Harmonic Dynamic Loading Research Articles

Verification of damped bipedal inverted pendulum model against kinematic and kinetic data of human walking on rigid-level ground

In this study, kinematic and kinetic data for 14 test subjects walking on a treadmill were recorded to verify a damped bipedal inverted pendulum (DBIP) model. The verification aim was for the DBIP model to match the step frequency and first harmonic dynamic load factor (DLF1) extracted from the measured data, as these are key parameters of interest in civil engineering applications. The verification was conducted in several phases. First, kinematic data from 39 markers attached to the human body were used to get the trajectory of body’s centre of mass (BCoM). This trajectory, in conjunction with the vertical and longitudinal ground reaction forces (GRFs) were then used to plot the leg force – leg length relationship. Linear curve fitting yielded the spring stiffness and spring length parameters. These parameters, together with the body mass and damping coefficient, were fed into the DBIP model to identify initial conditions for the motion of BCoM leading to the stable periodic gait. For the 14 test subjects, the model produced excellent agreement with the measured step frequency and DLF1, while relative error for the walking speed was between -12.6% and 2.0%. The simulated waveform of the vertical BCoM displacement was found to match the measured signal well. In addition, match between simulated and measured GRF profiles was satisfactory except for one test subject. Regression functions have been established for estimating model parameters, based on which step-by-step procedures have then been proposed for modelling a pedestrian within the population. The results suggest that the DBIP succeeds in modelling pedestrians walking on rigid level surfaces. In the next step the model should be considered for modelling pedestrians on vibrating civil engineering structures.

Fracture Mechanism of Crack-Containing Strata under Combined Static and Harmonic Dynamic Loads Based on Extended Finite Elements

Based on the existing research results, a theoretical fracture model of strata under the compound impact of static and harmonic dynamic load is improved, and the fracture characteristic parameters (stress intensity factor, T-stress, and fracture initiation angle) under the two far-field stress are determined according to the crack dip angle. Additionally, the effects of harmonic dynamic load on the distribution of the stress field and the fracture characteristic (the crack initiation angle, the fracture degree, the number of fracture units, and the fracture area) are further calculated and discussed by theoretical model solution, extended finite element simulation, and the secondary development of the simulation module, respectively. The research results show that the far-field stress, stress intensity factor, and T-stress vary in harmonic form with time under the compound impact of static and harmonic dynamic loads. The frequency of dynamic load affects the number of reciprocal fluctuations of stress intensity factor and T-stress as well as the crack initiation time, but has less influence on the crack initiation angle and fracture degree. While the amplitude of dynamic load affects the stress intensity factor, the extreme value of T-stress and fracture characteristics of the crack. This study has theoretical guiding significance for parameters’ optimization and realization of resonance impact drilling technology.

Study on Failure Characteristics and Rock Burst Mechanism of Roadway Roof under Cyclic Dynamic Load

Rock burst is a catastrophic phenomenon that often occurs in underground rock mass engineering. In order to reveal the essence of rock burst of a hard roof in the process of roadway excavation, the particle discrete element method is used to establish a roadway model and simulate the disturbance of harmonic dynamic load based on the analysis of a rock burst accident in a deep mine. The crack field, stress field, displacement field, and kinetic energy of roadway surrounding rock disturbed by cyclic dynamic load were analyzed, and the disaster mechanism of roadway impacting roof instability was discussed. The results show that, compared with the roadway support structure under static load that can give full play to its control function of surrounding rock, the roadway surrounding rock will collapse and lose stability in a large area under the roof cyclic dynamic load, and the ordinary supporting structure cannot give full play to its control function of surrounding rock, resulting in the surrounding rock destruction and supporting structure failure. In addition, the essence of rock burst in a hard thick roof is due to the instantaneous superposition of static stress and dynamic load, leading to the instantaneous instability and collapse of roadway roof in a large area. The research is of great significance to further understand the deformation and failure mechanism of roadway surrounding rock under strong impact load, to guide the safe production and prevent the occurrence of rock burst hazard in underground rock mass engineering.

