Degree Of Freedom System Research Articles

Using image-based inspection data to improve response predictions of earthquake-damaged unreinforced masonry buildings

Explicit representation of uncertainties is essential to improve the reliability of seismic assessments of earthquake-damaged buildings, particularly when dealing with unreinforced masonry buildings. Modern inspection techniques use images for detecting and quantifying the damage to a structure. Based on the principle of falsification, this paper evaluates how the use of information of damage that is obtained from images taken on earthquake-damaged buildings reduces the uncertainty when predicting the seismic response under a future earthquake. New model falsification criteria use information on the residual state of a building, such as shear cracks, residual roof displacements, and observation of out-of-plane failure. To demonstrate the effectiveness of these criteria in reducing the uncertainty in response predictions, results from a four-story unreinforced masonry building stiffened with reinforced concrete walls, which was experimentally tested under a sequence of ground motions, are assessed. Three commonly used modeling approaches (single degree of freedom (DOF) systems, multi DOF systems with four DOFs, and equivalent frame models) are used, where uncertainties in model parameters and model bias are included and propagated through the analysis. Out of the models used, and in the absence of any additional source of information, the proposed falsification criteria are most effective in connection with the equivalent frame model because this model can simulate the response at the element-level, while the simpler models can only represent the global response or the response at the storey-level. The results show that when using only the information on the presence of shear cracks, which might be the first and only source of information after an earthquake, the effectiveness of model falsification is increased, thus reducing the uncertainty in model parameter values and seismic response predictions through the use of image-based inspection.

Smart whole-body vibration attenuation, cushion for heavy equipment seating: Model and simulation

Off-road mobile machine operators are exposed to whole-body vibration (WBV) which can result in adverse health effects. Seat suspensions are used to reduce WBV exposure, but typical passive seats cannot attenuate frequencies below 1.13 Hz. The proposed device is designed to minimize transmissibility from 0 to 20 Hz because this bandwidth contains the dominant frequency for most off-road vehicles. The semi-active smart device uses bang-bang control and is designed to be installed in place of the seat-pan cushion in OEM passive seats. Modelled as a two degree of freedom system, simulations were performed using a lumped mass model (ωn = 3 Hz; sinusoidal base excitation 0-20 Hz). Using a hexapod robot, a prototype reduced transmissibility compared to a passive OEM seat. The device was up to 5 times more effective than a passive seat in reducing vibration transmissibility. Simulations revealed that operator mass and seat stiffness variations have little effect on device WBV attenuation performance.

Experimental encircling of an exceptional point in a two degrees of freedom system: overview and application to noise control

When a resonator is added to an acoustic cavity or a vibrating structure, a new resonance frequency, or pole, is created in the system. When dissipation is present, this may breakdown when some parameters are finely tuned. This phenomenon, typical of non-Hermitian dynamics is called an exceptional point in the parametric space where two (or more) eigenvalues, as well as their associated eigenvectors, coalesce. In the recent years, EPs have gained interest in physics because of the counter-intuitive concepts associated with them. In the fields of acoustics and vibration, understanding EP may lead to a better comprehension of modal energy exchanges and decay. This work aims at exploring the key concepts related to EPs by revisiting the well-known coupled pendulums problem in the presence of damping. First, the free response of the experimental system is investigated after tuning it on an EP. Then an encircling is performed by varying the parameters through time. Our experimental results illustrate in a pedagogical manner nearly-optimal dissipation, energy exchange and chirality effects which have been recently evidenced in physics.

Cr-Cr distance and magnetism in the phase diagram of triangular lattice antiferromagnets: A systematic comparative study

In this study, we investigate the influence of Cr-Cr distances on the magnetic properties of triangular lattice antiferromagnets through the lens of the recently synthesized Cr compounds LiCrSe2, LiCrTe2, and NaCrTe2. Our comprehensive analysis integrates existing magnetic structure data and new insights from muon spin rotation measurements, revealing a striking mutual influence between strongly correlated electrons and structural degrees of freedom in systems possessing very different magnetic properties despite having the same crystal symmetry. In particular, we delineate how Cr-Cr distances specifically dictate the magnetic behaviors of the triangular lattice antiferromagnets LiCrSe2, LiCrTe2, and NaCrTe2. By crafting phase diagrams based on these distances, we establish a clear correlation between the structural parameters and the magnetic ground states of these materials together with a wide variety of trivalent Cr triangular lattice layered magnets. Our analysis uncovers a transition range for in-plane and out-of-plane Cr-Cr distances that demarcates distinct magnetic behaviors, highlighting the nuanced role of lattice geometry in the spin-lattice interaction and electron correlation dynamics. Published by the American Physical Society 2024

