Structural Damping Research Articles

A fins-shaped bidirectional linear ultrasonic motor driven by a single-phase signal

Abstract Inspired by the propulsion mechanism of fish swimming through tail-fin oscillations, we have developed and experimentally studied a high-performance miniature bending vibration linear ultrasonic motor driven by a single-phase standing wave. A symmetrical structural design achieves bidirectional motion with consistent output characteristics. Two lead zirconate titanate (PZT) piezoelectric patches are symmetrically distributed on a metal elastic body’s upper and lower sides. In the stator, a sinusoidal signal is applied only to the piezoelectric patch on one side, while the patch on the opposite side is either left open or short-circuited to the ground. This results in an asymmetry in the structural damping between the upper and lower sides of the stator. The first-order bending vibration of the stator generates displacement in an inclined direction at the end of the driving foot. The motor achieves forward and backward motion by applying the same voltage to the piezoelectric patches on different sides. The dimensions of the stator have been finalized, and a prototype of the designed motor has been fabricated. Subsequent experimental tests were conducted to evaluate the prototype’s performance, including its mechanical output characteristics. At a frequency of 138.3 kHz, the maximum speed of the motor without load is 134.58 mm s−1. Under a voltage of 200 Vp-p and a preload of 3 N, the motor’s maximum output thrust is approximately 0.3 N. The actual mass of the motor is approximately 1.2 g, resulting in a thrust-to-weight ratio of 25.

A novel strategy for mitigating the vortex-induced vibration of long-span bridges by using flexible membranes

The structural damping of a long-span bridge girder after completion is difficult to predict accurately in the design stage, and could be obviously lower than the value suggested by the code of wind-resistance design, which could lead to large-amplitude vortex-induced vibration (VIV) of the girder after completion. To address this problem, proposed here is a novel VIV mitigation strategy for a long-span bridge: in the design stage, aerodynamic design involving VIV of the girder is conducted based on the normal structural damping suggested by the design code, and flexible membranes (FMs) are designed for emergency VIV mitigation of the girder in case of very low structural damping after completion; if the girder experience large-amplitude VIV after completion because of very low structural damping, then the pre-designed FMs are used as a temporary emergency aerodynamic measure for fast VIV mitigation, providing a transition period until permanent measures (such as mechanical dampers, or aerodynamic measures) are implemented. To investigate the feasibility of this strategy, a case study was conducted involving a series of wind tunnel tests on a cable-stayed bridge with a Π-shaped girder, and the results indicate that appropriate FMs are effective for suppressing the VIV of the girder under very low structural damping. The FMs have great potential for emergency VIV mitigation because of the low cost, convenience, and rapidity.

Research of tangential cyclic loading on mechanical properties between cosine contact surfaces

Abstract The investigation of the mechanical properties of contact surfaces under tangential cyclic loading is very important for understanding the stiffness and damping of combined structures. In this paper, using Hertzian contact theory and Coulomb's friction law, the contact mechanical mechanism of a common cosine cylindrical contact model subjected to tangential loading, unloading, and reloading is investigated, and the load-displacement curves (hysteresis curves) and the energy equations of a complete displacement cycle are deduced. The results show that under the action of tangential cyclic load, the shear stress increases immediately, and the micro slip zone outside the contact area gradually expands inward until it becomes a slip zone. At this point, the hysteresis curve changes from a "shuttle shaped" to a "quadrilateral" shape. In addition, nonlinear finite elements are used for static simulation to verify the accuracy of the hysteresis curve, tangential stiffness, and energy dissipation analysis of the cosine contact model under different axial crossing angles. The energy equation's fluctuation with tangential displacement under different conditions, as well as the impact of friction coefficient, axial intersection angle of the contact surface, external load, and cosine surface characteristics on the mechanical properties of the contact surface. With the increase of surface roughness or normal load, energy increases nonlinearly with the increase of displacement. Finally, when the Von Mises stress reaches the yield limit, reciprocating displacement loading will lead to plastic accumulation, resulting in wear and tear.

Vibration Behavior of 3D-Printed Graded Composites: Fabrication and Testing.