Nonlinear Young\u2019s Modulus of New Red Sandstone: Experimental Studies

Young’s modulus of New Red Sandstone was investigated experimentally to gain insight into its nonlinear nature. A large experimental programme was carried out by applying a controllable quasi-static and dynamic uniaxial loading to 286 dry sandstone samples of four different sizes. The static and dynamic tests, similar to those aiming at determining the uniaxial compressive strength, were conducted using the state-of-the-art experimental facilities at the University of Aberdeen including a custom-built small experimental rig for inducing a dynamic uniaxial compressive load via a piezoelectric transducer. The obtained results have confirmed a complex nature of Young’s modulus of sandstone. Specifically, under a harmonic dynamic loading, it shows strongly nonlinear behaviour, which is hardening and softening with respect to frequency and amplitude of the dynamic loading, respectively.

Function and Application of Geogrid in Flexible Pavement under Dynamic Load

Nowadays, the increasing demand for road transport makes maintenance and repair of road infrastructures key tasks of road engineering. The current experimental work consists of laboratory model experiments to understand the conduct of sand as a subgrade under dynamic load and its effect on the flexible pavement and base layer. The reinforcement is applied at the interface between the base and subgrade using SS2 type of geogrid. The road layers are exposed to harmonic dynamic load with two load amplitudes of 10 and 15 kN and two frequencies of 0.5 and 1 Hz. The vertical stresses in the road layers are measured using stress a gauge sensor. In the case of a reinforcing geogrid in the middle of the base course, the stress decreases by increasing the frequency and load amplitudes by about (23-42(. The best position for geogrid is in the middle of the crushed stone layer because it gives the lower displacement. In the case of a reinforcing layer at the middle of the base course layer, the stress and vertical displacement decrease with increasing in frequency and load amplitudes. When laying the geogrid between the base course and subgrade, a lower decrease in the stress and vertical displacement could be obtained with the increase in frequency and loads.

Reproducing vertical human walking loads on rigid level surfaces with a damped bipedal inverted pendulum

This study is motivated by the lack of a systematic way to reproduce vertical human walking loads with a damped bipedal inverted pendulum (DBIP). Measurements of vertical human walking loads for a sample of 16 Chinese test subjects were carried out with a non-commercial force plate on rigid surfaces, in which 2393 single-step forces were recorded and analyzed. The mean value of all the test subjects’ average step frequency of free walking is 1.73 Hz, which is lower than the reported data for other populations. Most test subjects are naturally slow walkers, whose first four harmonics dynamic load factors are found to be less than the well-reported data. Only the first harmonic dynamic load factor has a clear trend to increase with the step frequency. The best linear fitting curve is given in the form of y = a(x + b), in which a = 0.24 and b = −0.82. A previously developed DBIP, which can be described by four dimensionless parameters, i.e. the dimensionless energy input, leg stiffness, leg damping, and the attack angle, is then applied to reproduce these measured forces. The simulated force with a minimum root of the mean square error to the measured force is selected and calibrated to the required step frequency and amplitude, which usually has a smaller peak force compared with the measured data. The adopted model inputs are illustrated as functions of step frequencies. The DBIP is applicable for modelling part of the test subjects’ walking loads on rigid surfaces at different step frequencies.

DYNAMIC BIAXIAL STRESS ANALYSIS OF FLAT LAYERED CERAMIC COMPOSITES

We study theoretically the biaxial bending of symmetric, flat layered ceramic composites (laminates) due to external loading. We focus on three-layered alumina/zirconia laminates. We compare the principal stresses in the samples in the case of static and harmonic dynamic loading. The dynamic equation within the Kirchhoff theory for thin homogeneous plates is first generalized to the case of multilayered plates. It is solved numerically with the relaxation method, which we have developed for this purpose.

Distribution of Stresses in Reinforced and Unreinforced Flexible Pavement Layers under Dynamic Load

Nowadays, the increasing demand for road transport makes maintenance and repair of road infrastructures key tasks for road engineering. The current experimental work consists of laboratory model experiments to understand the conduct of sand as a subgrade under dynamic load and its effect on the flexible pavement and base layer. Geogrid reinforcement was applied at the interface between the base and subgrade using SS2 type of geogrid. The road layers were exposed to harmonic dynamic load with two load amplitudes 10 and 15 kN and two frequencies 0.5 and 1 Hz. The vertical stresses in the road layers are measured using stress gauge sensor. It revealed that when laying the geogrid between the base course and subgrade and when base course thickness is 150 mm, the stress and displacement decreased with increase in the frequency and load amplitudes. But in the case of reinforcing layer at the center of the base course layer, the displacement decreased with increase in the frequency and loads except for one case when the load was 15 kN and frequency 0.5 Hz. It can be suggested that the maximum vertical displacement increased with the increase of base course thickness for both reinforced and unreinforced base layers. Also, it can be observed that the vertical stress increased by increasing the base course layer-thickness for unreinforced models.