Local cochlear mechanical responses revealed through outer hair cell receptor potential measurements

Sensory hair cells, including the sensorimotor outer hair cells, which enable the sensitive, sharply tuned responses of the mammalian cochlea, are excited by radial shear between the organ of Corti and the overlying tectorial membrane. It is not currently possible to measure directly in vivo mechanical responses in the narrow cleft between the tectorial membrane and organ of Corti over a wide range of stimulus frequencies and intensities. The mechanical responses can, however, be derived by measuring hair cell receptor potentials. We demonstrate that the seemingly complex frequency- and intensity-dependent behavior of outer hair cell receptor potentials could be qualitatively explained by a two degrees of freedom system with local cochlear partition and tectorial membrane resonances strongly coupled by the outer hair cell stereocilia. A local minimum in the receptor potential below the characteristic frequency should always be observed at a frequency where the tectorial membrane mechanical impedance is minimal, i.e., at the presumed tectorial membrane resonance frequency. The tectorial membrane resonance frequency might, however, shift with stimulus intensity in accordance with a shift in the maximum of the tectorial membrane radial mechanical responses to lower frequencies, as observed in experiments.

Controlling the fold: proprioceptive feedback in a soft origami robot.

We demonstrate proprioceptive feedback control of a one degree of freedom soft, pneumatically actuated origami robot and an assembly of two robots into a two degree of freedom system. The base unit of the robot is a 41 mm long, 3-D printed Kresling-inspired structure with six sets of sidewall folds and one degree of freedom. Pneumatic actuation, provided by negative fluidic pressure, causes the robot to contract. Capacitive sensors patterned onto the robot provide position estimation and serve as input to a feedback controller. Using a finite element approach, the electrode shapes are optimized for sensitivity at larger (more obtuse) fold angles to improve control across the actuation range. We demonstrate stable position control through discrete-time proportional-integral-derivative (PID) control on a single unit Kresling robot via a series of static set points to 17 mm, dynamic set point stepping, and sinusoidal signal following, with error under 3 mm up to 10 mm contraction. We also demonstrate a two-unit Kresling robot with two degree of freedom extension and rotation control, which has error of 1.7 mm and 6.1°. This work contributes optimized capacitive electrode design and the demonstration of closed-loop feedback position control without visual tracking as an input. This approach to capacitance sensing and modeling constitutes a major step towards proprioceptive state estimation and feedback control in soft origami robotics.

Data‐Driven Structural Health Monitoring on Shaking Table Tests of a 3‐Story Steel Building with Sliding Slabs

Data‐driven structural health monitoring (SHM) is an approach which relies on the information contained in the data and through signal analysis techniques captures the features, variations, and uncertainties that data contain. This paper presents the response of shaking table tests of a full‐scale, 3‐story building with sliding slabs connected by horizontal buckling‐restrained braces for energy dissipation. First, the global dynamic characteristics of the structure were identified from a series of the building response data under different intensity level of base excitations. The variation of the identified modal parameters, such as the mode frequencies and modal shapes, was discovered. The influence of sliding slabs on the dynamic characteristics of the frame was also investigated through the measured response and the equation of motion with six degree of freedom systems. Comparison on the achieved interstory stiffness due to the implementation of sliding slabs and the fixed (locked up) slab was examined. The mechanism and dynamic characteristics of sliding slabs, including energy dissipation of the friction force, BRB hysteresis behavior, and unintended damping force during strong base excitation were analyzed directly using the ARX/recursive model. The extracted unintended damping force performed like a friction hysteretic response, which needs to be considered for frame modeling in shaking table tests. The findings through the data analysis have clarified the important aspects of sliding slabs and demonstrated the benefits and applicability of sliding slabs on reducing the frame response.

Dynamics of an omnidirectional pendulum energy harvester: A comparative analysis between numerical and experimental results

The spherical pendulum is a mathematically interesting model that has been studied extensively in the past. In the field of energy harvesting however, the pendulum energy harvesters are generally confined to planar motions. This minimisation of the available degrees of freedom potentially limits the areas of application of the energy harvester, and certainly its overall capability. In this work an omnidirectional pendulum energy harvester is proposed in the form of a two degree of freedom system which has the potential to harvest energy from motions along the three axes of translation and from the three corresponding rotations about those axes. The dynamics of such an energy harvester are examined experimentally for different power take-off modes and are subsequently compared to numerical predictions from an analytical model. An optimal operational point is proposed for the harvester and it is shown how an up-sweep and down-sweep of the excitation frequency can significantly broaden the operational range of the energy harvester by up to 130%.

