Single Degree Of Freedom Research Articles

Passive Control in a Continuous Beam under a Traveling Heavy Mass: Dynamic Response and Experimental Verification.

The motion of a heavy mass on a bridge span causes vibrations whose magnitude and frequency content depend on the mechanical properties of the structural system, including the magnitude of that mass and its speed of traverse. In order to limit vibrations that could potentially cause damage, a simple passive device configuration, namely the tuned mass damper (TMD), is introduced and its effect on the beam vibrations analyzed. Specifically, a TMD in the form of a single-degree-of-freedom (SDOF) unit comprising a mass and a spring is placed on the span to act as a secondary system for absorbing vibrations from the primary system, i.e., the bridge itself. A Lagrangian energy balance formulation is used to derive the governing equations of motion, followed by an analytical solution using the Laplace transform to investigate the transmission of vibratory energy between primary and secondary systems. Results are given in terms of time histories, Fourier spectra and spectrograms, where the influence of the TMD in reducing vibratory energy is demonstrated. The TMD is placed in the region where the beam's transverse motion is at a maximum, while its mechanical properties are sub-optimal, in the sense that there is no separate damper present and minimal damping is provided by the spring element itself. In parallel with the analysis, a series of experiments involving a simply supported model steel bridge span traversed by a heavy mass are conducted to first gauge the analytical solution and then to confirm the validity of the proposed passive scheme.

A two-level performance-based plastic design method for multi-story steel frames with double-yielding systems

The performance-based seismic design (PBSD) is usually conducted under design basis earthquakes (DBE), and then, the performance of the designed structures is examined under maximum considered earthquakes (MCE). As a result, it is challenging to simultaneously satisfy the performance targets associated with the DBE and MCE levels. To this end, this study proposes a two-level performance-based plastic design (PBPD) method. The fused steel frames exhibiting trilinear capacity curves are selected as the example structures. The peak interstory drift ratios under the DBE and MCE levels are defined as the performance targets and they are explicitly utilized at the beginning of the design procedure. The expressions of two energy modification factors are first obtained by establishing energy balance equations for single-degree-of-freedom (SDOF) systems under the DBE and MCE levels, respectively. Nonlinear time history analyses (NLTHA) for SDOF systems with various trilinear capacity curves are conducted to derive necessary design parameters. The versatility and flexibility of this design method are achieved by enabling both the primary and secondary yielding systems to yield under the DBE level. To demonstrate and validate the proposed design method, a six-story benchmark steel frame equipped with idealized metallic yielding damping braces is selected and designed with two sets of performance targets. The nonlinear static and NLTHA results proved that the designed structures can simultaneously meet the prescribed performance targets under both DBE and MCE levels.

Damage Spectra of SDOF Structures Under Tsunami Actions Considering the Nonlinear Dynamic Analysis Method

This paper studies the damage spectra of single-degree-of-freedom (SDOF) systems for tsunami loading. The 2011 Tohoku tsunami wave traces are computed and obtained by adopting the Cornell Multi-grid Coupled Tsunami (COMCOT) model and are further verified by the Tohoku Tsunami Joint Survey (TTJS) data. The tsunami response analyses of SDOF systems are conducted taking into account the dynamic analysis method. The classical ductility damage is considered as the damage performance. The damage spectra are computed for five force reduction factors and 791 tsunami loadings. The effects of inundation depths, hysteretic model, post-yield stiffness ratio, [Formula: see text], viscous damping ratio, [Formula: see text], are explored and interpreted scientifically and statistically. The results demonstrate that the effect of the hysteretic model, force reduction factor, R, post-yield stiffness ratio, [Formula: see text], viscous damping ratio, [Formula: see text], on the damage of the structure is evident. Comparison with the static method and influence analysis of structural damping indicate the necessity for the application of the dynamic method. A simplified predictive formulation is developed for the evaluation of structural damage for tsunami loadings.