A numerical method of lower bound dynamic shakedown analysis for 3D structures

PurposeThe safety assessment of engineering structures under repeated variable dynamic loads such as seismic and wind loads can be considered as a dynamic shakedown problem. This paper aims to extend the stress compensation method (SCM) to perform lower bound dynamic shakedown analysis of engineering structures and a double-closed-loop iterative algorithm is proposed to solve the shakedown load.Design/methodology/approachThe construction of the dynamic load vertexes is carried out to represent the loading domain of a structure under both dynamic and quasi-static load. The SCM is extended to perform lower bound dynamic shakedown analysis of engineering structures, which constructs the self-equilibrium stress field by a series of direct iteration computations. The self-equilibrium stress field is not only related to the amplitude of the repeated variable load but also related to its frequency. A novel double-closed-loop iterative algorithm is presented to calculate the dynamic shakedown load multiplier. The inner-loop iteration is to construct the self-equilibrated residual stress field based on the certain shakedown load multiplier. The outer-loop iteration is to update the dynamic shakedown load multiplier. With different combinations of dynamic load vertexes, a dynamic shakedown load domain could be obtained.FindingsThree-dimensional examples are presented to verify the applicability and accuracy of the SCM in dynamic shakedown analysis. The example of cantilever beam under harmonic dynamic load with different frequency shows the validity of the dynamic load vertex construction method. The shakedown domain of the elbow structure varies with the frequency under the dynamic approach. When the frequency is around the resonance frequency of the structure, the area of shakedown domain would be significantly reduced.Research limitations/implicationsIn this study, the dynamical response of structure is treated as perfect elastoplastic. The current analysis does not account for effects such as large deformation, stochastic external load and nonlinear vibration conditions which will inevitably be encountered and affect the load capacity.Originality/valueThis study provides a direct method for the dynamical shakedown analysis of engineering structures under repeated variable dynamic load.

Robust Optimal Tracking Control of a Full-Bridge DC-AC Converter

This paper develops a full-bridge DC-AC converter, which uses a robust optimal tracking control strategy to procure a high-quality sine output waveshape even in the presence of unpredictable intermissions. The proposed strategy brings out the advantages of non-singular fast convergent terminal attractor (NFCTA) and chaos particle swarm optimization (CPSO). Compared with a typical TA, the NFCTA affords fast convergence within a limited time to the steady-state situation, and keeps away from the possibility of singularity through its sliding surface design. It is worth noting that once the NFCTA-controlled DC-AC converter encounters drastic changes in internal parameters or the influence of external non-linear loads, the trembling with low-control precision will occur and the aggravation of transient and steady-state performance yields. Although the traditional PSO algorithm has the characteristics of simple implementation and fast convergence, the search process lacks diversity and converges prematurely. So, it is impossible to deviate from the local extreme value, resulting in poor solution quality or search stagnation. Thereby, an improved version of traditional PSO called CPSO is used to discover global optimal NFCTA parameters, which can preclude precocious convergence to local solutions, mitigating the tremor as well as enhancing DC-AC converter performance. By using the proposed stable closed-loop full-bridge DC-AC converter with a hybrid strategy integrating NFCTA and CPSO, low total harmonic distortion (THD) output-voltage and fast dynamic load response are generated under nonlinear rectifier-type load situations and during sudden load changes, respectively. Simulation results are done by the Matlab/Simulink environment, and experimental results of a digital signal processor (DSP) controlled full-bridge DC-AC converter prototype confirm the usefulness of the proposed strategy.

