Metastructures made of spring-mass resonators present a band gap at the natural frequency of the resonator. This rule cannot be generalized for more complex resonators. This work analyses the case of a metastructure composed by a periodic arrangement of vertical beams rigidly joined to a horizontal beam. The vertical beams work as resonators, and their natural frequencies play a strong role on the band structure of the whole system, however, different to the case with spring-mass resonators. Since this metastructure can be considered as a lattice, Bloch's theorem is applied to the unit cell and a numerical procedure based on the Finite Element Method permits to obtain the dispersion curves. Illustrative results show the influence of the natural frequencies of the horizontal and vertical beams on the band structure.

Despite widespread use of aft-fuselage mounted twin-engine aircraft in the business jet industry, a thorough investigation into the vibro-acoustic properties of this aircraft type has yet to be undertaken. Additionally, the effect of bulkhead pressurization on the vibro-acoustic properties of this aircraft fuselage has yet to be investigated in isolation. This work investigates the effect of bulkhead pressurization on two different designs of an aft-fuselage twin-engine mounted aircraft: a single, and a double bulkhead design. A modal analysis, a harmonic frequency response analysis, and an acoustic response analysis were performed. A split bulkhead pressurization methodology was introduced as a means of improving structural performance without impacting passenger comfort levels in double bulkhead aircraft. Modal coupling between components was seen to be the primary cause of increased cabin noise, peaking above 80 Hz. The bulkhead frequency response was highly dependent upon bulkhead pressurization, as the modal participation factors were significantly impacted by bulkhead pressurization. Therefore, the importance of understanding all bulkhead natural frequencies was highlighted, as the response changed as a function of bulkhead pressurization. Bulkhead resonance conditions generated a tone in the acoustic frequency response inside the passenger cabin, highlighting the importance of this component to passenger comfort levels.

This paper discusses the dynamic characteristics of plastic plates with bolted joints. The effects of tightening torque on the modal properties of the plates are investigated. Experimental and numerical modal analyses have been conducted on the plates made of acrylonitrile butadiene styrene (ABS), that are clamped by bolted joints. First, the effect of tightening torque on the vibration mode of the plates is investigated by experimental modal analyses. Modal testing has been conducted for various tightening torque values and the relationships between the modal parameters and the tightening torques are discussed. Second, the effects of tightening torque on the vibration mode are studied by using analytical models for the bolted joints based on finite element method (FEM). Based on the comparisons between the experimental and the numerical results, a modeling strategy for the boundary conditions between the plates is introduced, and its validity is discussed. From both experimental and numerical studies, it is shown that the natural frequencies of the structures with bolted joints tend to converge to specific values as tightening torque increases. Moreover, it is also shown that when modeling the bolted plates by FEM, the inter-plate motion should be constrained by a boundary condition to properly suppress the out-of-phase motion of the plates.

A pendulum-type tuned mass damper (TMD) - tuned sloshing damper (TSD) system is proposed as a cost effective device to reduce wind-induced structural motion. Lagrange's principle is employed to develop an equivalent mechanical model for the system. The sloshing liquid provides additional gravitational restoring force to the pendulum TMD, but does not provide a corresponding increase to its inertia. As a result, the natural frequency of the pendulum TMD is increased due to the TSD degree of freedom. Shake table testing is conducted on several pendulum TMD-TSD systems that are subjected to harmonic base excitation at discrete frequencies near the natural frequency of the pendulum TMD. The modelled and experimental results are in reasonable agreement when the liquid is not shallow, or the response amplitude is not large. The pendulum TMD-TSD is coupled to a linear structure and it is demonstrated through an analytical study that the device provides performance that is comparable to a traditional TMD. The proposed system is advantageous because it does not require a viscous damping system that is often one of the most costly components of traditional TMDs.

This paper presents a shape memory alloy actuator design using a bimorph structure capable of high-speed actuation and low power consumption. Two active layers of shape memory alloy wires are separated by a passive layer of thermoplastic polyurethane. This structure results in a bending actuator when current is alternated between the two active shape memory alloy layers. Actuators of lengths 20, 25, 30, 35 and 40 mm were tested at peak current input of 110, 120, 130 and 140 mA. The 40 mm actuator was shown to have a natural frequency of 11.4 Hz with a bending displacement of 26.4 mm perpendicular to the neutral position and a power input of 0.78 watts (140 mA peak current input). A relationship between the input current and the resulting vibratory characteristics was found. As the current increases, the natural frequency decreases and the damping ratio increases. The experimental results are compared with an FEM vibration analysis and an Euler-Bernoulli cantilever beam equations.

