Forcing Frequency Research Articles

A New Function for Frequency Analysis in the Risk Assessment of Offshore Oil-Related Platforms

_ Risk assessment of offshore oil-related platforms such as the floating production storage and offloading system (FPSO) is extremely important. In earthquakes prone to target sea areas, earthquakes should be considered as one of the important external forces that cause severe damage. In such risk assessments, for estimating the appearance frequency of seismic energy, the complementary cumulative distribution function (CCDF) of seismic energy of a considered area is usually based on the Gutenberg–Richter law. Furthermore, it is important to estimate the CCDF of the leak hole diameter when estimating the damage caused by an oil spill accident in an offshore oil-related platform. Some ship classification societies recommend using a formula based on the power law distribution as used in those processes. However, the power law distribution has a drawback in that, i.e., it is essentially impossible to accurately estimate the CCDF over the entire domain of the random variables. The authors have developed an enhanced power law distribution function that eliminates such defects in the power law distribution function and some practical methods for estimating its parameters. In this study, the developed function is applied to the CCDFs of the seismic energy and leak hole diameter. The results demonstrate that the function fits the existing data with sufficient accuracy. Therefore, the new function introduced here can be well used in the frequency analysis of the risk assessment of offshore oil-related platforms. Introduction In the risk assessment of offshore oil-related platforms like floating production storage and offloading system (FPSO), it is necessary to estimate probabilistic characteristics of external forces against them. Earthquakes are a major external force. Furthermore, it is necessary to estimate the damage when an external force is applied. The frequency of external forces, such as earthquakes, is low, but the damage is extensive. However, damage to offshore oil-related platforms is caused by not only these external forces, but also oil leaks resulting from some factors, such as operation errors and corrosion, that may cause accidents such as fire and explosion. Therefore, it is also essential to estimate the probabilistic characteristics of such damage for the risk assessment of offshore oil-related platforms.

Oscillations of Air Cavity Under Hull of Accelerating Boat

Abstract Substantial reduction of ship drag is achievable with air cavities arranged on the hull bottom. However, the air cavities can become unstable, particularly in unsteady environments such as sea waves. Oscillations of cavities can reach high amplitudes, especially near-resonance conditions, and this may lead to the cavity collapse and degradation of drag reduction. In the present study, a lumped-element model is applied for the analysis of dynamics of the air cavity under a boat hull moving in the presence of sea waves. When the hull accelerates from a low initial speed to a high operational speed, the forcing frequency can pass through the cavity resonance condition. Numerical modeling demonstrates that cavities on slowly accelerating hulls may exhibit dangerously high amplitudes. On the other hand, when the hull acceleration is sufficiently fast, then a cavity will not have enough time to develop large-amplitude oscillations. It is found that higher damping and faster acceleration can limit magnitudes of the cavity oscillations, preventing the air cavity from disintegration and enabling the hull to attain high speeds by keeping the drag-reducing air cavity intact.

The effect of a high-speed rotational oscillating cylinder on a heated cylinder

This study investigated the effect of a clockwise and counter-clockwise oscillating (control) cylinder on the flow structure and heat transfer on a heated (bare) cylinder placed in the downstream region of the flow experimentally. In this regard, temperature measurements were made regularly for heat transfer analysis. Particle image velocimetry (PIV) technique was used to determine the instantaneous and time averaged flow characteristics such as streamlines (<ψ > ), turbulent kinetic energy (<TKE > ), vorticity contours (<ω > ), the root mean square of streamwise velocity fluctuations < Urms>, and the root mean square of spanwise velocity fluctuations < Vrms >. The effects of oscillating amplitudes and oscillating speed (forcing frequency) on velocity distributions were also analysed at a specified location. The experiments were conducted at the Reynolds number (Re) 5000 based on the diameter of the bare cylinder with two different oscillating amplitudes 8π and 16π and three different forcing frequencies (FR) 3.5, 7 and 14. With the increase of forcing frequencies, it was observed that the wake region became narrower compared to the main cylinder, and then smaller after being moved towards the cylinder wall. In the case of FR = 3.5-16π, the boundary layer separation was found to be prevented by the effect of the oscillating speed and oscillating amplitude, and the dead zone in the rear of the cylinder was completely eliminated. The heat transfer was found to be evenly distributed at almost all points around the cylinder, and to show the best result especially in the rear of the cylinder among all the cases studied. The results obtained from the temperature and PIV experiments were consistent with each other.

