Natural Frequency Of System Research Articles

Numerical investigation on rotation accumulation and natural frequency degradation for offshore wind turbine in clays

Prolonged lateral cyclic loading leads to soil stiffness degradation around offshore wind turbine (OWT) foundations, which reduces the system's natural frequency and increases the accumulation of foundation rotation angle. Proper evaluation of natural frequency and rotation angle is crucial for the design of OWT foundations. This study develops a two-stages numerical approach to calculate the fundamental frequency of OWT systems considering the foundation stiffness degradation by integrating a stiffness degradation model of soft clays with a simplified three-spring model. Subsequently, it investigates the evolution of accumulated rotation and natural frequency for three foundation types—monopile, monopod bucket, and hybrid monopile-bucket—throughout their service life. It is observed that the hybrid foundation shows the smallest rotation in the first cycle, attributable to its relatively high initial stiffness compared to the other two foundations with the same steel consumption. However, it also exhibits the highest rate of cumulative rotation growth. At the same load level, the monopod bucket foundation exhibits the largest cumulative rotation angle due to its lower bearing capacity, and the degradation of natural frequency is most pronounced for monopod bucket OWT. For all three foundation configurations, increasing either the pile diameter or the bucket diameter is the most effective approach to reduce the cumulative rotation angle and improve natural frequency degradation, while maintaining the same steel consumption. These findings should be considered in the design of OWT foundations.

A mathematical model for the dynamic analysis of multi-body floating platforms with complex mechanical constraints

The new methodology based on generalised coordinates for the analysis of floating multi-body systems with nonlinear geometric constraints is developed, and it is demonstrated through numerical application for a hybrid floating wind-wave platform consisting of a floating offshore wind turbine and an articulated wave energy converter that moves a hydraulic piston. The formulation is applied to achieve explicit formulae regarding the dynamic response in a low-dimensional scenario used to verify a post-processing code. The verification considers the nonlinear geometric constraints, hydrodynamic interaction, the dynamics of articulated arms, and the dynamics of hydraulic power take-off systems. An analytical expression for the system's natural frequencies is attained and verified likewise. The results presented in this paper indicate significant improvement in the simulation and analysis of multi-degrees-of-freedom nonlinear hydrodynamic systems, which will ultimately be necessary for designing efficient hybrid floating wind-wave platforms.

Monte Carlo uncertainty quantification method of pneumatic measurement tube frequency response

Abstract The pneumatic tube plays a critical role in the frequency response of the pressure measurement system, which also greatly affects the accuracy of the measurement data. This paper applied the Monte Carlo uncertainty qualification method to the pressure measurement tube system frequency response and studied the effects of four parameters, including tube length, radius, temperature, and source pressure, on uncertainty characteristics for a given tube system configuration. The reported results show the technique's applicability and flexibility and the limitations of GUM. It is found that the frequency response and corresponding uncertainty are not directly related to frequency but are closely related to the natural frequencies. Comparative experimental results show that the longer tube significantly reduces the system's natural frequencies and intensifies the phase lag. In addition, larger tube radius and source pressure result in larger amplitude response peaks. Closed to the natural frequencies, with the increase of the parameter, the uncertainties of frequency response value and the corresponding variation range increase for tube radius and source pressure while decreasing for temperature and tube length.

A design method of large-scale partial similar model test for cementing casing string system

When the cementing casing string system (CCSS) is subjected to a large-scale equal-scale model test, the huge aspect ratio of the system makes the wall thickness of the model casing string too thin to be manufactured. Therefore, this paper proposes a design method for model test with unequal scale of axial size and radial size of the CCSS. Firstly, the dynamic model of the CCSS is established and solved by the transfer matrix method (TMM), and the modal test is carried out and the results show that the numerical calculation error of the first five natural frequencies of the system is less than 4 %. Then, based on the dynamic model, the similarity laws of the complete similarity model and the partial similarity model of the CCSS are derived by equation analysis method, and the design process of the similarity model test is given. The advantages of the research are elaborated in details through examples. To verify the correctness of the similarity model’s similarity laws of the CCSS, similarity models with different parameters are designed, and the prediction errors of prototype response are analyzed based on numerical calculations. The results show that the maximum prediction error of the first eight natural frequencies of the prototype system is less than 3 %, and the response prediction results of the system are also accurate. Finally, considering uncertain factors of the partial similarity test, the similarity model test with the axial size of double scale is designed, and the results show that the maximum prediction error of the first three natural frequencies is 7.06 %, which meets the engineering requirements. This study can provide useful theoretical guidance for the large-scale model test design of the CCSS.