Design of nine step switched capacitor multilevel inverter and its cascaded extension

SummaryConventionally, multilevel inverter topologies require components like boost converter, voltage balancing circuits in addition to its switches and gate driver circuitry resulting in increased complexity. A new multilevel inverter topology using the concept of switched‐capacitor (SC) is proposed in this article. The basic structure capable of generating 9 level (9L) output voltage waveform with magnitude twice the input voltage at its terminals is proposed. Further, two identical structures are cascaded horizontally to attain 17 level (17L) based on structural modification is suggested. Simulation results are used to analyze the performance of the proposed 9L‐SCMLI and 17L‐SCMLI in the aspects of total harmonic distortion, R, RL, and dynamic loading conditions. The 9L‐SCMLI prototype model is developed to validate the adaptability of the proposed system.

A damped bipedal inverted pendulum for human–structure interaction analysis

The bipedal inverted pendulum with damping has been adopted to simulate human–structure interaction recently. However, the lack of analysis and verification has provided motivation for further investigation. Leg damping and energy compensation strategy are required for the bipedal inverted pendulum to regulate gait patterns on vibrating structures. In this paper, the Hunt–Crossley model is adopted to get zeros contact force at touch down, while energy compensation is achieved by adjusting the stiffness and rest length of the legs. The damped bipedal inverted pendulum can achieve stable periodic gait with a lower energy input and flatter attack angle so that more gaits are available, compared to the template, referred to as spring-load inverted pendulum. The measured and simulated vertical ground reaction force-time histories are in good agreement. In addition, the dynamic load factors are also within a reasonable range. Parametric analysis shows that the damped bipedal inverted pendulum can achieve stable gaits of 1.6 to 2.4 Hz with a reasonable first harmonic dynamic load factor, which covers the normal walking step frequency. The proposed model in this paper can be applied to human–structure interaction analysis.

Experimental Investigation on Human Walking Loading Parameters and Biodynamic Model

As part of a project to calibrate a biodynamic model of a walking person in view of the dynamic interaction with flexible structures, the paper aims at the determination of the dynamic load factors and corresponding phase angles of the Fourier series function representative of the load and the investigation on the consistency of the proposed biodynamic model. An experimental campaign was conducted with 53 people that walked individually along an instrumented rigid platform to measure the vertical ground force simultaneously to the acceleration of their waist. Expressions of the dynamic load factors were adjusted to the data and compared to results reported in the literature. The signals of the reaction forces and corresponding pedestrian accelerations are revealed to be in phase as expected by the mathematical formulation of the proposed biodynamic model. The first harmonic load factor expressed as a function of the step frequency displayed lower values compared to others researcher’s expressions. For this load factor, the subject height is shown to be a significant parameter especially for lower step frequency range in which taller people yield values up to 20% greater than shorter one did. The consistency of the proposed biodynamic model was demonstrated thus enabling the research continuity. Distinct employed procedures and pedestrian number and characteristics may explain the differences found between the present results and those of the literature. A new expression to the first harmonic dynamic load factor is offered in the paper in which not only the step frequency is considered but also the person’s height.

Numerical Study on the Elastic Deformation and the Stress Field of Brittle Rocks under Harmonic Dynamic Load

In order to study the deformation displacement and the stress field of brittle rocks under harmonic dynamic loading, a series of systematic numerical simulations are conducted in this paper. A 3D uniaxial compression simulation is carried out to calibrate and determine the property parameters of sandstone and a model of the cylindrical indenter intruding the rock is proposed to analyze the process of elastic deformation. Four main parameters are taken into account, namely the position on the rock, the frequency and the amplitude of dynamic load, the type of indenter and the loading conditions (static and static-dynamic). Based on the analysis undertaken, it can be concluded that both of the deformation displacement and stress field of the rock change in a harmonic manner under the static-dynamic loads. The frequency and the amplitude of harmonic dynamic load determine the period and the magnitude of the rock response, respectively. In addition, the existence of harmonic dynamic load can aggravate the fatigue damage of the rock and allow a reduction in static load. Our investigations confirm that the static-dynamic loads are more conducive to rock fracture than static load.