Multi-head 3D printers afford the ability to create composite structures with significant differences in properties compared to those created through traditional molding techniques. In addition to the usage of different viscoelastic polymeric materials, the selective spatial placement of the build materials enables the creation of layered and graded geometries to achieve specific mechanical and/or vibrational characteristics. This paper describes how the mechanical properties of the individual materials can be used to predict the damping and natural frequencies of a 3D-printed graded structure. Such structures can find usage in rotating machinery, beams, etc., where vibrational characteristics must be controlled. The simulation and experimental results are presented and two forms of the storage and loss modulus are considered: fixed and variable. For the latter condition, E' and E″ are established as functions of temperature and frequency. Modal vibration testing of the graded samples shows a good match between the simulation and experimental trials, thereby supporting the proposed model as a useful tool for prescribing the structure of a printed part with tailored dynamic properties.

Study of vibration transmission and energy distribution in spiderweb damping structures

Study of vibration transmission and energy distribution in spiderweb damping structures

Damage identification using Bayesian derivative method

Structural Health Monitoring (SHM) is one of the most challenging topics in structural dynamic analyses. This challenging characteristic comes from several uncertainties related to boundary conditions, damping description, material properties, and unknown excitation inputs. In this regard, formulating damage identification strategies based on the Bayesian framework is a feasible alternative to conjugating prior information, computational models, and measured data. Nevertheless, building metrics based on comparisons between experimental and computational dynamic features of structure leads to difficulties in determining the likelihood model. In this context, the present work brings an approach for damage identification that considers a metric for the inverse problem, which contains information about the relative difference of natural frequencies. The lack of knowledge about the likelihood structure is tackled using the Approximate Bayesian Computation (ABC), where draws from the approximate posterior are obtained using the Sequential Monte Carlo Approximate Bayesian Computation (SMC-ABC). The feasibility of this approach is assessed considering data from an experimental set-up composed of an aluminium beam containing lumped masses at some positions. The present strategy estimates the position and magnitude of the lumped masses attached to the supported beam. The central role of these lumped masses is to simulate structural anomalies. The inference process considers uncertainties related to structural damping by calibrating several concurrent structural models whose differences reside in the model damping. Finally, the strategy provides the probability of each concurrent model at the end of the process.

Assessment of the Human Comfort of Pedestrian Footbridges Utilising Probabilistic Response Spectra

Nowadays, the design of pedestrian footbridges is associated to light weight structures with low natural frequencies and low structural damping rates. These facts have generated slender footbridges, sensitive to human dynamic excitations, and consequently changed the serviceability limit states associated to the design. Thus, the current design codes and technical guides recommend the use of deterministic models to assess the dynamic structural behaviour of footbridges. On the other hand, the pedestrian walking is related to a stochastic phenomenon and the dynamic force generated at each step depends of the weight, the step frequency and the step length of each pedestrian. This way, this investigation aims to develop a probabilistic approach to assess the steel and steel-concrete composite footbridges dynamic behaviour, based on the use of design response spectra. To do this, the developed analysis methodology has considered the stochastic nature of the pedestrian’s walking, in order to evaluating the structural response having in mind excessive vibrations that may cause human discomfort. Based on the use of probabilistic methods, it becomes possible to determine the probability of the footbridge’s peak acceleration values exceeding or not the human comfort criteria. The results obtained in this research work reveal that the peak acceleration values calculated through the deterministic methods can be overestimated in project situations.

Exact H∞ optimization of dynamic vibration absorbers: Univariate-polynomial-based algorithm and operability analysis

H∞ optimization of dynamic vibration absorbers (DVAs) to minimize the maximum response amplitude of primary structures is a classic topic. The commonly used fixed-point method only provides approximate solutions requiring the primary structure is undamped. Instead, we perform exact optimization and investigate the less-reported parametric effects on optimization operability. To handle the known restrictions posed by grounded dampers, a typical DVA model mounted on a damped primary structure, with components connected to both the primary and the base, is considered. We explore three elaborated cases depending on the grounded dampers distributing in the primary structure and the DVA. Our findings reveal that the frequency responses of the primary structure with dual resonant peaks of equal height may not be the global optimum, and we establish a nontrivial necessary condition for operable exact optimization. Furthermore, we elucidate the effects of structural arrangements on the optimized results and provide design rules to maximize vibration suppression performance. The optimization follows the proposal of a so-called resultant-based algorithm that guarantees global optimum with high efficiency and a generalizable core by exclusively constructing univariate polynomial equations. This study contributes a systematic analysis framework alongside efficient calculation tools for exact optimization and DVA performance evaluation.