Probabilistic Analysis of Orbital Characteristics of Rotary Systems with Centrally and Off-Center Mounted Unbalanced Disks

Rotor dynamics plays a crucial role in the performance and safety of rotating machinery, with disk position and unbalance significantly impacting system behavior. This study investigates the dynamic characteristics of two rotor configurations: a centrally mounted unbalanced disk (Rotor05un) and an off-center unbalanced disk (Rotor025un). Using numerical simulations and Monte Carlo analysis, we examined critical speeds and orbital patterns for both configurations. Probability distributions of shaft orbital positions revealed distinct patterns for each configuration. Quantile analysis revealed approximate linear trends for Rotor025un, suggesting higher system stiffness and more predictable behavior near critical speeds. Cross-sectional analyses of the orbits provided insights into the complex interactions between disk position, gyroscopic effects, and system natural frequencies. These findings provide valuable insights for rotor system design, particularly for applications with non-ideal mass distributions. The study goes beyond traditional critical speed analysis to examine orbital patterns and point on orbit occurrence from a probabilistic perspective. Based on the simulation of the orbits, an orbital is determined that allows the probability of the shaft occurring at the analyzed distance from the origin to be determined. The paper also offers insights into the complex interaction behavior of chosen rotor configurations and highlights the importance of considering disk position in predicting and optimizing rotor dynamic behavior, contributing to the development of more robust and efficient rotating machinery.

Numerical Simulation Study on Vibration Characteristics and Influencing Factors of Coal Containing Geological Structure

Accurately determining the natural frequency of coal-containing geological structures is crucial for preventing mine dynamic disasters and utilizing vibration waves to break coal and enhance its permeability. Based on the modal theory of rock, vibration models of coal-containing geological structures, including layering and fractures are established. By analysis, the undamped vibration equation and its characteristic equation for both the layered coal system and the fractured coal system are derived. Subsequently, the Lanczos method is employed to solve the system’s vibration modes using ABAQUS. The effects of the layering position, layering thickness, layering physical properties, crack width, and crack length on the natural frequency and vibration response of coal-containing geological structures are investigated. The results indicate that when a single influencing factor is altered, the displacement response distribution of the coal body vibration system with geological structures remains essentially the same, and these single influencing factors have a minimal impact on the vibration displacement of the coal-containing geological structure. The natural frequency of the system decreases exponentially as the distance between the layering and the geometric center of the coal system with geological structures increases. The presence of layering in the coal system with geological structures significantly reduces the system’s natural frequency. The natural frequency of the coal system with geological structures increases in a power function manner as the layering elastic modulus increases. Conversely, the natural frequency decreases with an increase in crack length. When the change ranges of crack width and bedding thickness are the same, the natural frequency of the fractured coal body system exhibits more significant changes. The natural frequency of the coal system with geological structures initially decreases and then increases as bedding thickness and crack width increase. The trend in the natural frequency changes and the position of the extreme point are related to the ratio of the elastic modulus and density of the geological structure.

Simulations of design and high load operation of a model Francis turbine using bridged approach to turbulence modelling

Abstract Off-design operation of hydraulic turbines is contemporarily frequented for balance of variable energy intermittence in the electric grid. Being operationally highly flexible, these turbines allow a quick transition to off-design operation from the design point. However, such operational flexibility, and therefore the grid balancing capability is impeded by generation of flow instabilities like vortex breakdown during off-design operation. Vortex breakdown causes losses in efficiency and pressure recovery, pressure fluctuations and possibly mechanical vibrations in event of resonance between system natural and flow field fluctuation frequencies. While substantial experimental and numerical effort has already been made to study draft tube vortex breakdown, an accurate numerical flow characterization of the phenomenon is still a challenge. To this end, operation of a high head model Francis turbine under design and high load regimes using a bridged turbulence modelling approach is simulated. The approach allows a seamless transition between direct numerical simulation and Reynolds averaged Navier-Stokes equations. The highest attainable accuracy is limited by the mesh size. As such a satisfactory compromise between desired accuracy and invested computational effort is attained. The flow in the draft tube is free of anomalies under design specified operation. However, at high load an axial flow stagnation occurs centrally, and the flow is separated about the stagnated zone. The core of the vortex is enlarged with flow recirculation within it. Shear layers between the central stagnant zone and surrounding outflow kink and roll up transforming it into a spiral structure. In this work, a basic yet accurate numerical flow characterization of the aforementioned flow situations is achieved.

