In random vibration testing with multiple control channels, existing control laws require specification of a complete spectral density matrix at each control frequency. Spectral density matrices include autospectral densities on the diagonal and cross-spectral densities on the off-diagonal. In practice, the off-diagonal terms are often unknown, and recent vibration testing research has focused on fixing the diagonal and specifying the off-diagonal to minimize the required control energy, subject to a constraint that the target matrix is positive semidefinite. This paper shows that, even with a fixed diagonal, off-diagonal terms strongly affect control residuals. This overlooked effect occurs in both square and rectangular systems. By jointly considering input energy and control residuals, open-loop inputs are derived directly from the diagonal without specifying the off-diagonal terms. Vibration targets that can be used in closed-loop control are then derived using the optimal inputs, with positive semidefinite constraints applied during the derivation. The result is a set of Pareto-optimal control solutions. For each solution in the set, any other possible solution produces greater control error, greater input energy, or both. A balanced solution is selected automatically, though others can be chosen based on test needs. Simulations and experiments show that the proposed method outperforms state-of-the-art energy-minimizing approaches, achieving significant reductions in both control error and input energy.

Synchronized chaos is demonstrated in a system of two classical kicked rotors where one rotor is driven by the momentum of the other. Despite sharing a common momentum, a synchronized response of the rotors is not inevitable. The prevalence of synchronized chaos is studied in changes in initial conditions and kick strength. While both synchronized quasi-periodic and chaotic motions are possible, both types of motion may also be asynchronous. In some rare cases, the driving rotor can exhibit quasi-periodic motion while the driven rotor exhibits chaos. System equations are solved using an iterative map, and chaotic motion is distinguished from quasi-periodic motion using a heuristic interpretation of the frequency response. The relative simplicity of the analysis enables an accessible introduction to the intriguing phenomenon of chaotic synchronization.

This paper studies Tikhonov regularization (ridge regression) parameter selection for problems in vibrations and acoustics. The selection method is based on a popular Bayesian method, but it incorporates measurements of sensor noise. The regularization parameter is closely related to the ratio of system input energy to noise energy, so noise measurements inform the inference procedure and improve parameter identification. In cases where standard Bayesian regularization identifies zero as the optimal regularization parameter, noise measurements guarantee a unique nonzero optimum. Sufficient theoretical criteria are developed for this guarantee. The method is verified in even-determined and under-determined configurations in an acoustic source localization simulation and a vibration load identification experiment. It is shown to yield significant improvements over existing empirical Bayesian regularization. Improvements are larger in the even-determined case and smaller in the under-determined case, wherein the inverse solution is less sensitive to the regularization parameter.

The viscoelastic stiffness of asphalt concrete is commonly represented using relaxation modulus and dynamic modulus, which are functions of loading time and loading frequency, respectively. They are typically measured via experimental testing whereby only one of the moduli is determined, and interconversion techniques can be used to obtain the other modulus if needed. Although exact approaches exist for pavement modulus interconversion, they can be difficult to implement in practice, and approximate conversion techniques have therefore been developed for conventional use. A popular approach is to approximate a direct relationship between the time and frequency domains via an equivalency factor, but there is no apparent consensus on its proper value. In this paper, a new numerical technique is applied to experimental data to ascertain the optimal value of the time-frequency equivalency factor. Approximate conversions from dynamic modulus to relaxation modulus are conducted using the optimal factor, and results are compared to popular alternative approaches. The optimal factor is determined to be $ 0.0673 \pm 0.0009 $ 0.0673 & PLUSMN;0.0009 with 95% confidence. Using the mean value of 0.0673 produced conversion errors of 1.41% on average among 30 samples of hot mix asphalt.

This paper presents a novel Bayesian method for backcalculation of pavement dynamic modulus, stiffness, thickness, and damping using falling weight deflectometer (FWD) data. The backcalculation procedure yields estimates and uncertainties for each pavement property of interest. As a by‐product of the Bayesian procedure, information about measurement error is recovered. The Bayesian method is tested on simulated FWD backcalculations and compared with a state‐of‐the‐art trust‐region optimization algorithm, and it achieves estimation errors that are nearly an order of magnitude lower than the trust‐region solver. Confidence intervals are computed from thousands of simulated backcalculations and are shown to quantify uncertainty in estimated pavement properties. To cope with the computational expense of backcalculation, a fully parallel transitional Markov chain Monte Carlo procedure is developed. The fully parallel algorithm scales well to computation with many processor cores, and it yields up to a 50% reduction in computation time when compared to existing parallel implementations.