Simultaneous measurement for amplitude and frequency of time-harmonic force based on optomechanically induced nonlinearity

An accurate readout of the mechanical motion using optomechanical coupling is highly desired for on-chip sensing applications but it remains challenging due to the uncertainty caused by time-dependent parameters and noisy fluctuations. Here, we propose an efficient scheme to realize simultaneous measurement for both amplitude and frequency of the time-harmonic force (THF) in a hybrid optomechanical system via a nonlinear sum sideband effect. In this optomechanical system assisted by a degenerate parametric amplifier (DPA), the nonlinear optomechanical interaction between the external THF, optical, and mechanical modes is used to construct the frequency component of optical sum sidebands. Using experimentally achievable parameters, we find that the conversion efficiency of the sum sidebands has a significant enhancement when the nonlinear gain coefficient of DPA increases. In the scheme of the dual-parameter measurement, we also report that the amplitude of THF could be independently detected by observing the intensity variation of the lower sum sideband, while the frequency of THF could be separately read by monitoring the frequency of the prominent peak in this nonlinear spectrum. Benefitting from the optical cooling of a mechanical element, the theoretical results show that the minimum resolutions for detecting the amplitude and the frequency of THF are approximately 8.8×10−12N and 16Hz, respectively.

Directional sensitivity of the cerebral pressure-flow relationship in young healthy individuals trained in endurance and resistance exercise.

What is the central question of this study? Does habitual exercise modality affect the directionality of the cerebral pressure-flow relationship? What is the main finding and its importance? These data suggest the hysteresis-like pattern of dynamic cerebral autoregulation appears present in long-term sedentary and endurance-trained individuals, but absent in resistance-trained individuals. This is the first study to expand knowledge on the directional sensitivity of the cerebral pressure-flow relationship to trained populations. Evidence suggests the cerebrovasculature may be more efficient at dampening cerebral blood flow (CBF) variations when mean arterial pressure (MAP) transiently increases, compared to when it decreases. Despite divergent MAP and CBF responses to acute endurance and resistance training, the long-term impact of habitual exercise modality on the directionality of dynamic cerebral autoregulation (dCA) is currently unknown. Thirty-six young healthy participants (sedentary (n=12), endurance-trained (n=12), and resistance-trained (n=12)) undertook a 5-min repeated squat-stand protocol at two forced MAP oscillation frequencies (0.05 and 0.10Hz). Middle cerebral artery mean blood velocity (MCAv) and MAP were continuously monitored. We calculated absolute (ΔMCAvT /ΔMAPT ) and relative (%MCAvT /%MAPT ) changes in MCAv and MAP with respect to the transition time intervals of both variables to compute a time-adjusted ratio in each MAP direction, averaged over the 5-min repeated squat-stand protocols. At 0.10Hz repeated squat-stands, ΔMCAvT /ΔMAPT and %MCAvT /%MAPT were lower when MAP increased compared with when MAP decreased for sedentary (ΔMCAvT /ΔMAPT : P=0.032; %MCAvT /%MAPT : P=0.040) and endurance-trained individuals (ΔMCAvT /ΔMAPT : P=0.012; %MCAvT /%MAPT P=0.007), but not in the resistance-trained individuals (ΔMCAvT /ΔMAPT : P=0.512; %MCAvT /%MAPT P=0.666). At 0.05Hz repeated squat-stands, time-adjusted ratios were similar for all groups (all P>0.605). These findings suggest exercise training modality does influence the directionality of the cerebral pressure-flow relationship and support the presence of a hysteresis-like pattern during 0.10Hz repeated squat-stands in sedentary and endurance-trained participants, but not in resistance-trained individuals. In future studies, assessment of elite endurance and resistance training habits may further elucidate modality-dependent discrepancies on directional dCA measurements.

Automation of a Hybrid Control for Electrohydraulic Servo-Actuators with Residual Dynamics

In this paper, a hybrid position/force controller for electrohydraulic servo-actuators is designed in the presence of residual dynamics. The purpose is to apply a cycle of movement that is mostly used in industrial fatigue test applications, which consists in imposing a specified force on a flexible load after a movement to some position. This cycle can be repeated several times with different magnitudes and frequencies of force and position trajectories. Some damages could occur at switching times, especially in the presence of some residual dynamics. To avoid any damages at switching times, a force trajectory generator is designed. Then, our contribution defines a method to automatically generate the switching signal in order to commute between two controllers with any abrupt change of state. To show the effectiveness of the proposed approach, several simulation tests are carried out on the electrohydraulic system.