Identification of electro-mechanical interactions in wind turbines

Abstract. Large direct-drive wind turbines with a multi-megawatt power rating face design challenges, especially concerning tower top mass, due to scaling laws for high-torque generators. This work proposes to extend the design space by moving towards a more system-oriented approach, considering electro-mechanical interactions. This requires an extension of the state-of-the-art wind turbine models with additional degrees of freedom. To limit the computational effort of such models, a profound understanding of possible interaction mechanisms is required. This work aims to identify interactions of an additional degree of freedom in the radial direction of the generator with the wind turbine structure, the aerodynamics, and the wind turbine controller. Therefore, a Simpack model of the IEA 15 MW RWT is implemented and coupled to a quasi-static analytical generator model for electromagnetic forces. The analytical model, sourced from literature, is code-to-code validated against a finite element model of the generator in COMSOL Multiphysics. Electro-mechanical simulation results do not show interactions with the aerodynamics or the controller. However, interactions with the wind turbine structure occur. It is shown that the modelling approach can affect the system's natural frequencies, which can potentially impact the overall system design choices.

Exploring the mechanisms behind dual-peak formation in energy harvesting efficiency of semi-passive flapping airfoils with varied spring stiffness

Flapping airfoil energy harvesting has emerged as a promising paradigm inspired by birds and marine organisms. In this investigation, a semi-passive flapping airfoil device with a predetermined pitching motion was examined using a transient numerical simulation method employing an overlapping grid technique. The impact of the spring stiffness on the energy harvesting characteristics of the flapping airfoil was analyzed through the implementation of the integral momentum theorem and dynamic mode decomposition. The results demonstrated that the efficiency and power curves of the flapping airfoil exhibited a distinctive bimodal M shape in response to variations of the spring stiffness. The initial peak efficiency point, which corresponded to the system's natural frequency in proximity to the pitching frequency, was found to be heavily influenced by the presence of leading-edge vortexes, thereby influencing lift generation. By utilizing the integral momentum theorem, it was determined that the Lamb vector term, fluid acceleration term, and total pressure term predominantly contributed to the lift generation. The emergence of the second peak efficiency point was primarily linked to torque variations induced by trailing-edge vortexes.

Analisis Redaman Sistem Vibrasi Paksa Satu Derajat Kebebasan Pada Simple Vibration Apparatus

Vibration testing in the field of mechanical engineering has an important role in planning and maintaining machines to determine whether the design is safe and suitable for application. Newton's second law is a reference for back-and-forth movement around equilibrium both within the system and from outside the system which affects the machine itself, if the frequency of stimulation is equal to one of the system's natural frequencies, then resonance occurs, and dangerously large oscillations, resonance can cause damage to the system. The solution to avoid excessive resonance requires a damper. Forced vibration oscillations are applied by excitation using an unbalanced mass installed on a DC motor unit, the response is a mass deviation to obtain oscillations or time relationships with amplitude, the natural frequency of the system, mass-spring deviation, and characteristics of vibration. This activity aims to analyze the effect of the vibration amplitude of a forced vibration simulator under conditions without damping and using damping. The experimental test method was applied to a forced vibration system with one degree of freedom with an oil and air damper in a simple vibration apparatus simulator, 2 types of unbalanced masses, regulated by rotation up to 500rpm, tested under conditions without a damper, using an oil and air damper. The results of the activity showed that the air-dampening media can limit greater amplitude compared to the oil-dampening media.

Dynamic Load Identification at Natural Frequencies for Aircraft via Attention Based 1D-CNN

Since the frequency response function is ill-conditioned at the natural frequency of the system, the traditional load identification method based on the system parameters is no longer applicable. Aiming at the difficulty of dynamic load identification at the natural frequency of the structural system, a dynamic load identification method at the natural frequency of the structure based on one-dimensional convolutional neural network(1D-CNN) with attention mechanism is proposed. Specifically, the high-level features in the vibration response signal are first extracted through the convolution layer. Then the weight matrix of the network is updated by backpropagation algorithm, which represents the importance of different features. The mapping relationship between response and load is established to realize the task of load identification. From the trained data, the attention module learns the contribution of features according to the different contribution of different features to load prediction. The important components in the response signal are highlighted and noise pollution is suppressed. Excitation and response signals at the natural frequency of the system were acquired using exciters and an accelerometer mounted on the GARTEUR aircraft model. Excitation and response signals at the natural frequencies of the system are obtained by an exciter and accelerometer mounted on the GARTEUR aircraft model. The responses of the model at the first three natural frequencies of 6.4Hz,35.8Hz and 48.5Hz were obtained respectively. Experimental results show that compared with the traditional TSVD load identification method, the maximum error of this method is only 3.19%. Compared with the 1D-CNN method, the proposed method has stronger robustness under 20%, 50% and 80% noise levels.

