Dynamic Load Factor Research Articles

Membrane Action of Cladding Subjected to Blast Loading and Effects on the Supporting Structure

A recent blast design trend is to properly select cladding characteristics in order to limit blast consequences on its supporting structure. In this context, it is worth noting that cladding components may exhibit significant membrane action, and its effects may be decisive for the supporting structure. The main focus of the present study was to examine these effects through two-step dimensionless SDOF analyses, aimed at reaching conclusions that would be applicable to a large variety of cladding/supporting structure arrangements. The results of these analyses are presented by employing the dynamic load factor, representing the maximum supporting structure displacement. It was found that cladding membrane action has adverse effects over its supporting structure, as it does not allow for extensive plastic dissipation and leads to higher support reactions. On the contrary, insignificant membrane action leads to lower dynamic load factor for the supporting structure. Thus, membrane behavior should be activated only as a safety backup action in order to prevent cladding failure. A case study of a typical cladding/supporting structure is presented to demonstrate and verify the proposed two-step SDOF analyses and the obtained results.

A Simplified Design Model for Modular Steel Buildings Subject to Vapor Cloud Explosions (VCEs)

Background: Modular steel buildings (MSB) are extensively used in petrochemical plants and refineries. Limited guidelines are available in the industry for analysis and design of (MSB) subject to accidental vapor cloud explosions (VCEs). Objectives: The paper presents simplified engineering model for modular steel buildings (MSB) subject to accidental vapor cloud explosions (VCEs) that are extensively used in petrochemical plants and refineries. Method: A Single degree of freedom (SDOF) dynamic model is utilized to simulate the dynamic response of primary building components. Analytical expressions are then provided to compute the dynamic load factors (DLF) for critical building elements. Recommended foundation systems are also proposed to install the modular building with minimum cost. Results: Numerical results are presented to illustrate the dynamic response of (MSB) subject to blast loading. It is shown that (DLF)=1.6 is attained at (td/t)=0.4 for front wall (W1) with (td/T)=1.25. For side walls (DLF)=1.41 and is attained at (td/t)=0.6. Conclusions: The paper presented simplified tools for analysis and design of (MSB) subject accidental vapor cloud blast explosions (VCEs). The analytical expressions can be utilized by practitioners to compute the (MSB) response and identify the design parameters. They are simple to use compared to Finite Element Analysis.

Dynamic instability, free vibration, and buckling analysis of MR fluid sandwich plates with FG face layers using the HSDT-based finite strip method

In the present study, by using a higher-order shear deformation plate theory (HSDT) and considering the second model proposed by Frostig and Thomsen, Dynamic instability, static buckling, and free vibration of the Magneto-Rheological (MR) fluid sandwich plates subjected to an axial periodic force is investigated. MR fluids are a group of smart materials whose rheological properties change rapidly with the application of a magnetic field. The upper and lower layers of the core (face layers) are selected from two different types. In the first group, they are made of functionally graded materials (FGMs), and the second group, consists of a matrix phase reinforced with carbon nanotubes (CNTs). The mechanical properties of the nanocomposite are considered in accordance with the extended rule of mixtures. The governing equations are derived using Hamilton’s principle and discretized by the finite strip method. The results obtained from the finite strip method are compared with the results of available literature. The impact of various parameters such as magnetic field intensity, core thickness, static and dynamic load factors, different boundary conditions, and the CNT distribution on the critical static buckling, natural frequency, and instability zone of the structure are investigated. The results show that increasing the MR fluid thickness has a stabilizing effect on the dynamic instability of the MR fluid sandwich plates.

Evaluation of the Variation in Dynamic Load Factor Throughout a Highly Skewed Steel I-Girder Bridge

The Dynamic Load Factor (DLF) is defined as the ratio between the maximum dynamic and static responses in terms of stress, strain, deflection, reaction, etc. DLF adopted by different design codes is based on parameters such as bridge span length, traffic load models, and bridge natural frequency. During the last decades, a lot of researches have been made to study the DLF of simply supported bridges due to vehicle loading. On the other hand, fewer works have been reported on continuous bridges especially with skew supports. This paper focuses on the investigation of the DLF for a highly skewed steel I-girder bridge, namely the US13 Bridge in Delaware State, USA. Field testing under various load passes of a weighed load vehicle was used to validate full-scale three-dimensional finite element models and to evaluate the dynamic response of the bridge more thoroughly. The results are presented as a function of the static and dynamic tensile and compressive stresses and are compared to DLF code provisions. The result shows that most codes of practice are conservative in the regions of the girder that would govern the flexural design. However, the DLF sometimes exceeds the code-recommended values in the vicinity of skewed supports. The discrepancy of the DLF determined based on the stress analysis of the present study, exceeds by 13% and 16% the values determined according to AASHTO (2002) for tension and compression stresses respectively, while, in comparison to BS5400, the differences reach 6% and 8% respectively.