Temporal Instability of Liquid Jet in Swirling Gas with Axial Velocity Oscillation

In the present study, viscous potential flow theory is employed to investigate the temporal instability of a viscous liquid jet in swirling gas with axial velocity oscillation. The dispersion-relation equation is obtained between dimensionless growth rate and wave number. Because of the axial velocity oscillation of gas, there are more than one instability regions, including Kelvin–Helmholtz (K–H) instability region and parametric instability region. The results suggest that increasing gas swirling strength stabilizes the liquid jet in axisymmetric mode, while it enhances the instability in nonaxisymmetric modes. And the gas viscosity has a destabilizing effect. In addition, increasing the forcing frequency enhances instability in the K–H instability region. However, it has a stabilizing effect in the parametric instability region. Furthermore, increasing oscillation amplitude enhances instability in both the K–H instability region and the parametric instability region. Because of the competition between the parametric and K–H instabilities, the location of dominant wave number is uncertain.

Vibration Model of a Power Capacitor Core under Various Harmonic Electrical Excitations

Power capacitors are widely used in power transmission systems. During their operation, an electric force acting on the electrodes of the power capacitors actuates mechanical vibrations and radiates an audible noise. Considering a power capacitor as a general system, the frequency response with the electric force as the input and mechanical vibration as the output have been measured by engineers in recent years and used to evaluate the acoustic and mechanical features of products. Accidentally, it was found that the frequency of the capacitor vibration was not consistent with its excitation due to electro-mechanical coupling. This electro-mechanical coupling had not been considered in previous vibration models of power capacitors. Therefore, a new vibration model of power capacitors was built up in this paper and a so-called multi-frequency vibration characteristic was revealed. A theoretical analysis showed that the electric force and mechanical vibration of the power capacitors were coupled, which resulted in the multi-frequency vibration. The vibration frequency response was measured and the result was consistent with the vibration model proposed in this paper. Once the frequency of the electric force was near half the natural frequency of the power capacitor, a predominant multi-frequency vibration was triggered and the power capacitor was in a superharmonic resonance.

Comparison of Eccentricity Impact on Electromagnetic Forces in Internal- and External-Rotor Permanent Magnet Synchronous Motors

The influence of static eccentricity (SE) and dynamic eccentricity (DE) on the electromagnetic forces in internal- and external-rotor permanent magnet synchronous motors (PMSMs) is investigated in this article. First, the analytical model of the electromagnetic force is derived. By introducing the eccentricity coefficient, the influence of eccentricity on the electromagnetic force is then analyzed. The results show that SE changes the spatial component of the electromagnetic force in internal-rotor motors, while the frequency remains unchanged. While for the external-rotor motors, both the spatial order and frequency of electromagnetic force are affected by SE. Contrary to SE, DE introduces additional spatial components and sideband frequency harmonics to the electromagnetic force of internal-rotor motors. For external-rotor motors, only the spatial order is changed. In addition, axial-flux PMSMs suffer from the extra unbalanced bending moment (UBM), which is a unique feature that differs from traditional radial-flux PMSMs. The expression of UBM caused by eccentricity is further derived. Finally, the theoretical analysis is validated by the simulation and test results, respectively. This study will benefit the researchers and designers in terms of source identification and reduction of acoustic noise in PMSMs.