Optimal design of a clamp band system based on genetic algorithm and experimental verification

As one of the most common separation systems, the clamp band system (CBS) is widely used in the process of connection and release of spacecraft with the launch vehicle. An optimal design method and a separation shock response estimation method were proposed for a large-diameter CBS in this paper. First, a new application based on the parameter modeling method of MSC.Patran and genetic algorithm (GA) was proposed to design the CBS. Finite element techniques for 2D axisymmetric analysis of the CBS were developed, including the modeling of V-clamp, strap pre-tension, and loads, then the optimizing constraints and objectives were also defined. Secondly, a CBS with a diameter of 3 m was designed via the proposed method, which is verified by the 3D finite element analysis under MSC.Marc and a stiffness experiment. Thirdly, the separation process of the CBS and its high-frequency and high-amplitude shock response were calculated by an explicit dynamic solver, and the differences between the model and experimental results were discussed. Finally, a single degree of freedom (SDOF) spring-mass system was constructed to predict the weakening effect of the delay time on the shock response. The slow-release device was designed and the experiment was completed to verify the effectiveness of the method.

Dynamic Response Analysis of Reinforced Column Subjected To Shock Wave Loading

This study focuses on the dynamical response of reinforced concrete members subjected to shock-wave loading, which can cause catastrophic damage to structures. The effects of high strain rate loading and lateral confinement on the member’s behavior are considered in the analysis. The Moment-Curvature (M-ϕ) relations are assessed using stress block equilibrium at yield and ultimate state, and an analytical model is developed that integrates the high strain rate material behavior to predict the peak deflection of the structural member. The study evaluates the dynamic response of the member using a simplified model based on single degree of freedom (SDOF) idealization, and the response of the member in elastic and elastic-plastic phases is modelled using the bilinear resistance function. The governing equation of motion is explained using the Newmark-Beta algorithm, and the shock spectrum predicting the maximum deflection is developed by varying the load duration and magnitude. Additionally, a Finite Element (FE) model is developed to provide a more detailed understanding of the member’s behavior under shock loading. The results obtained from the FE model are compared with the analytical deflection for extreme combinations of load duration and magnitude. The study provides valuable insights into the behavior of reinforced concrete members under extreme loads, which can help structural designers in predicting and design structures that can withstand such loading conditions. The results can also be used in the development of building codes and standards to improve the safety and resilience of structures subjected to shock-wave loading.

Design, Manufacturing, and Testing of a Non‐Preload Variable Friction Damper for Seismic Application of Buildings

Friction dampers are widely used due to their simple structure, remarkable energy dissipation capacity, and frequency independence. However, existing friction dampers are prone to relaxing the preload force during long‐term service, which can lead to cold bonding or cold solidification. To overcome this critical shortcoming, a novel non‐preload variable friction damper (NVFD) was firstly proposed. The construction of the proposed NVFD is provided in detail. Furthermore, restoring the force model through the amplification factors of friction force and inertial mass was derived based on the principle of the proposed NVFD. Then, pseudo‐static tests with various parameters were conducted. Finally, a single‐degree‐of‐freedom (SDOF) structure was employed to compare the effectiveness of this paper’s new NVFD with a conventional friction damper (FD) under various earthquake levels. The results show that non‐preload characteristics avoided the problems of large preloads by traditional friction dampers; thus, the NVFD had stable and reliable variable friction performance, which can effectively adapt to different hazard levels.

Synthesis of flat mechanisms with single degree of freedom for foldable structures

Synthesis of flat mechanisms with single degree of freedom for foldable structures

Artificial neural network-based prediction model of elastic floor response spectra incorporating dynamic primary-secondary structure interaction