Turbulence and flapping pivot axis effects on torsional flutter harvester efficiency by closed-form formula

This “Short Communication” investigates the dynamics of a torsional-flutter energy harvester in atmospheric winds with stationary turbulence. This apparatus is an example of a flutter mill, which operates by exploiting aeroelastic instability as a competitive alternative and as a renewable energy supply for one or few housing units. The apparatus has a rigid blade-airfoil that rotates about a pivot to generate flapping motion. Contrary to recent studies by the second author, the effect of random stationary turbulence on flutter onset is examined by an analytical approach, employed by Scanlan (1997) for bridge flutter analysis. Turbulence effect is simulated by suitably modifying the span-wise coherence equation of the aeroelastic load. The incipient flutter threshold is found as a function of turbulence properties. Various configurations are studied, i.e., pivot position, aspect ratio, turbulence coherence decay parameter and structural damping. The objective is to perform a thorough sensitivity analysis as the necessary premise for the planned, future examination of post-critical instability and operational efficiency of the harvester by suitable modeling and wind tunnel tests.

Non-Linear Dynamic Analysis of Timber Frame Structure with Bolted-Fastener Connections

Understanding the dynamics of timber structures is essential for the timber structural engineering field, where it is necessary to build predictive numerical models and digital twins. Three similar-sized representative post-beam bracing frames with wood–metal assemblies were tested. Experimental modal analysis gave some indication of the non-linear behaviour of the structure. Then, the frame was submitted to a logarithmic sine sweep, which highlighted some specificities of the non-linear modes: dependence on the sweep direction and amplitude, jump, etc. These phenomena can be explained by friction and shocks in the assemblies. An accurate model of these non-linearities could lead to resilient and more earthquake-resistant timber structures, as the equivalent damping of a non-linear structure is way lower than for a linear one.

Electromechanical characteristics analysis of L-shaped pipelines with enhanced active constrained damping treatment

Abstract Fluid-conveying pipelines are widely employed in various engineering fields, such as aerospace, nuclear, and marine fields. These pipelines work in serious vibration environments, which can quickly damage the pipeline system. The vibration control of pipelines is a prominent challenge in the engineering field. This paper is aimed to investigate the electromechanical analysis characteristics of L-shaped pipelines with the enhanced active constrained layer damping (EACLD) structure. A finite element model of the L-shaped pipeline with EACLD is established. The dynamic behavior of an L-shaped pipeline with an EACLD structure was analyzed in both the time and frequency domains. The influence of the voltage and the position, the length and the elastic modulus, the thickness and the edge element parameters are all considered. Additionally, the influence of the EACLD patch orientation on static displacement and stress are considered. Simulation results indicate that reasonable selection of the parameters for the EACLD patch and edge element can enhance vibration damping effectiveness, which can provide effective design guidance for active vibration control of the pipeline system.

Dynamic Analysis of Soil-Structure Interaction in Earthquake-Prone Areas

This study used a thorough experimental method to examine the dynamic interaction between soil and structures in earthquake-prone locations. The study challenge concentrated on how different soil types and configurations influence the diversity of structural reactions under seismic loading conditions. The research utilized a mixed methods approach, which involved quantitatively analyzing soil parameters and assessing structure dynamics. The methods employed included the creation of scaled replicas depicting common architectural structures situated on various soil types, including sandy, clayey, and mixed compositions. We used high-precision sensors to record ground motion characteristics such as Acceleration, velocity, and Displacement. The data was then evaluated using statistical methods such as ANOVA and regression analysis. The results revealed substantial differences in the structural reaction based on the type of soil and the parameters of the structure. Structures built on sandy soils saw greater peak accelerations (up to 0.170 g) but smaller displacements. On the other hand, structures on clayey soils had moderate accelerations (up to 0.140 g) but had bigger inter-story drifts. The varied soil layers, ranging from 1.500 Hz to 1.780 Hz, influenced the natural frequencies of the buildings. The damping ratios ranged from 5.000% to 7.800%, indicating that structural damping effectively reduces seismic forces. The results emphasized the critical importance of the interaction between soil and structures in seismic design and the necessity for customized engineering solutions based on the individual soil conditions at the site. Suggested measures include improving methods for soil characterization, optimizing structural dynamics using cutting-edge dampening technologies, and upgrading seismic design codes to enhance the ability of structures to withstand earthquakes in places prone to seismic activity.

