This study directly addresses the problem of optimal control of a structure under the action of moving masses. The main objective of the study is to experimentally implement and validate an active control solution for a small-scale test stand. The supporting structure is modeled as an Euler-Bernoulli simply supported beam, acted upon by moving masses of different weights and velocities. The experimental implementation of the active controller poses a particular set of challenges as compared to the numerical solutions. It is shown both numerically and experimentally that using electromagnetic actuation, a reduced order controller designed using a time-varying algorithm provides a reduction of the maximum deflection up to 18% as compared to the uncontrolled structure. The controller performance and robustness were tested against a representative set of possible moving load parameters. In consequence of the variations in moving mass weight and speed the controller gain requires a supplementary adaptation. A simple algorithm that schedules the gain as a function of the weight and speed of the moving mass can achieve both a good performance and an adjustment of the control effort to the specific design requirements.

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.

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.

This article provides criteria for the design of electrostatic arch micro-tweezers. The tweezers can be operated in two modes: a traditional quasi-static mode where a direct current voltage commands the tweezers arms along a trajectory to manipulate objects and dynamic mode where a harmonic signal commands release or characterization of objects. While the arms are rigid and move in tandem in the static mode, this is not guaranteed in the dynamic mode. To satisfy this, we carried out modal analysis of the tweezers using a finite element model (FEM) and a reduced-order model (ROM). The results show that the arms kinetic and potential energies divide the beam span into a middle sub-span between the arms and two outer sub-spans and result in significant changes in the relative compliance of the sub-spans. The changes in the platform compliance place limitation on the tweezers dynamic operation, such that only the first symmetrical mode shape of the tweezers satisfies the design criteria. We also investigate the adequacy of an ROM using straight unbuckled beam mode shapes as basis functions to represent the tweezers response by comparing its results with those of FEM. A five-mode ROM is found adequate to represent small motions in the vicinity of the tweezers initial curvature. It is inadequate for larger motions involving snap-though motions between the initial and counter curvatures. To capture larger motions, ROM should be improved by incorporating higher order straight beam modes or using the actual tweezers modes.

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.

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.

Ladder frame structures are used as models for multistorey buildings. These periodic structures exhibit alternating propagating and attenuating frequency bands. Of the six different wave modes of propagation, two modes strongly attenuate at all frequencies. The other four modes have nonoverlapping stop band characteristics. Thus, it is challenging to isolate such structures when subjected to broadband, multimodal base excitation. In this study, we seek to synthesize a periodic ladder frame structure that has attenuation characteristics over the maximal range of frequencies for all the modes of wave propagation. We synthesize a unit cell of the periodic structure, which comprises two distinct regions having different inertial, stiffness, and geometric properties. The eigenvalues of the transfer matrix of the unit cell determines the attenuating or the nonattenuating characteristics of the structure. A novel pictorial presentation in the form of eigenvalue map is developed. This is used to synthesize the optimal unit cell. Also, design guidelines for suitable selection of the design parameters are presented. It is shown that a large finite periodic structure comprising a unit cell synthesized using the present approach has significantly better isolation characteristics in comparison to the homogeneous or any other arbitrarily chosen periodic structure.

Articular cartilage is a thin layer of a solid matrix swollen by fluid, and it protects joints from damage via poroviscoelastic damping. Our previous experimental and simulation studies showed that cartilage-like poroviscoelastic damping could widen the range of damping methods in a low-frequency range (<100 Hz). Thus, the current study aimed to realize cartilage-like damping capacity by single- and two-indenter–foam poroviscoelastic dampers in a low-frequency range. Multiple single-indenter–foam dampers were designed by combining foam sheets with different pore diameters and indenters with different radii. Their damping capacity was investigated by dynamic mechanical analysis in a frequency range of 0.5–100 Hz. Single-indenter–foam dampers delivered peak damping frequencies that depended on the foam’s pore diameter and characteristic diffusion length (contact radii). Those dampers maximize the damping capacity at the desired frequency (narrowband performance). A mechanical model combined with simple scaling laws was shown to relate poroelasticity to the peak damping frequencies reasonably well. Finally, combinations of single-indenter–foam dampers were optimized to obtain a two-indenter–foam damper that delivered nearly rate-independent damping capacity within 0.5–100 Hz (broadband performance). These findings suggested that cartilage-like poroviscoelastic dampers can be an effective mean of passive damping for narrowband and broadband applications.