A study on acoustically modulated bunsen flame and its impingement heat transfer

This study experimentally examines acoustic-field-flame-interaction by using a low-power loudspeaker to actuate the oscillation of a Bunsen flame. It is observed that under acoustic forcing, the flow dynamics are altered, different patterns of the flame front are triggered, and both flame temperature field and heat transfer characteristics are changed. Moreover, impingement heat transfer is found to be increased when the flame is under acoustic modulation, indicating that acoustics can be used to promote heat transfer for flame impingement heating applications. There is a threshold forcing frequency of 300 Hz, beyond which no interaction between the sound and flame exists. The response of the flame to acoustic excitation exhibits a double-cone structure to naked eyes, and is found to be convectively bubbling, wrinkling and shrinking flame front under high-speed photography. The oscillating flame front height has exactly the same frequency as the sound, but the waveform is non-sinusoidal. Both symmetric and asymmetric distorted flame fronts are observed, with the former occurring at low frequencies while the latter at relatively higher frequencies. The effect of acoustic field on the thermal field is to lower the high-temperature region of the flame. Therefore, the cool core in the centre is narrowed, leading to higher local heat transfer. A ten percent increase in total heat transfer rate is obtained when the optimum nozzle-to-plate distance is coupled with the most effective forcing frequency of 50 Hz. Therefore, acoustic modulation is a feasible technique for promoting heat transfer. • 1st study on promoting effect of acoustics on Bunsen flame heat transfer. • Both amplitude and frequency of the sound changes the shape of flame front. • Response of flame front to acoustics is similar to a turbulent one, broadening the space of heat release. • Broader space of higher temperature and heat release leads to higher heat transfer rate and efficiency.

Effects of acoustic excitation on pinch-off flame structure and NOx emissions in H2/CH4 flame

The flame structure and exhaust emissions of pinch-off flames, in which flames are separated under acoustic excitation conditions, were studied. Flame structure analysis was performed using OH∗ chemiluminescence measurements, and exhaust emissions analysis was performed with a gas analyzer. Structure analysis of the pinch-off flame for acoustic excitation was performed basis the OH∗ images, and various structures were confirmed according to the forcing frequency and velocity perturbation intensity. To analyze the correlation between the flame structure and NO x emission, the flame residence time and emission index of NO x (EINO x ) were analyzed according to the Strouhal number. The flame residence time and EINO x decreased as the velocity perturbation intensity increased; analyzing the NO x emission characteristics is limited when based only on the flame residence time. 1/2-power scaling was followed by EINO x analysis and the Strouhal number was normalized to the flame residence time. • Investigation of dynamic and exhaust emission characteristics of pinch-off flames. • Pinch-off flame structure is defined by detailed NO x emissions analysis. • Flame height decreases relative to an increase in the velocity perturbation. • Reduction of flame height reduces the flame residence time. • The τ res alone is insufficient for analyzing NO x emissions.

An Enhancement to Caesar Cipher using Euler Totient Function

In this modern world every communication including financial transactions are taking place through the open unsecured network. In order to communicate securely through open networks the messages need to be concealed by using the cryptographic methods. The mono alphabetic traditional Cipher is Caesar cipher is the simplest and fairly popular among the available cryptographic algorithms but it is prone to brute force attack and frequency analysis test. In this paper we propose an enhancement to Caesar cipher by using the Euler Totient function to generate the key to encrypt a text file. The Euler Totient function is applied on the total number of lines of the plain text file. The key value is generated from the plain text hence for different plain text the key value is different; this makes it difficult for the adversary to guess the key thus making the encryption scheme robust. It needs to design secured key distribution schemes to be taken up as the extension work of this scheme.

Effect of porous media on wake-induced vibration (WIV) in tandem circular cylinder

In practical engineering, cylindrical structures are frequently arranged in tandem under different flow environments. In this study, wake-induced vibration (WIV) of a solid circular cylinder in the wake of a stationary porous cylinder is numerically investigated. A numerical model including the porous medium and vibration modules is established by using the Immersed Boundary (IB) method and the calculation accuracy of the model is verified by the experiment. Seven porosities of the upstream cylinder from 0.0 to 1.0 are considered and the downstream cylinder is allowed to oscillate in both streamwise and transverse directions. The effects of the gap between the two cylinders, the Reynolds number (Re) and the reduced velocity (Ur) on the upstream-stationary-downstream-vibrating tandem cylinders are investigated in terms of shear layer reattachment, vortex impingement and wake interference. The wake flow pattern and the vortex shed from the porous cylinder are vulnerable to the porosity of the cylinder. As a result, the vibration of the downstream cylinder caused by the wake changes at different porosities. Besides, the hydrodynamic force and vibration frequency are also tightly associated with the wake interaction. At different reduced velocities (Ur) and Reynolds numbers (Re), the WIV and the force on the cylinder change significantly.

