numerical investigation on this type of transmission including an oval pulley. A specific test rig has been designed to enable the identification of the proper effect of an oval pulley on the transmission dynamics. The belt tensions, the speeds, and torques of the driving and driven pulleys were measured and analyzed for three different transmission configurations: (1) circular driving pulley and oval driving pulley without (2) and/or with (3) load torque applied. Analyses were carried out in the time and frequency domains by considering the driving pulley rotation angle as a reference. In parallel a numerical model has been developed, it accounts for the specific motions of the belt seating/unseating points on the oval pulley and its neighboring pulleys. The model considers the variation of lengths for the belt spans adjacent to the oval pulley. This induces variable longitudinal stiffness and influences the transmission dynamics that is predicted versus time and compared with experiments. The phasing angle of the oval driving pulley was adjustable in order to study its influence. With no resistant torque applied, it was found that, for low-speeds, the oval pulley has a pure kinematic effect on the transmission dynamics. When a load torque is applied, the effectiveness of the oval pulley regarding the belt tensions and transmission error fluctuations is verified experimentally for some specific intervals of the phasing angle.

This paper depicts the application of symbolically computed Lyapunov–Perron (L–P) transformation to solve linear and nonlinear quasi-periodic systems. The L–P transformation converts a linear quasi-periodic system into a time-invariant one. State augmentation and the method of normal forms are used to compute the L–P transformation analytically. The state augmentation approach converts a linear quasi-periodic system into a nonlinear time-invariant system as the quasi-periodic parametric excitation terms are replaced by “fictitious” states. This nonlinear system can be reduced to a linear system via normal forms in the absence of resonances. In this process, one obtains near identity transformation that contains fictitious states. Once the quasi-periodic terms replace the fictitious states they represent, the near identity transformation is converted to the L–P transformation. The L–P transformation can be used to solve linear quasi-periodic systems with external excitation and nonlinear quasi-periodic systems. Two examples are included in this work, a commutative quasi-periodic system and a non-commutative Mathieu–Hill type quasi-periodic system. The results obtained via the L–P transformation approach match very well with the numerical integration and analytical results.

Concrete box girder bridges occupy over 80% of the total mileage of the Chinese high-speed railway. The box girder structure has many natural modes of low frequencies, which can be excited by a train passing at high-speed, generating low-frequency bridge noise. This paper is concerned with the prediction of such bridge noise and reports a prediction model. The model, as other existing models of the same nature, also incorporates two parts, one dealing with vehicle–track-viaduct dynamics and the other dealing with sound radiation from the girders, but takes into account more features related to high-speed. In this model, vehicle–track-viaduct dynamics is dealt with in the frequency-domain based on the theory of infinitely long periodic structure and the Fourier-series method, predicting vibration frequency spectra for each and every box girder. The predicted vibration frequency spectra of all the box girders are expressed as a sum of propagating waves at different wavenumbers, and sound radiation from each propagating wave is evaluated using the 2.5D acoustic boundary element method. This approach to sound radiation enables contributions from all the box girders to be included at a reasonable computational cost. This paper continues with a comparison in bridge vibration and noise between prediction and measurement for a typical site. And finally, based on the parameters of that site, characteristics of noise radiation from the concrete box girders are studied using the prediction model.

In this paper, we present a control strategy for a micro-electro-mechanical gyroscope with a drive mode excited through parametric resonance. The reduced order two degrees-of-freedom model of the device is built, and the drive mode control is implemented using phase-locked loop (PLL) and automatic gain control (AGC) loop. A sense mode vibration control algorithm is developed as well for enhanced sensor performance. The analysis of the drive mode control loops is conducted using the multiple scales method. The robustness of the suggested control loops to parameters perturbation is demonstrated using the model. A simplified linear model of the control loops is shown to predict the device behavior with good accuracy.

The torsional vibration hinders the reduction of automobile exhaust gas emitted by using engines with a reduced number of cylinders. Centrifugal pendulum vibration absorbers (CPVA) have been used in engines to suppress torsional vibration. To clarify the dynamics of CPVAs, much analysis has been conducted using the point mass CPVA as the model of rigid body bifilar CPVA. However, few attempts have been made to analyze the rigid body unifilar CPVA on vibration suppression performance in frequency response. In this study, the authors have analyzed the dynamics of the rigid body unifilar CPVA, focusing on the influence of shape parameters. The results verified that the shape parameters, which relating to moment of inertia or radius of gyration of rigid body unifilar CPVA, influence the vibration suppression performance in frequency response. Moreover, the numerical simulation results were confirmed experimentally and showed in good agreement with the experimental results, and both indicated the dependence of the vibration suppression performance on the shape parameters of the rigid body unifilar CPVA.