The reactivity control system is a vital safety system for a nuclear reactor. One of the most challenging aspects in the design of these systems is the operation during critical situations, in particular during earthquakes to safely shut-down the reactor. To study these situations, the toolbox python Implementation for Reliability Assessment Tools (PIRAT) is used to model two types of excitation: single frequency and realistic. The main focus of this work is the comparison of the implementation of the contact models used to describe the interaction between the subsystems. For the dynamic tool in PIRAT (dynamic Euler–Bernoulli for seismic event (DEBSE)), this is done with a two-stage linear spring or Lankarani and Nikravesh-based models. For the sine excitation, the results show four distinct response types with the maximum displacement varying between the models. Low-frequency excitation showed little variance while higher frequency excitation showed large variations. The realistic excitation, however, did not show these variations and showed nearly identical results for the contact models tested. This gives confidence in the simulations since the user selected contact model did not greatly affect the simulation results for a realistic excitation.

A numerical methodology is described to study the influence of the contact location and contact condition of friction damper in aircraft engines. A simplified beam model is used to represent the blade for the preliminary design stage. The frictional damper is numerically analyzed based on two parameters, contact angle and vertical position of the platform. The nonlinear modal analysis is used to investigate the nonlinear dynamic behavior and damping performances of the system. The harmonic balanced method with the continuation technique is used to compute the nonlinear modes for a large range of energy levels. By using such a modeling strategy, the modal damping ratio, resonant amplitude, and resonant frequency are directly and efficiently computed for a range of design parameters. Monte Carlo simulations together with Latin hypercube sampling is then used to assess the robustness of the frictional damper, whose contact parameters involve much uncertainties due to manufacturing tolerance and also wear effects. The influences of those two parameters are obtained, and the best performances of the frictional damper can be achieved when the contact angle is around 25 deg–30 deg. The vertical position of the platform is highly mode dependent, and other design considerations need to be accounted. The results have proved that the uncertainties that involved contact surfaces do not have significant effects on the performance of frictional damper.

Momentum wheel assemblies (MWAs) play an important role in the attitude adjustment of the satellite by momentum exchange. The micro-vibration induced by the MWAs affects attitude adjustment and leads to unclear imaging and imprecise position. Considering the isolation of multi-directional vibration and transmission of the torque, a novel isolator inspired by rigid-flexible coupling characteristics of folded structure is proposed for the MWAs in this paper. Through the orthogonal arrangement of two Z-folded beams, the isolator has low stiffness in the translational directions and high stiffness in the direction of rotation. An equivalent dynamic model is developed to characterize the isolator. The experimental results verify that the developed model accurately predicts the response of the isolator under different excitations. The results also demonstrate that the prototype can effectively isolate vibration in low-frequency and a wide-frequency range under three excitation directions. Moreover, the isolator has been tested to verify that it has enough stiffness for torque transmission. The design is compact and can be applied to the MWAs of the satellite for multi-direction vibration isolation without influence on the attitude adjustment of the MWAs to the satellite.

The so-called locally resonant acoustic metamaterials (LRAMs) are a new kind of artificially engineered materials capable of attenuating acoustic waves. As the name suggests, this phenomenon occurs in the vicinity of internal frequencies of the material structure and can give rise to acoustic bandgaps. One possible way to achieve this is by considering periodic arrangements of a certain topology (unit cell), smaller in size than the characteristic wavelength. In this context, a computational model based on a homogenization framework has been developed from which one can obtain the aforementioned resonance frequencies for a given LRAM unit cell design in the sub-wavelength regime, which is suitable for low-frequency applications. Aiming at validating both the proposed numerical model and the local resonance phenomena responsible for the attenuation capabilities of such materials, a 3D-printed prototype consisting of a plate with a well selected LRAM unit cell design has been built and its acoustic response to normal incident waves in the range between 500 and 2000 Hz has been tested in an impedance tube. The results demonstrate the attenuating capabilities of the proposed design in the targeted frequency range for normal incident sound pressure waves and also establish the proposed formulation as the fundamental base for the computational design of 3D-printed LRAM-based structures.

This paper presents a new design of a high-static-low-dynamic stiffness (HSLDS) isolator with an adjustable cam profile. The interaction force between the cam and roller provides the negative stiffness force and the linear spring provides the positive stiffness force in the HSLDS isolator. Unlike previous studies, the cam profile in this paper can be individually designed to meet different working conditions. Firstly, the harmonic balance method is used to acquire the dynamic response of the HSLDS isolator. Then, the effects of the damping ratio, stiffness ratio, and external force amplitude on the frequency response amplitude and force transmissibility are discussed. Finally, the frequency responses of four designed nonlinear HSLDS isolators and a linear isolator are acquired by the numerical method. The results show that the nonlinear isolator begins to achieve vibration isolation at 0.11 Hz and the linear one is 8.9 Hz. The proposed HSLDS isolator realizes lower vibration isolation frequency than the linear isolator.