A new reduction method is proposed to investigate the behavior stability of rotor-bearing systems subject to a multifrequency rotational motion of their base. Combining the modal analysis and the construction of specific dynamic Ritz vectors, this method is able to deal with complex rotordynamics characteristics such as nonproportional damping, nonself-adjoint matrices, or time-varying parametric coefficients. This paper focuses first on assessing the accuracy and efficiency of the reduction method by computing time history and spectral responses of full and reduced models due to multifrequency base excitations. Its main potential is then highlighted in the parametric stability analysis through Floquet theory. The proposed numerical examples are composed with academic and industrial rotors, both modeled with one-dimensional Timoshenko beam finite element and supported by hydrodynamic journal bearings.

In this paper, we report the bending spectrum measured experimentally on oscillating beams with free extremes in a frequency range below and above the cutoff or critical frequency. The experimental setup used to obtain the bending spectrum consisted of a novel and selective method to excite mainly bending modes, as well as an identification process in which oscillation modes other than bending were discarded. For the first time, we identified bending modes above the cutoff frequency for square and circular cross-sectional beams and a good agreement is obtained when the measured frequencies are compared with the predictions of the Timoshenko beam theory (TBT) and those numerically obtained from the elasticity theory by using a three-dimensional finite element method (FEM) calculation. Higher frequency values at which TBT should cease to be valid were not achieved in the experiments. Instead, our experimental results show that TBT remains valid above the cutoff frequency, with an error smaller than 6%.

This paper evaluates the effects of uncertainties on the load capacity of a four-pad tilting-pad journal bearing, in which the pad radius, oil viscosity, and radial clearance are considered as uncertain information. The hydrodynamic supporting forces at the bearing pads are obtained by solving the Reynolds equation. In this case, the uncertain parameters are modeled as fuzzy type-2 variables. Fuzzy type-2 sets have been widely used due to their ability to model higher orders of uncertainties as compared with the fuzzy type-1 approach. They allow for inaccurate knowledge to be included in the membership functions used to describe the uncertain parameters. In the present contribution, the so-called α-level optimization was associated with the fuzzy type-2 technique for uncertainty analysis purposes. A sensitivity analysis was also carried out as an additional assessment of the considered uncertain parameters. The numerical results allowed to understand how the uncertain parameters affect the bearing supporting forces for three shaft speeds, namely, 3000, 9000, and 15,000 rpm. It was demonstrated that the effect of the uncertain parameters on the supporting forces increases according to the shaft speed. Additionally, the load capacity revealed to be more sensitive to variations on the oil viscosity and radial clearance than to the pad radius concerning the adopted uncertain interval. Consequently, the obtained results can provide suitable information for the design, manufacturing, and maintenance of tilting-pad journal bearings.

In this paper, the idea of an axially moving time-dependent beam model is briefly introduced. The nonlinear response of an axially moving beam is investigated. The effects of a time and spatial dependent tension depending on the external forces at the boundary and a tension dependent speed are highlighted, which gives a new model to study the parametric vibration of axially moving structures. This paper focuses on simultaneous resonant cases that are the principal parametric resonance of first mode and internal resonance of the first two modes. In general, the method of multiple scales can study nonlinear vibration of axially moving structures with homogeneous boundary conditions. Taking Kelvin viscoelastic constitutive relation into account, the inhomogeneous boundary conditions make the solvability conditions fail, which is also one of the highlights of this paper. In order to resolve this problem, the technique of the modified solvability conditions is employed. The influence of some parameters, such as material’s viscoelastic coefficients, viscous damping coefficients, and the axial tension fluctuation amplitudes, on the steady-state vibration responses is demonstrated by some numerical examples. Furthermore, the approximate analytical results are verified by using the differential quadrature method (DQM).

The objective of this study is to develop a novel methodology to assess the energy flow between a nonlinear energy sink (NES) and the primary system it is attached to in terms of energy orientation, which is directly related to the sign of the power present on the primary system. To extend the work done in previous studies, which have focused primarily on the analytical treatment, characterization, and performance evaluation of NES as passive nonlinear dampers for structures under different types of excitations, this study incorporates a methodology for determining whether energy is entering or leaving a primary oscillator when interacting with an NES, by means of considering the power flow of the primary oscillator. Several current measures for evaluating the effectiveness of the NES at extracting and dissipating energy irreversibly are considered through numerical simulations of systems with different damping cases of the NES. Each case provides a different dissipation scenario in the combined system, which is subjected to different types of base excitation signals such as impulse and seismic records. The methodology is further validated experimentally using a two degrees-of-freedom system with an NES attached to the second mass. Comparisons of the modeled responses versus the measured responses are provided for several physical damping realization scenarios in the NES.