During the industrial pecan shelling process, kernels are often damaged. To address this problem, a study is conducted to experimentally determine improved impactor geometries for end-to-end pecan cracking. Four impactors of varying internal angles (from 30° to 52.5°, in increments of 7.5°) are tested. After cracking, the pecans are passed through an image analysis software designed to detect and measure cracks in their shells. These measurements help classify each pecan into one of four categories: under crack, standard crack, ideal crack, or over crack. Cracked and ideally cracked pecans are preferred for their processability, so the impactor geometries are then evaluated based on their ability to maximize these crack types across the widest impact energy range. For the four impactors tested, the 30° impactor is found to more consistently produce preferred cracks in a larger energy range relative to the other impactors.

In many applications it is desirable to inverse-calculate the distributed loading on a structure using a limited number of sensors. Yet, the calculated loads can be extremely sensitive to the placement of these sensors. In the case of predicting point loading applied at a known location, best results are typically achieved when one sensor is collocated with the force. However, the extension of this rule to distributed loading remains uncertain, and even simple sensor system design scenarios often require the designer to directly optimize the sensor placements using a numerical model. In an effort to provide designers with guidance, we identify optimal sensor configurations for predicting static distributed loads on beams with classical boundary conditions. An influence coefficient method, wherein the strain is related linearly to the static load, is used to estimate the applied forces. The loading distribution on the structure is assumed to be either a piece-wise linearly-distributed load or a uniformly-distributed load, allowing for distributed loads to be estimated using the magnitudes of a small number of control points. Given the simplicity of the beam structure, the equations of the influence coefficient method are derived analytically, which allows for the sensor placement to be specified using continuous optimization methods. The condition number of the influence coefficient matrix is used as a surrogate for error during optimization. ‘Rules of thumb’ for sensor placement are presented based on the optimization results. Results show that the optimal and rule-of-thumb sensor configurations are more resistant to input noise than naïve configurations, with the rule-of-thumb configurations yielding similar force predictions relative to the optimal configurations. We expect the rules of thumb to be useful guidelines for engineers designing tests on beam-like structures such as aircraft wings or marine propellers where the inverse calculation of distributed loads is of interest.

Falling weight deflectometer backcalculation is a structural health monitoring approach for estimating the dynamic modulus of flexible pavements. It consists of two key aspects: a computational pavement model and an optimization routine. When using gradient-based methods, the optimization problem is commonly ill-posed, whereby a unique solution does not necessarily exist. In this paper, a new tandem trust-region optimization algorithm is proposed for ill-posed falling weight deflectometer backcalcula-tion. The algorithm's performance is tested against existing optimization methods in the context of dynamic modulus estimation for flexible pavements, and the performance tests are simulated computa-tionally using practical values for material properties and geometry. The tandem trust-region algorithm combines the relative strengths of the subspace trust-region interior reflective method with those of the Levenberg-Marquardt algorithm. The increased computational expense of executing these two methods in parallel is negligible compared to the expense of other essential steps in backcalculation. For ill-posed problems, the performance tests indicate the tandem trust region algorithm has an overall reliability that is 33.9% higher than using only the subspace trust-region interior reflective method, and 56.9% higher than using only the Levenberg-Marquardt algorithm. Further, the new optimizer is 13.5% more reliable than a robust commercial option. (c) 2022 Elsevier Ltd. All rights reserved.

The objective of this study was to collect and quantify three-axis acceleration data from six locations within commercial pig transport trailers during summer. Two trucks with straight-deck trailers transporting two loads per day were observed for 5 consecutive days ( N = 20). Accelerometers were placed under the floor of each trailer’s top and bottom decks (DECs) in the center of three sections (SECs): fore, middle, and aft. Data from each trailer section were processed to calculate z- and x,y-axis root mean square (RMS) values and vibration dose values (VDVs) during loading, transport, and unloading. There were no DEC × SEC interactions or SEC main effects for z-axis RMS or VDV during any transportation stage ( P > 0.06). The bottom deck had a greater x,y-axis RMS than the top deck during all transportation stages ( P < 0.01). The bottom deck had a greater x,y-axis VDV than the top deck during loading and transport ( P < 0.03), but there was no difference ( P = 0.52) during unloading. The bottom deck had a greater z-axis RMS and VDV than the top deck during loading and transport ( P < 0.01), but there were no differences during unloading ( P > 0.07). There were no SEC effects for x,y- and z-axis RMSs and VDVs during all transportation stages ( P > 0.06). Acceleration values were compared with exposure action values (EAV; injury possible) and exposure limit values (ELV; injury likely) vibrations thresholds. Over the 5 observation days during all transport stages, a greater percentage of compartments violated both RMS and VDV thresholds in the x,y orientation (average 90%) than in the z orientation (average 76%). Overall, these data indicate that bottom decks experience greater three-axis vibrations than top decks in straight-deck trailers and that pigs on bottom decks may experience greater discomfort during transportation that could contribute to fatigue or the non-ambulatory condition.