Next-generation civil aircraft and atmospheric satellites will have high-aspect-ratio wings. Such a design necessitates successive analysis of static, frequency, and time-domain dynamic responses based on a three-dimensional nonlinear beam model. In this study, a new successive-analysis framework based on an absolute nodal coordinate formulation with mean artificial strains (ANCF-MAS) is developed. While retaining the advantages of other three-dimensional (3D) ANCF approaches, such as constancy of the mass matrix and absence of velocity-dependent terms, ANCF-MAS uses the elastic force of the mean artificial strains to remove cross-sectional deformations that cause locking problems. The equation becomes a differential equation with an easily linearized elastic force that enables not only static and dynamic analyses but also frequency analysis using standard eigenvalue solvers. The solutions converge to the analytical frequencies without suffering from locking problems. A proposed successive-analysis method with model-order reduction reveals that the frequencies vary with the nonlinear static deformation because of the 3D deformation coupling. This reduced-order model agrees well with nonlinear models even when the wing experiences a large nonlinear dynamic deformation.

Controlling and manipulating elastic/acoustic waves via artificially structured metamaterials, phononic crystals, and metasurfaces have gained an increasing research interest in the last decades. Unlike others, a metasurface is a single layer in the host medium with an array of subwavelength-scaled patterns introducing an abrupt phase shift in the wave propagation path. In this study, an elastic metasurface composed of an array of slender beam resonators is proposed to control the elastic wavefront of low-frequency flexural waves. The phase gradient based on Snell’s law is achieved by tailoring the thickness of thin beam resonators connecting two elastic host media. Through analytical and numerical models, the phase-modulated metasurfaces are designed and verified to accomplish three dynamic wave functions, namely, deflection, non-paraxial propagation, and focusing. An oblique incident wave is also demonstrated to show the versatility of the proposed design for focusing of wave energy incident from multiple directions. Experimentally measured focusing metasurface has nearly three times wave amplification at the designed focal point which validates the design and theoretical models. Furthermore, the focusing metasurface is exploited for low-frequency energy harvesting and the piezoelectric harvester is improved by almost nine times in terms of the harvested power output as compared to the baseline harvester on the pure plate without metasurface.

Numerous nanometrology techniques concerned with probing a wide range of frequency-dependent properties would benefit from a cantilevered sensor with tunable natural frequencies. In this work, we propose a method to arbitrarily tune the stiffness and natural frequencies of a microplate sensor for atomic force microscope applications, thereby allowing resonance amplification at a broad range of frequencies. This method is predicated on the principle of curvature-based stiffening. A macroscale experiment is conducted to verify the feasibility of the method. Next, a microscale finite element analysis is conducted on a proof-of-concept device. We show that both the stiffness and various natural frequencies of the device can be controlled through applied transverse curvature. Dynamic phenomena encountered in the method, such as eigenvalue curve veering, are discussed and methods are presented to accommodate these phenomena. We believe that this study will facilitate the development of future curvature-based microscale sensors for atomic force microscopy applications.

During the drilling process in oil and gas fields, slender drill strings often experience a multitude of complex and simultaneous vibrational phenomena. Drill string vibrations hinder the drilling process and can cause premature wear and damage to the drilling equipment. Here, the suppression of drill string vibrations during drilling operations is experimentally investigated using a novel drill string design, based on the use of innovative periodic inserts that control the vibration transmissibility in different directions. These inserts are equipped with viscoelastic rings that act as sources of local resonances, surrounding piezoelectric actuators that generate internal axial loading when electrically excited. An experimental prototype that combined all these details was constructed and tested to demonstrate the periodic drill string's feasibility and effectiveness in minimizing undesirable vibrations. The obtained results indicate that the periodic inserts’ careful design can effectively enhance the drill strings’ dynamic behavior and conveniently regulate its bandgap characteristics. Both radial and axial vibrations were controlled, and the vibrations’ amplitude was reduced significantly over a wide range of frequencies. The proposed approach appears to present a viable means for designing intelligent drill strings with tunable bandgap characteristics.