An operational modal response method for application to the structure health and integrity of pipelines is investigated. The modal response characteristics of externally supported pipe structures are quantified through flow Reynolds number (Re d ) variation. Pipe flow turbulence and the resulting hydrodynamic pressure fluctuations on the interior pipe wall provide the structural forcing mechanism, and signals from wall-mounted accelerometers provide the system response. During experiments, the Reynolds number is varied from 51,000 to 154,000. Over this Reynolds number range, the pipe flow turbulence was found sufficient enough to excite the structure at frequencies up to 400 Hz. Modal response characteristics obtained through Reynolds number variation were found to be in agreement with results from impact hammer modal testing. The in-situ modal response method developed was applied to two different structural health monitoring investigations, one involving loss-of-material and the other involving loss-of-fluid. The loss-of-material scenario simulated the process of external pipe wall corrosion, and the developed method was able to detect material loss as small as 1.4%. The loss-of-fluid scenario simulated a small leak. Despite the low operating pressure of 0.024 MPa, the methodology was able to detect fluid loss as low as 0.1% of the bulk flow rate. The developed method has the potential to offer in-situ continuous pipeline health monitoring that relies on the continuous changes (flow rate, product viscosity, product density) that are inherent to an operational pipeline system.

In this paper, the single-sided vibro-impact track nonlinear energy sink (SSVI track NES) is studied. The SSVI track NES, which is attached to a primary structure, has nonlinear behavior caused by the NES mass moving on a fixed track and impacting on the primary structure at an impact surface. Unlike previous studies of the SSVI track NES, both the horizontal and vertical dynamics of the primary structure are considered. A numerical study is carried out to investigate the way in which energy is dissipated in this system. Assuming a track shape with a quartic polynomial, an optimization procedure that considers the total energy dissipated during a time period is carried out, to determine the optimum NES mass and track parameter. It is found that there is dynamic coupling between the horizontal and vertical directions caused by the SSVI track NES motion. The vibrational energy, originally in the structure in the horizontal direction, is transferred to the vertical motion of the structure where it is dissipated. Considering that many civil and mechanical systems are particularly vulnerable to extreme loads in the horizontal direction, this energy transformation can be beneficial to prevent or limit damage to the structure. The effect on energy dissipation of the position of the impact surface in the SSVI track NES and the ratio of the vertical to horizontal stiffness in the primary structure are discussed. Numerical results demonstrate a robust and stable performance of the SSVI track NES over a wide range of stiffness ratios.

Under excitation due to the environment or traffic load, cable vibration never ceases; thus, fatigue cycles generated by vibration-induced additional cable tension (VACT) owing to the change of the cable configuration from static to dynamic are significantly frequent. Therefore, VACT is a non-negligible cable-fatigue load. To investigate the cable dynamic stability and fatigue, it is necessary to determine VACT in a dynamic environment. Herein, a method for estimating VACT in the frequency-domain by using acceleration data is proposed. In this method, according to the cable vibration control equation, the frequency-domain relationship between the VACT and the vibration response of the measuring point is established based on the dynamic stiffness. Parameter analysis simplifies the proposed model to estimate VACT using only acceleration data. The proposed method is verified with cable acceleration data.

Built-up structures, such as airplanes, ships, and even refrigeration systems, which have many components, can be substructured to speed up and facilitate the process of calculating the vibratory response of the complete system. In many structures, there are rubber isolators that connect component parts, and these connections can each occur over a finite distributed area. It is often convenient and intuitive to substructure the system at the isolators. However, in previous work, it has been shown that the frequency response of the complete system does not always agree with the frequency response of the system calculated from the mobilities of the subsystems. It was thought that this was due to the distributed area connection of the isolators, and this motivated the study reported in this article. An investigation into some issues that occur when substructuring a system that contains soft distributed isolators is described. Using finite element models, it is shown that if a system is substructured, such that the interface between the substructures occurs at a soft rubber isolator, then there is a limited frequency range over which the frequency response function of the assembled system is accurate. It is further shown that it is far better to substructure the system, at stiff, discrete connections, if possible. The frequency range over which the frequency response of the assembled system should then be more accurate over a much wider frequency range.

By monitoring the structural vibration and analyzing the modal parameter, hidden damage can be identified at an early stage, preventing abrupt failures for important structural components. However, the modal parameter has exhibited a low sensitivity to the interfacial damage, such as the delamination in the composite beam. In this paper, a signal processing method is developed to increase the sensitivity of the modal parameter to the delamination. Both the first- and high-order modal parameters are transformed to an approximate waveform capacity dimension (AWCD). Based on the wave peaks of the modal parameters in the AWCD, the start and end of the delamination can be accurately pinpointed. Since the AWCD method can highlight the delamination-related waveform features of the modal parameters, the delamination can be identified without referring to the baselines. Both analytical and experimental investigations demonstrate that the AWCD method can modify the waveforms of the modal parameters and lead to an accurate identification of the delamination in composite cantilever beams.