Flexible structures adjacent to acoustic cavities are commonly encountered. In some instances, coupling between the structure and cavity causes non-negligible changes to the system frequency response. Here, we describe the use of modern dynamic substructuring techniques in coupling and decoupling structure-cavity systems. As input, free-interface in vacuo natural frequencies and modes of the structure are used along with an uncoupled modal representation of the cavity. In the acoustic model, the fluid-structure interface is typically modeled as pressure release, though faster frequency convergence is possible by enriching the representation with rigid-wall modes. The subsystems are assembled in modal coordinates with continuity at the interface enforced via Lagrange multipliers. This approach circumvents the calculation of coupling coefficients, and results in real-valued system natural frequencies and modes; however, the approach presents challenges when large numbers of interface degrees of freedom are present. Attempts to overcome these challenges with interface reduction techniques are described. Finally, this research led to the derivation of a formula approximating the in vacuo natural frequencies of test structures that are well coupled to adjacent acoustic cavities. The formula was successfully applied to an air-filled cylindrical test structure for which the frequency response was confounded by structure-cavity coupling.

Post-buckled structures are prone to snap-through instabilities when external loading causes the structure to lose local stability and jump to a remote equilibrium. However, using piezoelectric actuation, structures can undergo entirely stable transitions between remote equilibria, thereby avoiding snap-through. This paper investigates the linearized vibrational properties of post-buckled beams along these stable transition paths. Numerical results are calculated using an elastica model with allowances for piezoelectric actuation. The model is non-dimensionalized to provide a general view of how the natural frequencies and corresponding mode shapes evolve during stable transitions. Results are presented for two types of stable transitions—one in which the transition is accomplished by changing the external load under a constant actuation level, and one in which the actuation levels are changed without external loading. Results show that the first four natural frequencies of the beam undergo complicated changes during a stable transition. Results also indicate that the first two mode shapes tend to be asymmetric and localized during the early and later stages of the transition. Yet, during the middle of the transition, when the static configuration of the beam is an anti-symmetric “S” shape, the first two mode shapes are symmetric and global. The natural frequencies and modes predicted by the numerical model are validated with a series of experiments.

The higher-order static equilibria of post-buckled structures are nominally unstable. Recently it has been shown that by actuating two piezoelectric patches bonded to a post-buckled beam, the second-order equilibria can be stabilized and the beam can stably transition from one first-order post-buckled shape to the other, thereby avoiding snap-through. This paper considers the extent to which third- or fourth-order equilibria of clamped–clamped post-buckled beams can be stabilized using actuation of three or four patches of piezoelectric actuators. Using a numerical modeling approach that is validated with experiments, it is shown that stabilization of third- and fourth-order equilibria is physically realizable. Two actuation strategies are considered: a symmetric one in which voltages of equal magnitude are applied to all patches, and an asymmetric strategy in which two different voltage magnitudes are used. Various actuator lengths are also considered. Using either actuation strategy, it is shown that both the third- and fourth-order equilibria can stabilize over certain regions of parameter space. Stabilized third- and fourth-order equilibria are demonstrated experimentally and correlate well with numerical predictions.