Numerical simulation of stability and responses of dynamic systems under parametric excitation

The stability and responses of dynamic systems under parametric excitation are often encountered in many fields of science and engineering, such as slender columns and thin plates under axial loadings. This paper proposes a novel numerical simulation method to simultaneously construct stability diagrams and predict the responses of multiple degree-of-freedom (DOF) dynamic systems under arbitrary parametric loadings. The method divides an arbitrary load into discrete segments to approximate the variable excitation function by a step function and then accumulates the system responses of each segment using a matrix method. Dynamic stability and response analysis of undamped and damped 1DOF, 2DOF, 3DOF, and multiple DOF systems are conducted, and numerical examples are compared to conventional methods to show the accuracy and advantage of the proposed numerical simulation method. The instability diagrams are also substantiated by vibration response curves obtained from the same method. The method is applied to calibrate the validity and ranges of applicability of the Hill infinite determinants in the Floquet theory of 1DOF Mathieu-Hill equations. The second order approximation of the first instability region from the Hill determinant is acceptable. However, the fourth order approximation of the second instability region must be used to obtain a relatively accurate result. For 2DOF, 3DOF, and multi-parameter linear periodic systems, the method can simultaneously render four types of instability regions in a single procedure: no resonances, simple parametric resonances, combination additive resonances, and combination differential resonances. These results could provide a better understanding of stability and responses of dynamic systems under parametric excitation.

Kinematic Analysis of three degrees of freedom planar parallel continuum mechanisms

Parallel continuum mechanisms are a type of compliant mechanisms comprising a rigid end-effector connected to a fixed frame by flexible and slender elements in a closed-kinematic morphology, being their flexibility the source of mobility. Solving the position problem involves the static equilibrium of the whole device considering the nonlinear large deformations of slender elements. Numerical iterative solutions are already available to solve real-time simulations. However, an assembled solution, which meets both geometric conditions and static equilibrium, is needed to start the process. A comprehensive Kinematic Analysis in the classical sense is not fully established yet. The aim of the paper is to propose a procedure that solves the full inverse and forward kinematic problems for planar three degrees of freedom systems, hence obtaining the multiple solutions arising from the closed-loop structure and the multiplicity of the deformation mode of slender links. From those solutions, finding of the different aspects that comprise the workspace is possible, as well as determining singularities and instability loci.

Discrete and Continuum Modeling of Coulomb Friction Damping in Stone Blocks

Friction plays an important role in creating damping mechanism in structures.In this paper a study was conducted to analyze coulomb friction damping andfrictional energy dissipation mechanism with stone blocks in a single degreeof freedom system by discrete and continuum modeling in finite element-based software ABAQUS. Discrete and continuum modeling approach wasused in this study. It was found that both approaches gave similar results.

Seismic response prediction of structures based on Runge-Kutta recurrent neural network with prior knowledge

In the seismic analysis of structural systems, dynamic response prediction is an essential problem and is significant in every stage during the structural life cycle. Conventionally, response analysis is carried out by numerical analysis. However, when the structural parameter is unknown, the establishment of a numerical model will be difficult. Enlightened by the Runge-Kutta (RK) numerical algorithm, this paper proposes a novel recurrent neural network named Runge-Kutta recurrent neural network (RKRNN) to realize the seismic response prediction. A partition training strategy is formulated to train the proposed neural network and to improve the efficiency of training. The proposed model can be trained by using a limited number of samples. Three numerical examples are utilized to validate the feasibility of RKRNN model including a linear three degrees of freedom (DOFs) system, a nonlinear single DOF system with Bouc-Wen hysteresis, and a numerical reinforced concrete bridge model. Additionally, the site monitoring data from a real-world bridge is utilized to further validate the proposed network. The results show that the proposed RKRNN model can effectively and efficiently predict the structural response under seismic load and exhibits robustness to noise, with good potential for applications in engineering practice.