The electromagnetic coupling effect can generate electromagnetic damping to suppress disturbance, which can be utilized for vibration serviceability control in civil engineering structures. An electrodynamic actuator is used as a passive electromagnetic damper (EMD). Ideally, the EMD is assumed to be attached between the ground and the structure. The kinetic energy of the vibrating structure can be converted to electrical energy to activate the electromagnetic damping. To induce appropriate damping, the two terminals of the damper need to be closed and cascaded with a resonant shunt circuit as an electromagnetic shunt damper (EMSD). In this study, an resistance–inductance–capacitance (RLC) oscillating circuit is chosen. For determination of optimal circuit components and comparing against the tuned mass damper (TMD), existing H ∞ design formulae are applied. This work extends this with a detailed development of an H 2 robust optimization technique. The dynamic properties of a footbridge structure are then selected and used to verify the EMSD optimal design numerically. The vibration suppression performance is analytically equivalent to the dynamic characteristic of the TMD and has feasible installation and better damping enhancement. To further evaluate the potential application of the EMSD, multi-vibration mode manipulation via connecting multiple RLC resonant shunt circuits is adopted. The multiple RLC shunt circuit connecting to EMD is an alternative to the single mode control of a traditional TMD. Therefore, the EMSD can, in principle, effectively achieve suppression of single and multiple vibration modes.

An oblong ring-type structure is composed by two straight segments (length L) and two semicircular segments (radius R). It can be used to generate traveling waves, being applied to build linear piezoelectric motors and linear conveyor systems. The traveling waves to such applications occur at specific frequencies, generated by simultaneous symmetric and antisymmetric flexural vibration modes which, in general, have distinct natural frequencies. However, for specific designs, they may coincide or be very close. This may be achieved by finding the appropriate L/R ratio. For preliminary design, an analytical model is very desirable, due to its computational efficiency and the absence of a computational automatic identification of symmetric and antisymmetric flexural vibration modes among numerical solutions. Therefore, the objective of this work is to propose an analytical and practical model to determine classes of vibration modes of interest for producing traveling waves in oblong ring-type structures, being employed for conceptual design such that the L/R ratio is determined in an efficient way. The oblong ring is considered as a beam-like structure composed by straight and curved segments, employing Timoshenko and Euler–Bernoulli kinematic assumptions. A design method is proposed by solving sequentially and systematically distinct geometric proposals of oblong ring-type designs and, for each one, evaluating the candidates to produce the flexural traveling waves. Later, the strong-candidates are analyzed by finite element models to test the quality of the design with less assumptions. We show that the methodology provides convenient results as a design method for oblong ring-type structures.

Structural dynamic techniques have been proven accurate at predicting the vibrations of single parts (i.e., monolithic specimens), which are widely used in industrial applications. However, vibration analysis of such assemblies often exhibits high variability or nonrepeatability due to jointed interfaces. Inspired by advances in additive manufacturing (AM) and nonlinear vibration absorber theory, this research seeks to redesign jointed structures in an attempt to reduce the nonlinear effects introduced by the jointed interfaces. First, the nonlinear dynamics of a conventionally manufactured beam and an AM beam are measured in both a traditional (flat) lap joint assembly and also a “linearized” lap joint configuration (termed the small pad). Second, the internal structure of the AM beam is varied by printing specimens with internal vibration absorbers. With the two interface geometries studied in this experiment, the flat interface is found to be predominantly nonlinear, and introducing a vibration absorber fails to reduce the nonlinearities from the jointed interface. The small-pad responses are relatively linear in the range of excitation used in the analysis, and the nonlinear effects are further reduced with the presence of a center vibration absorber. Overall, the energy dissipation at the interface is highly dependent on the design of the contact interface and the internal vibration absorber. Adding a nonlinear vibration absorber alone is insufficient to negate the interfacial nonlinearity from the assembly; therefore, future work is needed to study the shape, location, and material for the design and fabrication of nonlinear vibration absorbers.

Vibration absorbers are commonly used to reduce unwanted structural vibrations. In this paper, a vibration absorber composed of a sprung mass is used to enforce a location of zero displacement (or node) at a specified location on a Euler–Bernoulli beam under harmonic base excitation. Closed-form expressions for the optimal tuning of the auxiliary spring-mass system are found, and the results are presented for the cases of the attachment and node located at the same and different locations. The assumed modes method is used, so the results can be applied for arbitrary boundary conditions. To aid in the design process, this paper also characterizes the sensitivity of the displacement at the desired node location to parametric variations. Sensitivities are considered with respect to the base excitation frequency and the attachment mass, stiffness, and location. The sensitivities of the system highlight some feasible but less desirable attachment locations. Numerical and experimental results for a cantilever beam are presented to illustrate the proposed method and the effects of mistuning.