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.

Investigation of dynamic buckling of fiber metal laminate thin-walled columns under axial compression

This paper presents an investigation of the dynamic buckling phenomenon in thin-walled Fiber Metal Laminate short columns subjected to axial compressive loading. The numerical analysis is performed with the FEM ANSYS software for three profiles differentiate in the laminate stacking sequence. Two groups of criteria were implemented to assess the structure resistance to dynamic pulse loading: the dynamic buckling criteria and strength failure criteria. Parametric analysis was performed to determine the effect of initial geometric imperfection, laminate stacking sequence, and the pulse load's shape on the dynamic stability. The value of the amplitude of initial geometric imperfection and the shape of pulse load influence the value of critical Dynamic Load Factor strongly. Aluminium yielding was observed as the primary failure source developed in the FML structure subjected to the pulse loading.

Non-linear response and buckling of imperfect laminated composite plates under in-plane pulse forces

This study presents a semi-analytical solution of the non-linear dynamic response, shock spectrum, and dynamic buckling of an imperfect angle-ply laminated composite plate under various types of in-plane pulse forces. The laminated composite plate is modeled using a higher-order shear deformation theory and von-Kármán geometric nonlinearity. The non-linear governing partial differential equations (PDEs) of imperfect laminated composite plates are derived via Hamilton’s principle. Using Galerkin’s method, the non-linear PDEs are transformed into non-linear algebraic equations for the static stability problems and non-linear ordinary differential equations for the dynamic problem such as dynamic response, shock spectrum, and dynamic buckling. The buckling load of the plate is obtained through the associated eigenvalue problem. The static failure load of the composite plate is evaluated using the post-buckling analysis based on the Tsai-Wu failure criterion. The dynamic response and shock spectrum of the composite plate are determined via Newmark’s method. The dynamic failure load of the plate is evaluated using Newmark’s method based on the Tsai-Wu failure criterion. Dynamic buckling is to be characterized by dynamic load factor (DLF), which is represented as the ratio of the dynamic failure load to the static failure load. Based on the pulse/shock duration time, the pulse forces are divided into three loading regimes known as impulsive, dynamic, and quasi-static. The study revealed that the DLF values are > 1, < 1, and [Formula: see text]1 respectively for the case of impulsive, dynamic, and quasi-static loading regimes of pulse force. The influences of various types of in-plane pulse forces, amplitude and time duration of pulse forces, and amplitude of initial geometric imperfections on the non-linear dynamic response, shock spectrum, and dynamic buckling behavior of the laminated composite plate are addressed in detail. The results will help in the appropriate design of the laminated composite plate against dynamic buckling.

Nonlinear Response and Buckling of Imperfect Plates Under In-Plane Pulse Forces: A Semi-analytical Investigation

This study presents a semi-analytical solution of the nonlinear dynamic response, shock spectrum, and dynamic buckling of a simply supported imperfect plate under various types of in-plane pulse forces. Here, the plate is modelled based on higher-order shear deformation theory (HSDT) considering the von-Karman geometric nonlinearity. The governing nonlinear partial differential equations (NLPDEs) of the imperfect plates are developed via Hamilton’s principle. Using Galerkin’s method, the NLPDEs are converted into sets of nonlinear algebraic equations (NLAEs) for static stability problems and nonlinear ordinary differential equations (NLODEs) for dynamic problems. The critical buckling load of the plate is obtained through the associated eigenvalue problem. The static failure load of the plate is evaluated using nonlinear static stability analysis based on the yield stress failure criterion. The dynamic response and shock spectrum of the plates are plotted via Newmark’s method. The dynamic failure load of the plate is evaluated using Newmark’s method based on the yield stress failure criterion. Dynamic load factor (DLF) is the ratio of dynamic failure load to static failure load. Based on the pulse duration time, the pulse forces are divided into three categories known as impulsive, dynamic, and quasi-static. In the case of impulsive, dynamic, and quasi-static loading regimes, DLF > 1, DLF < 1, and DLF $$\approx$$ 1, respectively. The results obtained from the current works will help in the appropriate design of the imperfect plates against dynamic buckling.