Normalization and reduction of the Stark Hamiltonian

<abstract><p>We detail a calculation of the second order normal form of the Stark effect Hamiltonian after regularization, using the Kustaanheimo-Stiefel mapping. After reduction, we obtain an integrable two degree of freedom system on $ S^2_h \times S^2_h $, which we reduce again to obtain a one degree of freedom Hamiltonian system.</p></abstract>

Algebraic Properties of Quantum Reference Frames: Does Time Fluctuate?

Quantum reference frames are expected to differ from classical reference frames because they have to implement typical quantum features such as fluctuations and correlations. Here, we show that fluctuations and correlations of reference variables, in particular of time, are restricted by their very nature of being used for reference. Mathematically, this property is implemented by imposing constraints on the system to make sure that reference variables are not physical degrees of freedom. These constraints not only relate physical degrees of freedom to reference variables in order to describe their behavior, they also restrict quantum fluctuations of reference variables and their correlations with system degrees of freedom. We introduce the notion of “almost-positive” states as a suitable mathematical method. An explicit application of their properties to examples of recent interest in quantum reference frames reveals previously unrecognized restrictions on possible frame–system interactions. While currently discussed clock models rely on assumptions that, as shown here, make them consistent as quantum reference frames, relaxing these assumptions will expose the models to new restrictions that appear to be rather strong. Almost-positive states also shed some light on a recent debate about the consistency of relational quantum mechanics.

Flat bands arising from spin-orbit assisted orbital frustration

We present general design principles for engineering and discovering periodic systems with flat bands. Our paradigm exploits spin-orbit assisted orbital frustration on a lattice to produce band structures that contain multiplets of narrowly dispersing bands whose bandwidth is smaller than all other energy scales of the problem including the band gap surrounding the flat bands. We present a series of models in 1D and 2D on various lattices with different intracellular spin-orbit like potentials that hybridize the degrees of freedom in the unit cell. As an alternative to machine learning based exhaustive searches, these design principles and models can be used to search for flat band systems in a variety of physical settings and can be used to investigate the role of weakly dispersing highly orbitally frustrated degrees of freedom in systems where the interactions dominate over the kinetic energy scales of the system.

Non-smooth dynamics of buckling based metainterfaces: Rocking-like motion and bifurcations

The non-smooth dynamics is investigated for an elastic planar metainterface composed by two layers of buckling elements, each one allowing motion on one side only. Through the analogy between buckling and unilateral contact and by assuming no-bouncing at impact, the motion of the relevant two degrees of freedom system is reduced to that of a single degree governed by a piecewise-smooth differential equation. The metainterface dynamics has strong similarities with the rocking motion of rigid blocks and displays several types of dynamic bifurcations in the presence of oscillatory forces, including period doubling, branch point cycle, grazing, as well as quasi-periodic and chaotic responses. Moreover, the multistable response is found to be broaden to conditions representative of monostable states within a quasi-static setting, disclosing a multistability anticipation by dynamics. The wide landscape of the dynamic response for the buckling based metainterface provides a novel theoretical framework to be exploited in the design of mechanical devices for vibration attenuation and for energy harvesting.

Analysis and Correction of Measurement Error of Spherical Capacitive Sensor Caused by Assembly Error of the Inner Frame in the Aeronautical Optoelectronic Pod.

The ball joint is a multi-degree-of-freedom transmission pair, if it can replace the inner frame in the aviation photoelectric pod to carry the optical load, which will greatly simplify the system structure of the photoelectric pod and reduce the space occupied by the inner frame. However, installation errors in ball joint siting introduce nonlinear errors that are difficult to correct and two degree of freedom angular displacement of the ball joint is difficult to detect, which limits application in the precision control of two degrees of freedom systems. Studies of spherical capacitive sensors to date have not tested sensors for use in an inner frame stabilisation mechanism nor have they analysed the influence of installation error on sensor output. A two-axis angular experimental device was designed to measure the performance of a ball joint capacitive sensor in a frame stabilisation mechanism in an aeronautical optoelectronic pod, and a mathematical model to compensate for ball joint capacitive sensor installation error was created and tested. The experimental results show that the resolution of the capacitive sensor was 0.02° in the operating range ±4°, the repeatability factor was 0.86%, and the pulse response time was 39 μs. The designed capacitive sensor has a simple structure, high measurement accuracy, and strong robustness, and it can be integrated into ball joint applications in the frames of aeronautical photoelectric pods.