Over the last decades, the search for fast and efficient transportation systems has raised the interest toward maglev technologies. In this scenario, the Hyperloop paradigm is regarded as a breakthrough for future mobility. However, its practical implementation requires the solution of key shortcomings. Among these, the stability of the electrodynamic levitation system remains partially unexplored. The state of the art presents numerous attempts to attain stable behavior. In recent works, the stabilization of maglev vehicles has been addressed only for the vertical dynamics. Nevertheless, stable operation of all degree-of-freedom is required for a successful implementation of these transportation systems. The present paper addresses the full stabilization of a downscaled vehicle where levitation and guidance are provided by electrodynamic means. To this end, a design methodology supported by analytical modeling is proposed, where the degree-of-freedom are stabilized by suitably introducing secondary suspension elements. The design of the secondary suspension and the guidance system is obtained through the optimization of stability and dynamic performance. Then, a multibody model is developed. Both numerical approaches are compared in the frequency domain for validation purposes. Finally, the multibody model is simulated in the time domain to assess system performance in the presence of track irregularities and evaluate coupling effects between the degree-of-freedom.

Acoustic beamforming array design methods are typically suited for circular and rectangular areas. A comparison of three array design methods is presented in this paper over irregular shaped areas, including L-shapes and arches. Partial-logarithmic spiral arrays that possess their geometric center either at the origin of the array area or the centroid of the irregular shaped area are compared against randomized array designs based on maximum sidelobe level (MSL) parameters and arrays generated using a recently published array design method named the adaptive array reduction method (AARM). In the AARM, a large array is reduced to a smaller array by seeking the removed microphone that possesses the minimum value of the MSL, the main lobe width (MLW), and a lobe distortion term. The AARM is also tested in two practical cases against a partial spiral array design used at the NASA Langley low-turbulence pressure tunnel and a hypothetical rectangular wall case. In both cases, the AARM showed superior performance to the logarithmic spiral arrays in all cases based on MSL and MLW criteria. Of the three methods compared, the AARM best utilizes the full potential array aperture of an irregular area and therefore produces the best MSL, MLW, and lobe distortion values.

In many structural applications like bridges, arches, etc., frames are used, and it is important to study their dynamic behavior. Finite element method (FEM) is usually used for computational simulation of vibration for such frame structures. However, FEM simulations for high frequency are computationally intensive and lack accuracy. This paper proposes a wave propagation-based approach for the vibration analysis of a frame having angular and curved joints. The reflection and transmission matrices for the joints are derived using the kinematic compatibility and equilibrium conditions. Reflection, transmission, and propagation matrices are assembled leading to matrix equation terms of the wave amplitudes. Modal analysis and harmonic analysis of frames having curved and angular joints are performed using the present formulation. The frequency response function for point harmonic forcing acting on such structures is also presented. The formulation and the results are non-dimensionalized for wider applicability. The results obtained using the present formulation are compared with those obtained through FEM simulation in a commercial package. It is found that the results obtained using the two methods are in excellent correlation. The computational efficiency of the present method over FEM simulation is also reported.

This work investigates how uncertainties in the balancing weights are propagating into the vibration response of a high-speed rotor. Balancing data are obtained from a 166-MW gas turbine rotor in a vacuum balancing tunnel. The influence coefficient method is then implemented to characterize the rotor system by a deterministic multi-speed and multi-plane matrix. To model the uncertainties, a non-sampling probabilistic method based on the generalized polynomial chaos expansion (gPCE) is employed. The uncertain parameters including the mass and angular positions of the balancing weights are then expressed by gPCE with deterministic coefficients. Assuming predefined probability distributions of the uncertain parameters, the stochastic Galerkin projection is applied to calculate the coefficients for the input parameters. Furthermore, the vibration amplitudes of the rotor response are represented by appropriate gPCE with unknown deterministic coefficients. These unknown coefficients are determined using the stochastic collocation method by evaluating the gPCE for the system response at a set of collocation points. The effects of individual and combined uncertain parameters from a single and multiple balancing planes on the rotor vibration response are examined. Results are compared with the Monte Carlo simulations, showing excellent agreement.

In-line inspection (ILI) is a non-destructive assessment method commonly used for defect assessment and for pipeline monitoring. Passing an ILI tool through an excavated or exposed section of a pipe during an integrity assessment can excite vibrations. The ILI tool’s weight and speed can exert substantial forces, stresses, and deflections on the pipe section. When the excitation frequency from the ILI tool’s movement is close to the pipe’s natural frequency, the dynamic stress generated within the pipe can become great enough that it creates integrity concerns on the pipeline. This research aims to study the effects of an ILI tool’s passage through exposed and partially supported pipes under a variety of boundary and loading conditions. A finite element model of an exposed pipe section is developed based on the Timoshenko beam theory to predict the pipe’s displacement, strain, stress, and frequency responses under a wide range of excitation frequencies. The model is further validated using a lab-scale experimental setup with a mass that moves at different speeds. A comparison between the simulation and the experimental results shows that the proposed model can effectively predict the pipe’s dynamics.