Modal Decomposition Analysis of Combustion Instability Due to External Perturbation in a Mesoscale Burner Array

AbstractIn this work, the growth regime of combustion instability was studied by analyzing 10 kHz OH planar laser-induced fluorescence (PLIF) images through a combination of dynamic mode decomposition (DMD) and spectral proper orthogonal decomposition (SPOD) methods. Combustion instabilities were induced in a mesoscale burner array through an external speaker at an imposed perturbation frequency of 210 Hz. During the transient growth phase of combustion instability, 10 kHz OH PLIF imaging was employed to capture spatially and temporally resolved flame dynamics. Increased acoustic perturbations prevented flame reignition in the central recirculation zone and eventually led to the flame being extinguished inward from the outer burner array elements. Coherent modes and their growth rates were obtained from DMD spectral analyses of high-speed OH PLIF images. Positive growth rates were observed at the forcing frequency during the growth regime. Coherent structures, closely associated with thermoacoustic instability, were extracted using an appropriate SPOD filter operation to identify mode structures that correlate to physical phenomena such as shear layer instability and flame response to longitudinal acoustic forcing. Overall, a combination of DMD and SPOD was shown to be effective at analyzing the onset and propagation of combustion instabilities, particularly under transient burner operations.

Design of Particle Dampers for Laser Powder Bed Fusion

Additively manufactured particle dampers can significantly improve component damping. However, if designed incorrectly, the damping can be worsened. For the design of additively manufactured particle dampers, there are not yet sufficient design rules and models to describe the effect due to numerous design parameters. The research question answered in this paper describes how the effect of particle damping can be characterised as a function of excitation force and excitation frequency for different cavity sizes. To characterise the effect of particle damping, a 33 full factorial test plan is constructed, and the damping is determined experimentally. It is shown that the damping can be reliably evaluated with the circle-fit method. The effect of particle damping is investigated for beams made of AlSi10Mg, 1.2709 and Ti6Al4V. As a result, a positive effect of the particle damping in a frequency range from 500 to 30,000 Hz and partly up to the 9th bending mode can be proven. It is shown that, for the first bending mode, there is an optimum at approx. 2000 Hz. For the optimum, the increase of the damping for the tool steel 1.2709 to 28 and for the aluminium alloy AlSi10Mg to 18 can be proven.

A novel ZnS nanosheets-based triboelectric nanogenerator and its applications in sensing, self-powered electronics, and digital systems

The development of triboelectric nanogenerators (TENGs) based on inexpensive inorganic materials has attracted significant attention to envisage next-generation self-powered electronic devices and sensors. In this research work, the fabrication of a triboelectric nanogenerator (TENG) based on ZnS nanosheets arrays was investigated for the first time. This TENG was fabricated with ZnS nanosheets films, polydimethylsiloxane (PDMS) as active tribo-layers. The originality of this work lies in the choice of materials; pure ZnS nanosheets and PDMS-Al cover foils. By hand excitation force, the developed TENG (5 ×5 cm2) produced an output voltage and a short-circuit current of ~8 V and ~7.12 µA respectively. In addition, the present TENG with pure ZnS nanosheets on Al substrate produced an output voltage almost twice than TENG that involved only Al substrate. In this current study, introducing ZnS nanosheets on Al substrate increased the surface area and roughness, resulting in improved performance. The study of TENG parameters confirms that the TENG (10 ×10 cm2) with 2 cm spacing between tribo layers, applied force frequency of ~ 4–5 Hz were optimum to obtain the maximum output voltage of ~33 V. The high stability of TENG was confirmed by testing TENG response over 1000 cycles. Further, TENG was used to power portable electronic devices such as a digital watch, thermometer, calculator, and 64 LEDs when coupled to a capacitor. Finally, TENG was demonstrated for sensing force and pressure, TENG output response was used as a clock pulse for the digital circuits. The proposed TENG is easy to handle, simple and economical, and ZnS-based TENG's performance can be improved using other tribo-materials instead of PDMS.