Parameter optimization of tuned inerter damper for vibration suppression in structures with damping

This study investigates the parameter optimization of tuned inerter damper (TID) in a single degree of freedom (SDOF) system, with a focus on vibration mitigation. As a type of inerter based dynamic vibration absorber (IDVA), TID achieves vibration suppression of the primary structure by replacing the mass block in traditional dynamic vibration absorber (DVA) with an inerter, thereby minimizing the increase in physical mass. With the displacement response of the primary structure as the objective function, this study first employs the classical fixed point theory (FPT) to derive the analytical formulations for the optimal parameters of TID following the H∞ optimization approach and neglecting the inherent damping of primary structure. The influence of optimal parameter deviations on the vibration mitigation effect of TID is also analyzed, revealing that the deviation of the optimal natural frequency ratio has a significant impact on the vibration mitigation performance. By flattening the amplitude curve of the displacement transfer function of primary structure between the fixed points, this study derives the analytical solution for the optimal damping ratio of TID using the extended fixed point theory (EFPT). When the inherent damping of primary structure is considered, this study employs the approximate extended fixed point theory (AEFPT) to derive the approximate optimal parameters of TID. A comparative study of the optimal natural frequency ratios obtained using FPT, AEFPT and numerical searches reveals that the discrepancies among the three methods are minimal for structures with low inherent damping. However, as the inherent damping ratio of the primary structure increases, the optimal natural frequency ratio obtained using FPT deviates significantly from the exact value, whereas the approximate optimal natural frequency ratio derived using AEFPT can significantly reduce this deviation. Combining the conclusion that the vibration mitigation effect of TID is significantly influenced by the natural frequency ratio, this study suggests that for highly damped primary structures, the use of AEFPT can yield more optimal TID parameters, thereby enhancing the robustness of vibration mitigation performance.

Experimental Investigation of Tensile, Shear, and Compression Behavior of Additional Plate Damping Structures with Entangled Metallic Wire Material

To fulfill the vibration damping requirements of plate structures under complex conditions, additional damping structures with entangled metallic wire material (EMWM) are proposed based on the excellent physical properties of EMWM. A batch of specimens with different filament diameters, densities, and thicknesses are prepared. The stiffness and loss factors are taken as the evaluation indexes, and orthogonal tests are conducted to obtain the tensile, shear, and compression properties. The results show that the optimal parameter combinations can be obtained through orthogonal tests. For the specimens with optimal parameter combinations, the mechanical tests under different loading rates and loading displacements are carried out. With the increase in loading rate, the tensile and shear forces appear to display fracture failure in advance, and the compression performance is stable without significant changes. The change rule under each mechanical test is explored using the stiffness and loss factor evaluation index. It provides a reference for the analysis of the preparation parameters of subsequent additional damping structures with EMWM.

H2 Optimization of a New Type of Tuned Lever Inerter-like Mass Damper (TLIMD) for Attenuating Structure Vibrations

The lever or the lever-type mechanism can achieve an inertia amplification effect by appropriately calibrating its structural configuration, and it is also proven to be one of the most cost-effective solution for the inerter realization compared with other mechanical devices. Benefitting from this property, the present paper adopted a new type of tuned lever inerter-like mass damper (TLIMD) for attenuating stochastic load-induced structure dynamic responses. A set of closed-form formulae for the TLIMD optimal parameters are developed by the use of H2 norm optimization criterion, wherein the structure’s inherent damping is explicitly accounted for. It is theoretically demonstrated that the TLIMD optimal parameters are mainly dominated by three critical parameters, i.e., the damper mass ratio, the lever length ratio (known as the inertia amplification ratio) and also the host structural damping. The proposed formulae for the TLIMD optimization are validated through the seismic analysis, where two classic inerter-based dampers (i.e., the tuned mass damper inerter (TMDI) and the tuned inerter damper (TID)) optimized by the numerical technique are included in the discussion. It is found that the TLIMD has a superior advantage in reducing the structure responses and also exhibits stronger robustness for the detuning condition than the classic inerter-based dampers. Furthermore, the increase in the damper mass ratio and the lever length ratio can be beneficial for enhancing its performance.