In this paper, the nonlinear modeling of beam energy harvester embedded with piezoelectric transducers is presented. Starting from a multibody dynamics perspective, a fully coupled electromechanical nonlinear beam model was derived and a geometrically exact finite volume beam element, including the circuit equation is developed. In this model, the beam resultants-strain constitutive law and mass properties are obtained from a two-dimensional beam cross-sectional modeling in which the electromechanical coupling effects are included. The results are verified against numerical and experimental results reported in the literature.

Structures possessing cyclic symmetry such as turbine bladed disks, ultrasonic motors, and toothed gear wheels can experience elevated vibration levels when small deviations from circumferential periodicity exist. Detection of these perturbations via classical system identification approaches is time-consuming, indirect, and exhibits low sensitivity to defects, and is affected by measurement noise. The present work utilizes low-level forces that automatically lock onto a weighted rotating projection of the system modes at resonance frequency to enhance the detectability of small structural imperfections. The spatial localization of defects is exploited to identify multiple, localized, isolated defects’ locations. The defects’ severities are estimated based on the deviation from the circular structure's analytical mode shapes. The fast and enhanced precision of defect identification is obtained by employing the modal-filtered autoresonance technique. To validate the presented method, an experimental system consisting of a ring of coupled Helmholtz acoustic resonators was developed. Experimental results show good agreement with numerical simulations, verifying the method's capabilities to identify the location and severity of multiple defects. Thus, the implementation of the suggested method provides fast and precise structural health monitoring of cyclic-symmetric systems.

This study aims at the systematical improvement and comparative analysis of analytical crack models for the rotating blade. Part I of this study focuses on analytical modeling, model modification, and model validation of transverse crack for the rotating blade. The most widely applied analytical crack models for the rotating blade are reviewed and compared, and then their limitations are discussed. It is indicated that the conventional analytical crack models suffer from low physical interpretability and vibration prediction accuracy. By considering these limitations of conventional analytical crack models, model modification is performed to enhance the physical meaning and improve the accuracy. First, the stress-based breathing crack model is modified by direct calculation of the breathing function based on the theory of linear elastic fracture mechanics and resetting the correction factor of centrifugal stiffening stiffness. Second, the vibration-based breathing crack models, including bilinear breathing crack model and cosine breathing crack model, are modified by introducing the coupling effect between bending stress and centrifugal stress based on the stress state at the blade crack section. The additional bending moment induced by the blade part outside the crack section is considered in all analytical models. The modified crack models’ validity is verified by comparing vibration responses obtained by the modified crack models, the finite element contact crack model, and the conventional crack models. The comparative results suggest that the modified models promote the physical interpretability and improve the vibration prediction accuracy of analytical crack models.

This study aims at the comparative analysis and improvement of different analytical crack models for rotating blade. Part II of this study focuses on the comparative analysis of dynamic characteristics based on modified models mentioned in Part I. A nonlinear damage indicator (NDI) and an equivalent energy indicator (EEI) are introduced to characterize the nonlinear effect of crack from different perspectives. EEI offers a physical mechanism explanation of crack closing behavior, which is invisible. Meanwhile, NDI offers an observable indicator to quantify the nonlinearity of crack. It is demonstrated through the numerical study that the variation of NDI and EEI varies the same with each other, which cross-verified the validity of NDI and EEI for quantifying the nonlinear effect of crack. Comparative investigations are performed to analyze the effects of load amplitude, crack depth, and crack location on the nonlinear dynamics of cracked blade, and both NDI and EEI are utilized to quantify the nonlinear effects of crack. The comparative results suggest that NDI of the second-order super-harmonic component increases with the increasing crack depth and excitation load amplitude and decreases with the increasing crack locations, while the variation of EEI follows the variation of NDI. This phenomenon indicates that the crack, which is deeper and closer to blade root under a larger load will be more dangerous. This study’s comparative results may provide some guidance for choosing the analytical crack models when analyzing the nonlinear dynamics of rotating cracked blade and blade health monitoring.

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.