Characteristics analysis of the new flexible ring gear for helicopter reducer

As a key component of the vibration generation and transmission of planetary transmission system, the design of ring gear will directly affect the vibration of the system. After considering the advantages and disadvantages of the traditional ring gear structure, the new flexible ring gear was designed by scholars and applied to helicopter reducer. There is a dearth of reported analysis in the meshing characteristics of the new flexible ring gear, which leads to the blind selection of the ring gear. By building an accurate parametric finite element model, the meshing characteristics of the new flexible ring gear and the difference in dynamic characteristics between the new flexible ring gear and the traditional ring gear are obtained. The analysis shows that the new ring gear is superior to the traditional ring gear in many aspects, but it also has the characteristic of unbalance loading on the tooth surface. In addition, a test method is proposed to accurately measure the load sharing coefficient and dynamic load factor of planetary transmission and the simulation results of flexible ring gear are verified by comparison.

Enhancing Design Features of Asymmetric Spur Gears Operating on a Specified Center Distance Using Tooth Sum Altered Gear Geometry

Asymmetric gears have evolved from the rising demand for power transmission drives with high load-carrying capacity, surface durability, and service life. Direct design and S± profile shifted system are the most common approaches used for enhancing design features by geometry modification in asymmetric gears. This paper aims at establishing asymmetric gear geometry modification using tooth sum alteration for a family of gears running on a specified center distance as a feasible design approach. A complete mathematical treatment of the design approach is provided, and an in-house developed computer program is used for numerical simulation. The paper explores the influence of dynamic load factors, location factors for bending, specific sliding on load-bearing capacity, and surface durability on different tooth sum alterations. The study concludes that tooth sum altered asymmetric gear geometry can be employed as an effective design technique that offers designers flexibility in designing gears for surface wear, load-bearing, and tooth life.

Design and dynamic performance analysis of high-contact-ratio spiral bevel gear based on the higher-order tooth surface modification

To reduce the running vibration of high-contact-ratio (HCR) spiral bevel gear transmissions, an innovative higher-order tooth surface modification (HTSM) method is proposed to reduce the vibration excitation of gear transmission. First, according to the meshing characteristic of HCR spiral bevel gear transmissions, an innovative modification curve is proposed. Second, the auxiliary tooth surface modification (ATSM) method is used to generate the higher-order modified spiral bevel gear. Third, the loaded transmission error (LTE) and meshing impact (MI) of higher-order modified spiral bevel gear transmissions are calculated based on the LTCA method and the impact theory while considering tooth deformation. Last but not least, based on the ease-off technology, an optimization model is built to reduce the LTE and MI of HCR spiral bevel gear transmissions. Through simulation analysis, it is found that compared with the second-order modified spiral bevel gear, the high-order tooth surface modification method can not only effectively reduce the LTE, MI and dynamic load factor (DLF) of HCR spiral bevel gear, but also improve its dynamic performance within full speed range. This study provides an effective way for improving the dynamic performance of HCR spiral bevel gear transmissions within full speed range.

Meshing Stiffness Parametric Vibration of Coaxial Contrarotating Encased Differential Gear Train

Planetary gears are widely used in mechanical transmission systems, but the vibration and noise affect their reliability and life. In this paper, the torsional dynamic model of an encased differential planetary gear with coaxial contrarotating outputs considering the time-varying meshing stiffness, damping, and phase difference of all gear pairs is established. By solving the equations of the derived system, three types of natural frequencies with different multiplicities of the system are obtained. The multiscale method is used to study the parametric vibration stability caused by the time-varying meshing stiffness, and the results are verified by numerical simulation. The dynamic characteristics of elastic meshing force are analyzed from time domain and frequency domain. The variation of the dynamic load factor of each gear pair with input speed and the relationship between its peak position and the natural frequency of the derived system are discussed. The results show that there is an unequal coupling phenomenon of meshing frequency between the meshing forces of different planetary sets. In the absence of external excitation, the meshing stiffness parameters not only excite the main resonance response of the system but also cause superharmonic resonance, subharmonic resonance, and combined resonance.

Parameters Optimization and Energy Absorption Evaluation of the Steel Ball Friction Energy Absorber

The energy absorber is used to simulate the reaction of a working piece subjected to a vibration stimulus, by which the consistent and repeatable reactions to the tool’s vibration inputs could be achieved. According to the proposed coupling simulation model by using commercial software RecurDyn and EDEM, the energy dissipated by the energy absorber and the contact force between the drill rod and the piston are evaluated under different load conditions such as the impact frequency and impact stroke. Moreover, the effects of the ball diameter, ball column height, and diameter on the energy absorption characteristics are also studied. The results show that the impact frequency and stroke influence the energy absorber by changing the impact force; the energy absorption is more obvious under higher impact frequency and long impact stroke. The filling ball diameter influences the energy reflectivity by changing the porosity, which is negatively correlated to the energy reflectivity, and a 6 mm filling ball diameter is suggested. The energy reflectivity is inversely proportional to the ball column height and diameter, and the suggested ball column diameter and height are 160 mm and 600 mm, respectively, with energy reflectivity of 0.045. Even when the increase in impact frequency and stroke will increase the contact force, the dynamic load factor decreases. The contact force and dynamic load factor are inversely proportional to the ball column height, but they are not influenced by the ball diameter and the ball column diameter.