Effect of mode of vibration on the response of machine foundation on sand

In this paper, the influence of the following parameters on different modes of vibration response of model footings on sand is studied: (vertical, rocking and pitching load amplitude and frequency). To achieve the objective of this study, the model footing was selected to be rectangular footing with an aspect ratio (L/B= 1.33) i.e (L= length and B= width). A physical model was manufactured to simulate a steady-state harmonic dynamic load applied at different operating frequencies with the same load amplitude (0.5 ton). A total of (9) cases was performed taking into account different parameters. The loading frequency ranged from (0.5) to (2) Hz and the footing was rectangular with an aspect ratio (L/B = 1.33). The soil type used was dry sand having a relative density of (50%). The behavior of the soil underneath the footing was examined by measuring the strain using a shaft encoder and the amplitude of displacement using a vibration meter. It was found that the change in vibration mode made little effect of the final strain values under the same frequency and the amplitude of displacement in (Z) direction, while the amplitude of displacement in (Y) is higher, occuring under rocking vibration and higher value amplitude of displacement in (X) direction under pitching vibration under the same frequency.

Fuzzy Input Parameters Influence on the Oscillation of a 2D Frame Structure Subjected to Harmonic Dynamic Load

In [1], we presented a new method for solving the fuzzy differential equations of oscillation with fuzzy input parameters. The new method is based on the domain mode analysis method combined with a differential evolution algorithm to determine the fuzzy output parameters and the fuzzy displacements at each floor of the frame. In this article, we continue to develop and expand the solution of the fuzzy vibration differential equations of the 2D frame under the excitation of harmonic dynamic load. The solution based on the domain mode analysis method is combined with a hybrid crossover differential evolution algorithm. This algorithm is more advanced than previous traditional differential evolutionary optimizations because it converts quickly and prevents the search process from falling into a local solution. An example for illustrating the algorithm is to analyse the oscillation of the 2-span and 9-storey 2D frame structure subjected to harmonic dynamic load with fuzzy input parameters. The calculation results in the MATLAB software show the results of the fuzzy displacements and fuzzy internal force of the frame. Next, they show the relationship between the oscillation frequency and the displacement and moment of the frame structure. This is important and should be considered in the design as well as in the reliability assessment of the structures.

Evaluation of Full Interaction Composite Columns Subjected to Static and Dynamic Loading

Composite column such as other columns made from two or more materials worked as partially or fully. The composite column consists of hot steel section with filled reinforced concrete behaving as compression member and mainly to resisting axial force and moments. The high strength capacity of composite columns with a reduction in cross-sectional area as compared with the reinforced concrete columns gave benefits to adopt this type of construction in building, especially in high-rise and complex buildings. In this paper, an evaluation of composite columns under the effects of static and dynamic loadings to check the adequacy of such composite column that analyzed and designed under static load and then after subjected to dynamic load. Theoretical analysis and numerical solution by finite element approach through ANSYS software program are adopted and assumed that full interactions between reinforced concrete and steel section to check out the performance of composite column taking into account parameters such as loading type as static and dynamic loading, concrete type and method of analysis as modal and harmonic dynamic loading. The results showed that the increasing of core concrete strength delayed the occurrence of local buckling of steel tube. Therefore, the harmonic analysis must be taken into account to check out in the analysis and adopted in the design of composite column in case of the presence of this type of dynamic loading because of the performance of the column is different under this type of loading.

Performance of Self-Compacted Reactive Powder Concrete Slab Under Harmonic Dynamic Loading

Many types of loading the structure must sustain in addition to dead and live loads according to the function of structural element type that must be taken in analysis. Dynamic resistance to loading of reinforced concrete slabs using self-compact reactive powder concrete, with different boundary conditions at the sides in addition of static loading was studied. The reinforced concrete slabs were designed under static load according to ACI-318R-2014 and then the adequacy was checked under harmonic dynamic loading. The static loading consists of dead load and residential live load considering according to ASCE-07-2010. Modeling analysis was performed to determine the eigenvalues and eigenvectors values and then frequency response analyses of the slab by finite elements method that adopted for analysis. The results indicated that in case of self-compacted reactive powder concrete rather than normal concrete gave deflection less and also there was a different result of deflection according the type of slab boundary condition supports.

Investigation of Optimum Helix Angle of a Wire Rope Subjected to Harmonic Dynamic Loading

Investigation of Optimum Helix Angle of a Wire Rope Subjected to Harmonic Dynamic Loading

Stress Concentration of One Microvoid Embedded in an Adhesive Layer under Harmonic Load

AbstractThis paper investigates the stress concentration of an adhesive material containing a micro air void subjected to a harmonic dynamic surface load. The elastodynamic Green’s function was use...