The evaluation of the Floor Response Spectrum (FRS) holds paramount significance in assessing the seismic behavior of secondary structures. Precise FRS prediction empowers engineers to make informed decisions concerning structural design, retrofitting, and safety precautions. This study aims to scrutinize the impact of dynamic interaction between primary and secondary structures on FRS. Both the elastic primary structure (PS) and elastic secondary structure (SS) employ a single-degree-of-freedom (SDOF) system. Governing motion equations for both coupled (with dynamic interaction) and uncoupled (without dynamic interaction) systems are formulated and solved numerically. The study investigates how variations in the vibration period of PS (Tp), tuning ratio (Tr), mass ratio (μ), and damping ratio (ξs) of SS influence FRS. The FRS impact remains minimal at μ = 0.001 (0.1%); however, with increasing mass ratio, PS-SS dynamic interaction significantly affects SS's spectral acceleration response. Coupled analysis is crucial only for secondary structures tuned to the primary structure's vibration period (0.8≤Tr≤1.2). This study utilizes two-layer feed-forward Artificial Neural Networks (ANNs) for FRS prediction. The Levenberg-Marquardt (LM) backpropagation (BP) algorithm trains the network using a comprehensive dataset. In summary, it is evident that the ANNs, once trained, enable accurate prediction of the FRS, exhibiting a R2 of 99%. Additionally, a design expression is formulated utilizing the ANN model and subsequently compared with the existing formulation.

Performance of round-ended CFST columns under combined actions of eccentric compression and impact loads

Round-ended concrete-filled steel tubular (RECFST) columns are gaining increasing usage in bridge structures. During their service life, RECFST columns under eccentric compression may suffer from impact loading. This study conducted test and numerical investigations to assess the performance of RECFST columns under the coupled actions of compression, bending and lateral impact loads. Fourteen columns were fabricated and tested, considering the influences of axial-load ratio, bending moment and impact energy. The damage mode and the time histories of impact force and displacement were accessed and analyzed. The experimental findings revealed that the initial bending moment negatively affected the impact resistance of RECFSTs. In addition, finite element model was established in ABAQUS and calibrated against the test results. The calibrated model was then employed to conduct the failure mechanism analysis and parametric study. Finally, a single-degree-of-freedom (SDOF) analysis was conducted to predict the mid-height deflection of RECFST columns under combined action of compression, bending and lateral impact loads, by incorporating the influences of pre-axial load and initial bending moment.

Variation in carrying angle - A normative study

The synovial joint that comprises the elbow is a hinge joint with a single degree of freedom, allowing for flexion and extension movements. The primary objective of this study was to investigate the varying carrying angles that were observed. An observational study was conducted in the Department of Orthopaedics Heritage Institute of medical sciences Varanasi. Around 500 samples were taken for a period of 2 years. All patients of both genders inclusive of age group 8 to 19 years were taken with their consent. Asymptomatic individuals without any deformity, fractures, anomalies and previous history of surgery around elbow were included. All with previous elbow injuries and anomalies around elbow, history of Endocrine disorders, athletes and deformity occurring after any elbow injury were excluded.The present study was conducted in the Department of Orthopaedics, Heritage Institute of Medical Sciences, Varanasi with the objective to observe the physiological factors responsible for the change in the carrying angle in normal individuals in a tabulated manner. A total of 500 patients were included in the study. There was no significant (p>0.05) difference in carrying angle between male and females among different age groups. There was no significant (p>0.05) difference in carrying angle between male and females among different height groups. Only age was positively significantly (r=0.48, p=0.001) correlated with carrying angle.Females had a considerably higher carrying angle (12.96±2.44) than males (12.19±1.74) (p=0.001). There was no significant difference in carrying angle across height groups or genders (p>0.05). Age correlated positively with carrying angle (r=0.48, p=0.001).

Entanglement monogamy in indistinguishable particle systems

Recently, it has been realized that indistinguishability is a resource for quantum information processing. A new method to represent the indistinguishable particles by Franco et al. (Sci Rep 6:20603, 2016, https://doi.org/10.1038/srep20603) and measure the concurrence is developed by Nosrati et al. (npj Quantum Inf 6:39, 2020, https://doi.org/10.1038/s41534-020-0271-7). The monogamy property says that quantum entanglement cannot be shared freely between more than two particles. For three distinguishable particles, the monogamy of entanglement was first expressed as an inequality using squared concurrence where each particle has a single degree of freedom (for pure or mixed states). Using multiple degrees of freedom, similar inequality was shown to be held between two distinguishable particles. However, for two indistinguishable particles, where each particle cannot be addressed individually, the monogamy inequality was shown to be violated maximally for a specific state. Thus a question naturally arises: what happens to the monogamy of entanglement in the case of three or more indistinguishable particles? We prove that monogamy holds in this scenario and the inequality becomes equality for all pure indistinguishable states. Further, we provide three major operational meanings of our result. Finally, we present an experimental schematic using photons to observe our result.