An enhanced hypoid gear mesh model that incorporates the Hertzian impact damping function is developed in this study to reveal the mechanisms of damping during gear mesh. Two types of impact damping models, namely viscous and non-viscous type based on first principle of mechanics are compared to previous empirical damping models with constant damping coefficient. Parametric studies are performed for both steady-state and transient analyses to investigate the impact damping effect under numerous load conditions or physical parameters of meshing gear pair. Comparative study between viscous and non-viscous damping models are also performed to examine their effects on dynamic response for various load levels. It is shown that impact damping can significantly reduce the amplitude of dynamic mesh force. Non-viscous damping has more significant effect on dynamic response under heavy torque load due to influence of greater elastic deformation. Furthermore, it is observed that impact damping can turn double sided impact into single sided impact and suppress response peaks in certain mesh frequency range during speed ramp up.

Electromagnetic resonant shunt tuned mass damper-inerter (ERS-TMDI) has recently been developed for dual-functional vibration suppression and energy harvesting. However, energy harvesting and vibration mitigation are conflicting objectives, thus rendering the multi-objectives optimization problem a very challenging task. In this paper, we aim at solving the design trade-off between these two objectives by proposing alternative configurations and finding the model with the best performance for both vibration suppression and energy harvesting. Three novel configurations are presented and are compared with the conventional ERS-TMDI. In the first two configurations, the primary structure and the absorber are only coupled through the spring. Both inerter and electromagnetic devices are connected to the ground in the first configuration, whereas only the inerter is connected to the ground in the second configuration. The third configuration is inspired by the recently developed three-element vibration-inerter (TEVAI), but in this case an electromagnetic device is sandwiched in between the primary structure and the absorber. Closed-form expressions are presented for optimum vibration mitigation and energy harvesting performances using H 2 criteria for both ground and force excitations. The obtained explicit expressions are validated using matlab optimization toolbox. Simulation examples reveal that the first configuration performs the best, whereas the second performs the worst in terms of both vibration mitigation and energy harvesting. It is also demonstrated that replacing the series RLC with a parallel circuit can improve or degrade the vibration mitigation performance, but it constantly enhances the energy harvesting performance in all four models.

In this paper, a simple and efficient method to enforce nodes, or points of zero vibration, on an arbitrarily supported rectangular plate subjected to multiple harmonics with distinct excitation frequencies is developed. This vibration suppression is achieved by attaching a chain of properly tuned oscillators, configured in series, to the host plate. The governing equations of the combined system are first obtained using the assumed-modes method. Enforcing the node conditions for the given excitation frequencies, a set of constraint equations are formulated, from which the sprung mass parameters can be determined. Two special cases are considered: when the attachment and node locations coincide (or collocated) and when they do not (or non-collocated). For the former case, determining the required oscillator parameters requires one to solve an inverse eigenvalue problem, and for the latter case, it requires one to use a generic optimization algorithm. Procedures to tune the parameters of the oscillator chains are outlined in detail, and numerical experiments validate the proposed method of enforcing nodes to mitigate excess vibration when the plate is subjected to multiple harmonic excitations.

Lock-in flow tones can occur for many different types of flow instabilities and structural-acoustic resonators at low Mach number. This paper examines the interaction between a shear layer instability generated by flow over a shallow cavity and the modes of an elastic cantilevered beam containing the cavity. A describing function model indicates that a cavity shear layer instability capable of producing lock-in with acoustic pipe resonances cannot achieve lock-in with equivalent structural beam resonances, particularly resonances of submerged structures. Fluid-elastic cavity lock-in is unlikely to occur due to the high level of damping that exists for a submerged structure, the high fluid-loaded modal mass, and the relatively weak source strength a cavity generates. Limited experimentation using pressure, acceleration, and particle image velocimetry (PIV) measurements has been performed which are consistent with the describing function model. A stronger source produced by a larger scale flow instability—separated flow over a bluff body—was able to lock-in with modes of the same submerged structure, further demonstrating that the concern for lock-in from a cavity shear layer instability is isolated to systems capable of stronger coupling or those dominated by fluid-acoustic resonances.

The purpose of this study is to investigate the dynamics of motorized spindle, in which the tilting effect of tandem duplex angular contact ball bearing is considered. First, the quasi-static model of the duplex angular contact ball bearing is developed based on the Jones's bearing model. Then, the model is numerically solved using the Newton–Raphson method to obtain 16 stiffness coefficients (including the tilting ones). Later, a modified transfer matrix method is used to establish the dynamic model of the motorized spindle system with 16 stiffness coefficients. Finally, experiments have been performed to detect the stiffness of the tandem duplex angular contact ball bearing and the unbalance response of the motorized spindle. Results show that the modified transfer matrix method can be used to analyze the dynamic behavior of the motorized spindle supported on tandem duplex angular contact ball bearings, the tilting effect of the tandem duplex angular contact ball bearing affects the dynamic behaviors of the motorized spindle, and the theoretical dynamic characteristics using the proposed model agree with the experimental ones.