Vortex-induced vibration of a two degree-of-freedom flexibly mounted circular cylinder in the crossflow direction

Vortex-induced vibration (VIV) of a two degree-of-freedom (DOF) circular cylinder, placed in the test section of a recirculating water tunnel and free to oscillate in its first two vibrational modes in the crossflow direction, is studied experimentally. The dynamic response of the cylinder is studied for a reduced velocity range of $U^*=4\unicode{x2013}30$ for eigenfrequency ratios in the range of 1.3–3.0. For the two DOF system, while the onset of the VIV response followed a similar lock-in region as those observed for a classical VIV response of a single DOF system, by increasing the reduced velocity a secondary lock-in region was observed over which the oscillations of the cylinder were locked into the system's second mode. In addition, there existed an intermediate range of reduced velocity over which the VIV response consisted of oscillations at a combination of the first two natural modes of the system. As the eigenfrequency ratio between the first two modes increased, the secondary lock-in range was extended to higher reduced velocities and the reduced velocity range over which multi-modal oscillations were observed was decreased. A full map of vortex dynamics in the wake of the cylinder was developed qualitatively and quantitatively using hydrogen bubble flow visualization and time-resolved volumetric particle tracking velocimetry techniques, respectively. A Q-criterion analysis revealed the existence of highly three-dimensional vortex structures in the wake of the cylinder. The spatiotemporal mode analysis using the proper orthogonal decomposition technique revealed strong coupling between the vortex shedding modes in the wake of the cylinder and the structural vibration modes.

Acoustic computing: At tunable pseudospin-1 Hermitian Dirac-like cone.

Hermitian Dirac-like cones are proposed for creating acoustic logic gates herein. The predictive phenomenon of creating Dirac-like cones near a bipolar antisymmetric deaf band was found to be useful for acoustic computing of Boolean algebra. Unlike previous approaches, Dirac-like cone creates exclusive opportunity to perform all possible Boolean algebra computation with valid inputs. The phenomenon is demonstrated in two-dimensional phononic crystals (PnCs), consisting of tunable square columns in air media. By predictive tuning of the deaf bands, a triply to doubly degenerated Dirac-like cone is reported to form and is particularly useful for acoustic computing. It is only possible when a bottom band has a negative curvature that is lifted from a nearby doubly degenerated band with positive curvature, which is again degenerated with a deaf band. On the contrary, similar computing possibilities are difficult when the bottom band degenerates with the deaf band and the top band is lifted. Using these phenomena, acoustic logic gates are designed to perform Boolean algebra through AND, NAND, OR, and NOR gate operations. A simple one degree of freedom system and a complex six degrees of freedom system are proposed and demonstrated in which simple rotation of the PnCs activates a specific gate.

Multi-Mode Motion Dynamics of a Top Tensioned Riser Excited by Vortices and Varying Tension

A coupled model of a top tensioned riser (TTR) under combined excitations from vortices and time-varying tension is proposed. And the van der Pol oscillator is introduced to simulate the time-varying characteristics of vortex shedding. The first three mode approximations as a six degree-of-freedom (DOF) system of vibrations of the fluid-structure interaction system are derived. Two cases of resonances are analyzed by using the numerical method. One case is on the vortex induced vibration (VIV) of the six DOF system, where the 1-to-1 internal resonance (also named “lock-in” phenomenon) between frequencies of the first modes of structure and the wake oscillator are investigated. Bifurcation curves between dynamic responses in terms of the shedding frequency are derived. Comparing to the vibrations of the first order mode, the “lock-in” phenomenon for vibrations of the higher order modes can occur in the wider parameter range with large values. The second case is on the combined resonance between the 1-to-1 internal and 1-to-2 parametric resonance. Response curves versus the shedding frequency under different amplitude ratios are calculated by the Runge–Kutta method. Effects of system parameters including the amplitude ratio of the parametric excitation, shedding frequency on the response curves are investigated. Comparing to the case when only considering the 1-to-1 internal resonance in the VIV, results of the combined resonance show those large-amplitude responses of the structure and wake oscillator can be induced. Responses will increase rapidly as the amplitude of the varying tension increases. Unstable responses can occur within a large frequency band of nondimensional shedding frequency. Furthermore, the dynamic characteristics of the responses of the six DOF system including the bifurcation diagrams, time histories, phase-plane projection and Poincaré sections are computed for different amplitude ratios. Results indicate that complex dynamics such as the quasi-periodic and chaotic solutions can occur for different amplitude ratios. The analysis can be helpful for the parameter design of deep-water risers.