Review of Bridge Structure Damping Model and Identification Method

Damping is a fundamental characteristic of bridge structures, reflecting their ability to dissipate energy during vibration. In the design and maintenance of bridges, the damping ratio has a direct impact on the safety and service life of the structure, thus affecting its sustainability. Currently, there is no suitable theoretical method for estimating structural damping at the design stage. Therefore, the modal damping ratio of a completed or under-construction bridge can only be obtained through field dynamic tests to ensure compliance with design specifications. To summarize the latest research findings on bridge structure damping models and identification methods, and to advance the development of damping identification techniques, this paper provides an in-depth review from several perspectives: Firstly, it offers a comprehensive analysis of the theoretical framework for structural damping. Secondly, it summarizes the damping models proposed by researchers from various countries. Thirdly, it reviews the research progress on identifying the modal damping ratio of bridge structures using time domain, frequency domain, and time-frequency domain methods based on environmental excitation. It also summarizes the methods and current status of identifying the modal damping ratio using artificial excitation. Finally, the future prospects and conclusions are discussed from three aspects: damping theory, test and identification method and data processing. This research and summary provide a solid theoretical foundation for advancing bridge structural damping theory and identification methods and offer valuable references for bridge operation and maintenance, as well as damage identification. From the perspective of modal parameter identification, it provides a theoretical basis for the sustainable development of bridges.

Comprehensive Insight into Regular Damped Oscillatory Structures from Effective Electromagnetic Form Factor Data of Some Mesons and Nucleons

Regular damped oscillatory structures from the “effective” electromagnetic form factors of the hadrons h=π±,K±,K0,p,n were investigated. The “effective” electromagnetic form factor behaviors were calculated from the experimental data on the total cross-sections σtot(e+e−→hh¯) with errors. The apparent oscillations were observed for the first time for the proton, and we show, also taking other hadrons into consideration, that they are an arbitrary artifact resulting from a very simplistic theoretical description based on an elementary three-parameter model. If the data are described by a more appropriate and physically well-founded Unitary and Analytic model, then the oscillations disappear. In spite of this, if the three-parameter model is used to describe the “effective” electromagnetic form factor data, an interesting phenomenon is observed. The oscillations are opposite for particles which form an isospin doublet. By using the physically well-founded Unitary and Analytic model, it is demonstrated that this feature originates from the special transformation properties of the electromagnetic current of the corresponding particles in the isotopic space.

Standing Solitons Tuned by Impurities in Damped Nonlinear Lattices under External Excitation.

Periodic chains of nonlinear oscillators are known to support solitonic solutions within a specific range of physical parameters when damping effect is considered. This Letter investigates the dynamics of stationary solitons in damped nonlinear lattices under external excitation, focusing on the influence of impurities related to the natural frequency of the oscillators. We demonstrate experimentally and numerically that incorporating impurities into externally driven periodic lattices can expand the solitonic stability diagram under high-damping areas and near the Hopf bifurcation of periodic structures. A mathematical description that closely aligns with experimental realities is presented through the disordered damped nonlinear Schrödinger equation. Specifically, we prove how impurities along the chain can spontaneously nucleate the lattice solitons. The obtained results open the way toward the functionalization of disorder to control nonlinear energy localization in damped nonperiodic structures.

Evaluation of Inherent Damping Feature of Beam Structure Based on Complex Modulus

Structural damping, which has been widely used to quantify the energy dissipation of engineering structures, plays an important role in dynamic analysis during the design phase and the assessment of existing structures. However, the development of an accurate damping model remains an open question due to the unclear mechanism. In this study, structural damping was identified based on loss factors for beam structures, which were used for presenting the damping behavior during vibrations. The equation of motion for the bending deformation of a Timoshenko beam was derived, accounting for the material damping. To identify the loss factor of the beam from the response signals at a limited number of measurement points, an inverse algorithm based on wave coefficient estimation was developed, considering the numerical stability for data interpretation. Based on the proposed loss factor identification method, several beam models with different shapes of cross-sections were investigated, focusing on the feasibility of the method of varying cross-section cases. Comparing the spectral element model with the loss factor and the finite element model with Rayleigh damping, it was confirmed that the loss factor can better describe the actual energy dissipation behavior of the structure. It provides a more accurate theoretical model for estimating structural damping in practical engineering.

Exponential Stability of a Kirchhoff Plate Equation with Structural Damping and Internal Time Delay

In this manuscript, we investigate the exponential stability of a Kirchhoff plate equation with free boundary conditions in a bounded domain of R2. First, we consider the case where the model is subjected only to structural damping and, using the energy method, we prove the exponential decay of the energy associated with this model. Second, we consider the case where structural damping with a linear internal time delay term is applied, and we use the same technique to derive the exponential stability of the new model. Finally, we examine the scenario where the model is governed by structural damping with an added fractional time delay term and, by constructing an appropriate Lyapunov function, we show that the energy associated with the system is exponentially stable. This work improves upon prior results concerning the Kirchhoff plate equation with frictional damping, where exponential stability could not be achieved.