A numerical study of a lifted hbox {H}_2/hbox {N}_2 flame excited by an axial and flapping forcing

The large eddy simulation method combined with the Eulerian stochastic field approach has been used to study excited lifted hydrogen flames in a stream of hot co-flow in a configuration closely corresponding to the so-called Cabra flame. The excitation is obtained by adding to an inlet velocity profile three types of forcing [(1) axial; (2) flapping; (3) combination of both] with the amplitude of 15% of the fuel jet velocity and the frequency corresponding to the Strouhal numbers St=0.30,, 0.45,, 0.60, ,text {and}, ,0.75. It is shown that such a type of forcing significantly changes the lift-off height (L_h) of the flame and its global shape, resulting in the flame occupying a large volume or the flame, which transforms from the circular one into a quasi-planar one. Both the L_h and size of the flames were found to be a function of the type of forcing and its frequency. The minimum value of L_h has been found for the case when the axial and flapping forcing were combined and acted at the forcing frequency close to the preferred one in the non-excited configuration. The impact of the flapping forcing manifested through a widening of the flame in the flapping direction. It was shown that the excitation increases the level of temperature fluctuations caused by an intensified mixing process. The computational results are validated based on the solutions obtained for the non-excited flame for which experimental data are available.

Offloading Effects on Impact Forces and Patellofemoral Joint Loading During Running in Females

BackgroundStructure-specific loading is being increasingly recognized as playing a role in running related injuries. The use of interventions targeted at reducing patellofemoral joint loads have shown effectiveness in reducing symptoms of patellofemoral pain. Use of bodyweight support (BWS) has the potential to reduce loading on the patellofemoral joint during running to augment rehabilitation efforts. Research Question:How is patellofemoral joint loading different when using a harness-based BWS system during running? MethodsTwenty-five healthy females free from lower extremity injury were included. Participants completed four running trials on an instrumented treadmill with varying amounts of BWS using a commercially available harness system. Kinematic data from a 3D motion capture system and kinetic data from the treadmill were combined in a computer model to estimate measures of patellofemoral joint loading, knee kinematics, ground reaction force, and stride frequency. ResultsPeak patellofemoral joint stress and time-integral were reduced when running under BWS conditions compared to control conditions. Incremental decreases in patellofemoral loading were not observed with incremental increases in BWS. Peak knee flexion angle was reduced in all BWS conditions compared to control but was not different between BWS conditions. Knee flexion excursion was reduced in only the high BWS condition. Peak ground reaction force and stride frequency incrementally decreased with increased amounts of BWS. SignificanceHarness-based BWS systems may provide a simple means to reduce patellofemoral joint loading to assist in rehabilitation efforts, such as addressing patellofemoral pain.

Low-Frequency Oscillations and Force Control Capabilities as a Function of Force Level in Older Women

Force variability is potentially related to altered low-frequency oscillations in motor outputs. This study examines the contributions of low-frequency oscillations in force to altered force control performances from lower to higher targeted force levels in older women. Fourteen older women executed unilateral hand-grip force control tasks at 10% and 40% of maximum voluntary contraction (MVC). Force control performances were estimated by calculating force accuracy (root-mean-square-error), force variability (standard deviation), and force regularity (approximate entropy). We additionally quantified low-frequency oscillations in force using absolute powers across four different frequency bands: (a) 0–0.5 Hz, (b) 0.5–1.0 Hz, (c) 1.0–1.5 Hz, and (d) 1.5–2.0 Hz. The findings reveal that from lower to higher targeted force level older women show greater force error, force variability, and force regularity with increased values of absolute power in force across the four frequency bands. The multiple regression models identified a significant relationship between greater force frequency power below 0.5 Hz and more impairments in force control performances. These findings suggest that force frequency oscillation below 0.5 Hz is a key predictor indicating altered stability of task performances across different targeted force levels in older women.

Normalized Ratcheting Diagram Under Sinusoidal Vibration Waves

Abstract Ratcheting is a progressive incremental inelastic deformation or strain which can occur in a component that is subjected to variations of mechanical stress, thermal stress, or both. This study concentrated on the ratcheting occurrence of the piping model under the combined effect of constant external force and dynamic cyclic vibrations. Bent solid bars represented piping models, and sinusoidal acceleration waves were loaded. Characteristics of seismic loads between load-controlled and displacement-controlled properties were studied from the viewpoint of the frequency ratio of the forcing frequency to the natural frequency of the piping model. Besides, the ratcheting occurrence conditions of the beam and the piping model were compared in one normalized diagram to display the general mechanism of ratcheting with the consideration of the effect from the difference of shape and material. Results show that ratcheting occurs easily with a lower frequency ratio in both beam and piping models. In addition, it is meaningful to use beam models to understand the ratcheting mechanism of piping models. Describing the occurrence of ratcheting using the normalized ratcheting diagram for different components is feasible.