Static and dynamic instability analysis of tapered CNTRC sandwich plates under uniform and non-uniform in-plane loadings using spline finite strip method

This paper presents the buckling analysis of rectangular sandwich plates with pure polymeric tapered cores and functionally graded carbon nanotube (FG-CNT) reinforced composite face sheets under static and harmonic dynamic loads. One uniform and four linearly-varying patterns are considered for the applied in-plane loads. The effective material properties of face sheets, in which the polymeric matrix is reinforced with aligned single-walled carbon nanotubes (SWCNT), are estimated using the extended rule of mixture. A higher-order zigzag shear deformation theory, which has the same number of dependent unknowns as the first-order theory, is employed to express the plate's displacement field. The governing equations are derived using Hamilton's principle and discretized by the spline finite strip method. The dynamic instability regions of plates with uniform and variable thickness are obtained by employing Bolotin's method. The accuracy of the present method is demonstrated by considering the problems for which solutions are available. A detailed numerical study is conducted to examine and compare the effects of different parameters, including the taper angle, type of the applied in-plane load, static and dynamic load factors, length-to-width ratios, the volume fraction of CNT, distribution pattern of CNTs along the thickness direction, temperature, and boundary conditions on the behavior of sandwich plate.

Meshing impact analysis of planetary transmission system considering the influence of multiple errors and its effect on the load sharing and dynamic load factor characteristics of the system

The meshing impact on transmission system and internal meshing gear pair and its impact on the load sharing and dynamic characteristics of the system are not well understood yet. In this paper, the meshing impact models of internal gear pairs and planetary transmission system were successfully constructed, and the meshing impact point, meshing impact time and meshing impact force were accurately obtained. Meshing impact in gear transmission system is obviously affected by eccentricity error, installation error, and other errors. Due to the difference in error of each component, the internal and external gears of each branch lead to different meshing positions, which causes the constant change in meshing impact point, meshing impact time and meshing impact force. This creates difficulties in the analysis of meshing impact characteristics of gear transmission system. Load Tooth Contact Analysis (LTCA) method can be used to accurately analyse the change in position of gear tooth under load condition. Through the dynamic model of planetary transmission system, the influence in component errors on the contact position of tooth surface is obtained. Combining the loaded transmission error of the tooth surface under load and the geometric transmission errors under the influence of component errors, the model of meshing impact for accurately solving the system is deduced, and the influence of meshing impact on the system's load sharing coefficient and dynamic load factor coefficient is analysed. By comparing the planetary transmission system before and after considering the meshing impact of the system, it is found that the system's load-sharing coefficient increases slightly, dynamic load factor coefficient fluctuates significantly, and meshing force becomes more clutter after considering meshing impact.

Pedestrian-Induced Load Identification from Structural Responses Using Genetic Algorithm with Numerical and Experimental Validation

A reliable pedestrian load model is a prerequisite for the accurate calculation of human-induced structural vibration. In recent years, many researchers have proposed pedestrian load models based on direct force measurements, such as force plates. However, direct measurement techniques often suffer from incapability when applied to real structures in operation and can hardly be used to measure crowd loads. In this paper, an inverse load identification method is proposed to extract pedestrian vertical load from structural responses. Through a genetic algorithm, the pedestrian’s pacing frequency, dynamic load factors, and phase angles in the Fourier-series model are identified from structural acceleration responses. The proposed algorithm is further investigated for the identification of multiple-pedestrian load parameters, where structural displacement responses are used to give an equivalent number of pedestrians. Numerical examples demonstrate that the pedestrian load parameters are estimated with high accuracy and robustness against noise and modeling errors. A sensitivity analysis is given to explain the different estimation accuracies among the parameters. Finally, the proposed method is validated through an experimental test, showing its practicality for identifying pedestrian loads in real structures.