Seismic assessment and qualification of acceleration-sensitive nonstructural elements through shake table testing: Reliability of testing protocols and reliability-targeted safety factors

Shake table testing represents the best option for assessing and qualifying acceleration-sensitive nonstructural elements (NEs). Several testing protocols are defined in regulations and codes and implemented in the literature, but no commentaries or literature studies provide information regarding the expected reliability or recommend applicative safety factors. The study investigates the seismic reliability of shake table testing protocols for seismic assessment and qualification of acceleration-sensitive NEs. Numerical analyses are carried out considering an incremental procedure and modeling NEs as inelastic single degree of freedom (SDOF) systems, over a wide range of frequencies of interest and NE structural properties. Real floor motions recorded in instrumented reinforced concrete (RC) buildings are considered as a reference. The reliability is estimated considering several damage states and various floor motion sets. In particular, the seismic capacities associated with the real (shake table protocol) floor motions are considered as actual-demand (nominal-capacity) measures, and the demand to capacity margin is meant as the protocol overestimation of the NE capacity. In the light of the estimated protocol reliability, reliabiliy-targeted capacity safety factors are assessed, and applicative factor abaci and closed-form criteria are proposed.

Insights into the nonlinear dynamic characteristics of a water turbine generator set considering the coupled effects of a fractional-order broadband foundation

The analysis of the coupled shaft-foundation system (CSFS) of a water turbine generator set is an extremely complicated task owing to its structural complexity and inherent nonlinear broadband dynamic characteristics. Thus, the coupling relationships of the CSFS remain unclear. The broadband vibration of the foundation subsystem has an evident influence on the vibration of the shaft subsystem of the unit; however, for the analysis of the dynamic characteristics of the water turbine generator, an overly complicated foundation can be reasonably simplified. To this end, this paper reports the development of novel energy-equivalent broadband modeling approaches to investigate the nonlinear vibration characteristics of CSFS. First, a relatively traditional integer-order lumped parameter model of the foundation subsystem was constructed, and its parameters were determined by fitting the response spectra obtained from an accurate hydropower house model. To improve the narrow-frequency limitation of the integer-order model and account for random disturbances, a novel fractional-order broadband modeling method is proposed. The advantage of the proposed fractional-order equivalent foundation model is that it can simultaneously reveal the broadband characteristics of complex structures at low frequencies of less than 1 Hz to high frequencies of hundreds of Hz with a single degree of freedom. Finally, coupled dynamic equations for the fractional-order CSFS model were derived and solved by considering the actions of various nonlinear factors and hydraulic pulsation excitation. A comparison of the dynamic responses of the CSFS with field test data demonstrated the effectiveness and practicability of the proposed modeling approaches. The results of the integer- and fractional-order CSFS models provide insights into the abundant dynamic laws and inner mechanisms of the nonlinear coupled dynamic system. Furthermore, they provided a reliable theory for the design and stability analysis of a hydropower unit, considering the varied vibrations of the coupled foundation.

A novel tuned torsional mass damper (TTMD) for seismic protection of structures

Energy dissipators are being increasingly utilized in the seismic protection of both newly constructed and retrofitted buildings. However, their control effectiveness would decline when applied to the stiff structures with small responses, such as drifts and inter-story velocities. To more effectively dissipate the vibration energy, this paper proposes a novel energy dissipator dubbed as tuned torsional mass damper (TTMD) based on the amplification effect of inerter. In particular, the conceptual design and ideal mechanical model of the proposed TTMD are firstly elaborated. A single degree of freedom (SDOF) system is then established to derive the optimal parameters of TTMD, namely the frequency and damping ratios, based on the fixed-point theory. Subsequently, a three-story benchmark building is adopted to demonstrate the control effectiveness of TTMD in the frequency domain. For comparison, the control effectiveness of the conventional viscous damper (VD) and viscous mass damper (VMD) are also examined. Moreover, parametric studies are conducted to investigate the influences of the mass ratio, secondary mass ratio, and lead of ball screw on the control performances of TTMD, and sensitivity analyses are also performed to assess the robustness of TTMD against the structural uncertainties. Finally, case studies are performed to further illustrate the control performance and the hysteretic behaviors of TTMD in the time domain. The results show that the proposed TTMD is more effective than the conventional VD and VMD in reducing the seismic responses of building; the relative angle of TTMD can be effectively reduced by increasing either the mass ratio or the lead of ball screw. The proposed TTMD could be a promising and viable alternative to conventional dampers in the field of structural vibration control.