The objective of this study was to collect and interpret three-axis acceleration, temperature, and relative humidity data from six locations within commercial transport trailers shipping market-weight pigs. Transport was observed in Kansas (n = 15) and North Carolina (n = 20). Prior to loading, three-axis accelerometers were affixed to six locations on the trailers: top fore (TF), top center (TC), top aft (TA), bottom fore (BF), bottom center (BC), and bottom aft (BA) compartments. Data were post-processed to calculate root-mean-square (RMS) accelerations and vibration dose values (VDV) in the vertical direction and the horizontal plane. These values were compared with exposure action values (EAV) and exposure limit values (ELV), vibration levels deemed uncomfortable and potentially dangerous to humans. Additionally, RMS and VDV were compared among the trailer compartments. The vertical RMS accelerations for all compartments exceeded the EAV for loads measured in Kansas, and for the majority of the compartments measured in North Carolina. Many compartments, specifically the BA compartment from all trips, exceeded the vertical ELV. Regardless of where the data were collected, fewer compartments exceeded the EAV in the horizontal orientation. Only BA compartments exceeded the ELV in the horizontal orientation. There were Area × Level interactions for vertical and horizontal RMS and VDV (P < 0.01). The BF compartment had a greater vertical RMS value than the TF, TC, and BC (P < 0.02) compartments, but did not differ (P = 0.06) from the TA compartment. The vertical RMS of the TA compartment did not differ from the TF, TC, and BC compartments (P > 0.13). The BF compartment had a greater (P = 0.02) vertical VDV value than the TC location, but did not differ from the other locations (P > 0.16). All other locations did not differ in vertical VDV (P > 0.12). The BF compartment had greater horizontal RMS than the TC and TA compartments (P < 0.01), but did not differ from TF and BC compartments (P > 0.12). All other compartments did not differ in horizontal RMS (P > 0.34). All compartments, aside from the BA compartment, did not differ in horizontal VDV (P > 0.19). Vibration analyses indicated the BA compartment had the greatest vertical and horizontal vibrations and a large percentage of the compartments exceed the EAV and ELV, which indicated pigs may have experienced uncomfortable trips that could cause discomfort or fatigue.

Landing gear doors on aircraft have experienced flutter during preliminary flight testing. While designs vary widely, landing gear doors are typically plate-like structures with a relatively rigid actuator attached to their inside surface. To better understand the aeroelasticity of landing gear doors, this study investigates the aeroelastic stability of an idealized model. The model consists of a hinged plate with an interior constraint approximating the actuator attachment. The plate is subject to uniform flow, and an unsteady vortex lattice model is coupled to the structural model to predict critical flow velocities. The location and footprint area of the internal constraint, along with plate aspect and mass ratios, are varied to investigate a large parameter space. Results reveal that the critical flow speed and instability mechanism are sensitive to the postulated actuator placement. In general, flutter is the dominant mode of instability when the actuator is postulated in the leading quarter of the plate. In other postulated locations, divergence dominates. However, the exact shape and location of the boundary between flutter and divergence is configuration dependent and found to be especially sensitive to changes in aspect ratio.

A new sliding-mode triboelectric energy harvester in the form of a cantilever beam with a tip mass that is acted upon by both magnetic and friction forces is modelled and simulated. A numerical scheme based on the trapezoidal rule with the second-order backward difference formula (TR-BDF2) method is introduced to solve the combined non-smooth mechanical and stiff electrical system. This is the first study of the structural dynamics of the sliding-mode triboelectric energy harvesting; additionally, a magnetic field that induces multistability is present. A comparison between the coupled and uncoupled electromechanical models suggests that the electrostatic force between the electrodes can be ignored, which makes the uncoupled model preferable in the dynamical analysis. The influence of the non-conservative force (the friction force) on the multistability of the system is investigated. It is found that the distribution of the multistability on the parametric plane changes even when a small amount of friction is involved, and the areas of bistability and tristability shrink while that of the monostability expands. A comparison among these three types of stability reveals the superiority of invoking bistability as it facilitates broadband energy harvesting. The excitation level plays an important role in inducing the snap-through motion (the interwell oscillation) by enabling the crossing of the energy barriers between wells. The increase in the friction shrinks the frequency band of interwell oscillations from high frequencies down to low frequencies on the discrete frequency sweep. An analysis of the basins of attraction finds that at low frequencies the bistable system can undergo only interwell oscillations, while the tristable system can merely experience intrawell oscillations. The basins can intermingle with each other in both bistable and tristable systems. Finally, an increase in the excitation level can break the basins into discrete pieces and/or points.

Post-buckled and curved structures experience snap-through instabilities when external loads from mechanical, fluid, or thermal environments result in a loss of local stability and a dramatic jump to a remote stable equilibrium. Fatigue caused by snap-through is a concern in many engineered systems because of the large stress reversals involved. This paper studies the extent to which the strategic placement and actuation of piezoelectric materials bonded to clamped-clamped post-buckled beams can influence the loads at which snap-through occurs. The electromechanical system is modeled using elastica theory with extensions to account for the influence of piezoelectric actuation on the structure. Static equilibrium positions and their stability are computed across a large configuration space using numerical integration and a shooting method. The results indicate that the effect of piezoelectric actuation on critical snap-through load depends on the degree to which the beam is buckled, the location of the external load, the placement of the piezoelectric material, and the applied actuation voltage. Experiments are performed to validate the numerical results and provide a physical demonstration of changing snap-through loads with piezoelectric actuation. Experimental results demonstrate that critical snap-through loads can be altered by factors ranging from 0.4 to 2.0, and numerical results indicate that even larger changes to snap-through loads are physically realizable.