Pulse Buckling of a Thin Walled CFRP Cylindrical Shell – A Numerical Approach

The present study investigates the behaviour of a CFRP cylindrical shell under compressive pulse loading. The in-pulse analyses are performed numerically, using the finite element code ABAQUS. The dynamic buckling load is determined using the Budiansky & Hutchinson criterion. Parameters like the shape of pulse loading and pulse duration were varied, and their influence on the Dynamic Load Factor (DLF) was investigated. The investigation shows that DLF tends to increase well above unity for short duration impulses, while for the larger duration the value is decreasing towards unity. The shape of the pulse also has a significant influence on the DLF value. DLF<1 was found only for a trapezoidal pulse. For sinusoidal pulse shape, the static buckling load of the CFRP shell was consistently below the dynamic one.

Dynamic loads in self-aligning gear transmissions of heavy loaded machines

Purpose. Development of a mathematical model of a heavy loaded gear transmission with a self-aligning drive gear; evaluation of the dynamic load on the gear transmission in the gear alignment process. Methodology. The calculation schematic and equations of the relative motion of the self-aligning drive gear are formed using the methods of rigid body dynamics. Analytical expressions for the gear self-alignment time, collision velocity during the alignment and dynamic load factor are obtained by integrating an ordinary differential equation. Methods of the linear theory for oscillations are used to determine the dynamic factor. Findings. The article investigates the state-of-art design and mathematical models of the self-aligning gear. An equation for the relative motion of the moving part of the gear has been formed using the methods of rigid body dynamics. It is shown that by using the proposed hypotheses, the movement of the gear can be reduced to rotation about the instantaneous axis. The influence of geometric and dynamic parameters of the ball mill drive on dynamic loads in the open gear transmission is investigated. The gear alignment speed dependences on the tooth mesh misalignment angle in the gear transmission and the inertial parameters of the gear have been obtained. The obtained dependencies were used to calculate the time and speed of the gear alignment in the open gear transmission of the ball mill 5.5 6.5 (central discharge ball mill). It is shown that in the real range of mesh misalignment angles and gear parameters, the time of the gear alignment is several orders of magnitude less than the time of teeth re-engagement. In the presence of the variable component of the mesh misalignment angle, the gear will constantly make a relative motion with strikes; depending on the current value of the mesh misalignment angle, the dynamic load on the gear transmission can be significant. It is shown that when assessing the efficacy of self-aligning gears, it is necessary to take into account a possible increase in dynamic loads. The dynamic factor and the load factor are calculated for the nominal value of the mesh misalignment angle in the open gear transmission of 5.5 6.5 ball mills. Originality. A mathematical model of the dynamics of a self-aligning gear transmission in heavy duty machine drives has been developed. A quantitative assessment of internal dynamic load factor in an open gear transmission of 5.5 6.5 ball mills has been carried out. Practical value. A method for determining the dynamic component of the load on a gear transmission containing a self-aligning drive gear has been developed.

Numerical and experimental study of the dynamic factor of the dynamic load on the urban railway

Abstract This paper presents simulation calculations and experimental measurements to determine the dynamic load factor (DLF) of train on the urban railway in Vietnam. Simulation calculations are performed by SIMPACK software. Dynamic measurement experiments were conducted on Cat Linh – Ha Dong line. The simulation and experimental results provide the DLF values with the largest difference of 2.46% when the train speed varies from 0 km/h to 80 km/h

Influences of gear design parameters on dynamic tooth loads and time-varying mesh stiffness of involute spur gears

Gears are one of the most significant machine elements in power transmission due to the many advantages such as high load capacity, long life, and reliability. Due to the increasing power and speed values, the characteristics expected from the transmission elements are also increasing. Significant changes occur in the dynamic behavior of the gears at high speed due to the resonance. For this reason, determining the resonance frequencies is becoming an important issue for designers. This paper presents a method for determining the resonance regions of the gear system under different design parameters. The main purpose of this study is to examine the effects of different gear design parameters on spur gear dynamics. For this aim, the effects of these parameters on the mesh stiffness and contact ratio are examined, and the interaction of mesh stiffness, contact ratio, and dynamic response is presented. Different mesh stiffness calculation methods used to calculate time-varying mesh stiffness and a parametric gear dynamic model are proposed. To solve the equations of motions, a computer program is developed in MATLAB software. Five different design parameters, which are teeth number, pressure angle, reduction ratio, profile shifting factor, addendum factor, and damping ratio, are taken into consideration. The dynamic factor variation is calculated for 1600 rpm a constant pinion speed for each parameter for a single mesh period. Furthermore, the dynamic factor is calculated for the pinion speed between 400–30000 rpm and the frequency response and the resonance regions of the gear system are defined. As a result of the study, the profile shifting and the addendum factor are the most effective two parameters on the gear dynamics. Also, the contact ratio and mesh stiffness have a great effect on the dynamic response of the system. The methods decreasing dynamic load factors are also discussed at the end of the study.