Design of an ultrathin passive isolator based on multi-layer plain-woven wire mesh

Spacecraft devices have strict restrictions on weight and volume for high fuel efficiency and endurance requirements. In this paper, a method for designing an ultrathin passive vibration isolator based on multi-layer plain-woven wire mesh is proposed. The isolator is structurally inspired by O-type wire rope isolators, and the wire mesh is pre-compressed to buckling for lower stiffness and higher stability. The isolator stiffness in the post-buckling process is analyzed by simplifying the single wire as a strut. The motion equation of the strut is constructed and calculated by the fourth-order Runge–Kutta method and the shooting method. The morphology and stiffness variation of the wire mesh during pre-compression process and repeated compression process are analyzed, and the structural compaction ratio is calculated. This computational method has been experimentally validated and proven to be effective. To prevent collisions between the protected objects and the base during the shock process, the system is simplified and described using a single-degree-of-freedom (SDOF) system with displacement restrictors. The system’s motion equation is formulated and solved using the central difference method. Subsequently, the maximum compression displacement of the isolator is determined through the calculation. A wire mesh isolator with a thickness of less than 10 mm is fabricated for a specific application. Experimental results confirm that the isolation efficiency surpasses 65%, and the isolator is capable of withstanding a peak acceleration of 60 g while maintaining a shock acceleration magnification below 1.2.

A New Method Using Pseudovelocity-Based Fatigue Analysis to Determine the Effectiveness of Acoustic Fields Used for Acoustic Testing

Abstract This paper summarizes results from the use of advanced adaptive multiple-input, multiple-output (i.e., MIMO) control for direct field acoustic testing to excite an aluminum-honeycombed 1.22 m × 2.44 m (4 ft × 8 ft) test panel with MSI-DFAT's near-diffuse acoustic field and four nondiffuse acoustic fields using three panel orientations, and two speaker configurations. The five fields have the same overall sound pressure level (OASPL) and 1/3-octave sound-pressure-level (SPL) spectrum. Test and analysis results demonstrate a dependence of the test panel's response characteristics to each acoustic-field excitation, showing that the near-diffuse field excites experimental-modal-analysis-identified test panel modes effectively, whereas nondiffuse fields excite these modes ineffectively. Differences are attributed to the relative diffuseness of fields. Partial fatigue damage values from 20 accelerometer locations are determined from pseudovelocity (PV) outputs from single-degree-of-freedom (SDOF) models at each modal frequency excited by their response time histories, for each acoustic field, to quantify the relative ability of acoustic fields to detect workmanship flaws of typical test articles. Fatigue-damage values are obtained from PV response time histories of SDOF models at identified modal frequencies, which are rainflow-cycle counted with the partial-damage coefficients calculated using the Palmgren-Miner rule. A new form of vibro-acoustic gain based on PV power spectral densities (PSDs) is also introduced and correlated with these experimental results, since the PV response PSDs of a test article undergoing random vibration are proportional to modal stress at their frequencies. This paper shows that the modal stress caused by acoustic-field types is an important consideration for acoustic testing of satellites and other spacecraft, since using a nondiffuse field may result in an acoustic test that doesn't detect workmanship flaws in a test article, even though the acoustic environment is achieving the same specified OASPL and average acoustic 1/3-octave SPL spectrum.