Vibration energy harvesting has been a popular research topic in recent years and is a promising technology in the development of the Internet of Things. Triboelectric energy harvesting, as a relatively new energy harvesting technique, is drawing attention. However, relevant studies from the perspective of structural dynamics are rare, and a study on how the electrical properties of triboelectric energy harvesters (TEHs) affect their vibration is still missing. In this paper, we perform such a study for TEHs that use the two most common working modes—namely the lateral sliding mode and the vertical contact-separation mode. In the first part of the paper, the coupled electromechanical model of a sliding mode TEH—based on a cantilever beam system involving friction—is established. The effects of the tribo-charge surface density and the load resistance on the vibration of the harvester are investigated. It is found that the effects of the tribo-charge surface density on vibrations are similar to those of mechanical damping, while the load resistance can result in an interesting resistive shunt damping phenomenon which is distinct from the one found in piezoelectric energy harvesters. In the second part, the modelling of a vertical contact-separation mode TEH is established based on a single-degree-of-freedom vibro-impact oscillator, and the effects of the same electrical properties on vibrations are studied. The variation of the tribo-charge surface density can result in both vibration amplitude attenuation and resonance frequency shifting, while the change of the load resistance can influence vibrations only in the case of large tribo-charge surface densities. This study further unveils the electromechanical coupling mechanisms in TEHs and sheds some light on achieving desirable dynamic responses of TEHs via tuning their electrical properties.

This paper considers the extent to which a clamped-clamped post-buckled beam bonded to two elongating piezoelectric actuators can be made to stably transition between remote equilibria. The electromechanical system is modeled using elastica theory with extensions to account for the influence of the actuators on the structure. It expresses this piezoelectric coupling effect in terms of a non-dimensional parameter, σ, that can be easily calculated for candidate substrate/actuator configurations. Parameter studies determining the threshold values of σ required to execute stable transitions under different actuation and loading situations are presented. The results indicate that the lowest threshold values of σ occur when the beam is actuated from approximately 15%–85% of its span. Experiments validate the numerical results and offer the first physical demonstrations of the use of piezoelectric actuators to achieve stable transitions between remote equilibria.

This study considers the hydroelastic damping of cantilevered flat plates undergoing free vibration in flowing water. Of particular interest are plates with aspect ratios (defined as span length divided by chord length) less than one. Experimental trials involving plates of aspect ratios from 0.3 to 0.7 are conducted in a high-speed water tunnel. The tests involve flow velocities well below those corresponding to hydroelastic instability. Additionally, an unsteady, linear vortex lattice model is coupled to a structural dynamic plate model to predict flow-induced damping as a function of flow speed. The numerical model has been previously used with air, but never with water as the fluid medium. The model is able to predict the hydroelastic damping associated with the first several plate modes with less than 30% error in most cases. While the hydroelastic damping remains linear in the experimental flow regime, at higher flow speeds more complicated hydroelastic damping behavior is predicted. Numerical studies involving mass ratio, aspect ratio, and reduced velocity are conducted to predict hydroelastic damping across a wide parameter space. All else being equal, chordwise bending modes are found to exhibit two to three times greater hydroelastic damping than spanwise bending modes. There is also an inverse relationship between mass ratio and hydroelastic damping. Further, for plates with low aspect ratios and at fixed reduced velocities, hydroelastic damping increases with increasing aspect ratio.

Acoustic–structure coupling can substantially alter the frequency response of air-filled structures. Coupling effects typically manifest as two resonance peaks at frequencies above and below the resonant frequency of the uncoupled structural system. Here, a dynamic substructuring approach is applied to a simple acoustic–structure system to expose how the system response depends on the damping in the acoustic subsystem. Parametric studies show that as acoustic damping is increased, the frequencies and amplitudes of the coupled resonances in the structural response undergo a sequence of changes. For low levels of acoustic damping, the two coupled resonances have amplitudes approximating the corresponding in vacuo resonance. As acoustic damping is increased, resonant amplitudes decrease dramatically while the frequency separation between the resonances tends to increase slightly. When acoustic damping is increased even further, the separation of the resonant frequencies decreases below their initial separation. Finally, at some critical value of acoustic damping, one of the resonances abruptly disappears, leaving just a single resonance. Counterintuitively, increasing acoustic damping beyond this point tends to increase the amplitude of the remaining resonance peak. These results have implications for analysts and experimentalists attempting to understand, mitigate, or otherwise compensate for the confounding effects of acoustic–structure coupling in fluid-filled test structures.