A simplified method for the dynamic analysis of structures under column loss

The progressive collapse of buildings as a dynamic phenomenon can be fully understood only within a transient dynamic analysis context considering for damping and inertia effects. The response of a typical beam-column substructure is usually dominated by a single mode of deformation, thus the single-degree-of-freedom (SDOF) modelling assumption provides an accurate representation of the problem. In this study, the dynamic response of an inelastic SDOF system with damping was investigated analytically. Closed form analytical equations of the model were derived that describe the complete dynamic response in the time domain. Moreover, simplified formulae to estimate peak responses and Dynamic Increase Factors (DIFs) were provided. Numerical dynamic analyses in OpenSees were performed to verify the accuracy of the analytical model. The results indicate that the analytical model can trace the full dynamic response accurately while peak displacements can be accurately estimated with the proposed formulas. The estimated DIFs were in agreement with available from the literature results and demonstrate the significant effect of damping and hardening. Application of the analytical methodology on the progressive collapse analysis of a 10-storey steel frame demonstrated the effectiveness and potential of the proposed SDOF system.

Finite element modeling of piezoelectric cantilever-beam energy harvester

Piezoelectric energy harvesting from mechanical vibrations has attracted considerable attention during the last decade. The homogeneous harvesters were studied experimentally or numerically by various models such as single degree of freedom (SDOF) modeling, finite element (FE) modeling as well as using analytical solutions. In this work, FE models for simulating a piezoelectric beam bimorph power harvester consisting of a laminated piezoelectric beam, a proof mass, and an electrical load (series or parallel connections) configurations are developed. The effects of the material and size of the substrate, the proof mass have been studied on the resonance frequencies and the output parameters of the piezoelectric generator (PEG). Numerical results obtained using the proposed procedure for piezoelectric bimorph power harvesters are in good agreement with the experimental data available in the literature. The proposed method can be used for modeling accurately this class of energy harvesting devices.

A creative wide-frequency and large-amplitude vibration isolator design method based on magnetic negative stiffness and displacement amplification mechanism

Negative stiffness vibration isolation devices have attracted significant attention and research interest for their ability to enhance the low-frequency vibration isolation performance of passive vibration isolators. However, their narrow linear negative stiffness region has hindered their broader application. To address this limitation, a novel design method for vibration isolators is proposed, integrating the permanent magnetic negative stiffness device (NSD) with the displacement amplification mechanism (DAM). The paper begins by presenting a specific vibration isolator design method and analyzing the kinematic relationship. Next, a single-degree-of-freedom (SDOF) nonlinear equivalent model of the vibration isolator is established using the pseudo-rigid-body model (PRBM) approach. Numerical simulations are then conducted to obtain the transmissibility of the isolator. Furthermore, two isolators—one with the displacement amplification effect and another without—are manufactured, and experimental investigations are carried out. The experimental results confirm that the incorporation of the displacement amplification mechanism effectively expands the linear negative stiffness region of the negative stiffness magnet pair, enabling wide-frequency and large-amplitude vibration isolation. Notably, these experimental findings align well with the simulation results. In summary, this paper proposes a creative design method for wide frequency and large amplitude vibration isolators, and proves it through theoretical analysis and experimental validation.

Effects of crumb rubber particles on the dynamic response of reinforced concrete beams subjected to blast loads

Crumb rubber particles (RPs) can improve the impact resistance of concrete structures owing to their high toughness. In the current paper, the dynamic behaviours of RPs reinforced concrete beams under blast loads were investigated. The near-field explosion tests were first performed on the rubber-modified reinforced concrete (RRC) beams with different content of RPs (0%, 10%, 20%, 30%, and 50%). Numerical simulations based on the ConWep, Karagozian and Case concrete (KCC) models were then used to analysis the deformation/failure mechanisms of RRC beams. Finally, an improved single-degree-of-freedom (SDOF) method was proposed to predict the dynamic deflection of RRC beams. The experimental results indicated that the crack patterns of the RRC beams changed from bending cracks to shear–bending cracks as the scaled distance decreased. When the blast load had a small scaled distance (0.234 m/kg1/3), the number of cracks decreased with increased rubber content, particularly shear cracks. The numerical simulation revealed that due to the low damping ratio of RRC beams, the vibration amplitude of the RRC beams was lower than that of the beams without RPs. It is believed that the current study can provide valuable insights into the key factors for designing the blast resistance of RPs reinforced concrete structures.