Parameters design for feel system of aircraft active inceptor controller

To provide the pilot with feedback on flight states, aircraft active inceptor controllers deliver appropriate tactile feedback through the feel system. Current research on the feel system often relies on conventional models, with limited analysis of its unique characteristics. Investigating the dynamic properties of the feel system and their impact on flying quality can inform the parameters design of the feel system. In this paper, we designed various feel system parameters with different natural frequencies and damping ratios and selected three typical aircraft dynamic models. A human-vehicle closed-loop system model is established, including the pilot model, feel system model, and aircraft dynamic model. Combining different flying quality criteria, including bandwidth criterion, Neal-Smith criterion, and Open-Loop Onset-Point (OLOP) criterion, the flying qualities of Type I and Type II pilot-induced oscillations (PIO) are evaluated separately. The influence of aircraft configuration, feel system natural frequency and damping ratio on flying quality is explored. Finally, design recommendations for the feel system are proposed, aiming to reduce the adverse aircraft pilot coupling and improve flying quality.

Efficient design of truss footbridges with stiffness-proportional inerters

Absract Excessive vibrations in footbridges have recently received more attention from researchers and professionals. This has resulted in a surge in popularity for passive energy dissipation systems, such as tuned mass dampers, viscous dampers, and inerters. While design methods with tuned mass dampers and viscous dampers exist, the design of footbridges using inerters is still a challenge. This paper proposes a design procedure for truss-like footbridges incorporating inerters. The concept of the approach is based upon a mathematical derivation of the eigenproblem of a multi-degree-of-freedom structural system, enhanced with stiffness-proportional inertances. This outcome enables tuning the highest natural frequency of the system to a predefined value. The proposed design procedure adjusts all natural frequencies, such that the highest natural frequency of a structural system is set lower than the frequency of the load. As implemented in the article, the procedure can be used for back-of-the-envelope estimations, or for achieving an efficient final design. The designs achieved by the suggested methodology are compared to the current traditional design, optimal design achieved through gradient-based sizing optimization, and designs with various common topologies. The methodology’s high potential and its proximity to optimal for a chosen topology are revealed.

Assessing patient transport conditions during ambulance transit.

Emergency ambulances play a vital role in medical rescue and patient transportation, but their transit can impact patient health due to vehicle dynamic forces and vibrations. This study evaluates patient transport conditions on a stretcher subjected to vertical vibration excitation from road unevenness. Using an eight-degree-of-freedom numerical model, we analyze the construction parameters of a medical stretcher's support and vehicle suspension. Actual experimental data from an emergency vehicle were utilized to assess the vibration conditions experienced by both the stretcher and the ambulance floor. The model is adjusted based on measurements, specifically targeting the main vibration modes. The investigation involves determining temporal responses for vertical accelerations and characterizing vibration modal parameters under various transportation conditions. Notably, several system natural frequencies fall within the range of human body frequencies, making them susceptible to mechanical excitation, particularly in the human neck, abdomen, and spine. A sensitivity analysis underscores the influence of medical stretcher support structure parameters on patient comfort. Increasing support stiffness, which alters the stretcher's natural frequency, and damping coefficient reduce vibration propagation between the vehicle and the patient. Additionally, the research predicts the model's dynamic behavior on roads with low-quality pavement, indicating vibrational amplitudes that could potentially be discomforting and unhealthy for individuals. The study illustrates a vibration exposure period on a class E road, revealing that transportation longer than 25 min may cause damage to patient health.

Angular vortex-induced vibrations of a cylinder

We consider the response of a flexibly-mounted cylinder placed in flow and free to oscillate on a curved path about a pivot point. The curved path could be concave (i.e., bent toward the incoming flow) or convex (i.e., bent away from the incoming flow). We consider different radii of curvature for both the concave and the convex paths and show that oscillations are observed for radii of curvature larger than one cylinder diameter. In general, we show that the oscillations are of larger amplitudes in the convex orientation, reaching angles of oscillations of up to 38° and normalized (with respect to the cylinder's diameter) amplitudes of oscillations in the transverse and inline directions of up to 1.1 and 0.35, respectively. The oscillations on the concave path are of smaller amplitudes, but last up to higher values of reduced velocities than those in the convex orientation. The shedding and oscillation frequencies increase with increasing reduced velocity for the concave orientation reaching values of around 1.8 times the system's natural frequency in water at the end of the lock-in range, while for the convex orientation, the frequencies stay close to the natural frequency and only jump from values slightly lower than the natural frequency to values slightly higher than the natural frequency when the oscillation amplitude drops from an upper branch to a lower branch in the VIV amplitude response. Two single vortices are observed in the wake when oscillation amplitudes are relatively low, and two pairs of vortices of different sizes are observed in the wake when amplitudes are relatively larger. When two pairs of vortices are observed, the cylinder carries two bound vortices with it during its transverse oscillations and sheds them in the form of a pair of vortices of different sizes at the end of each half cycle. In the cases with the largest amplitudes of oscillations, besides the vortices that are shed synchronized with the oscillation frequency, several smaller-size vortices are shed in the wake as the cylinder traverses its crossflow path. We relate the reason for observing larger amplitudes of oscillations on the convex path to the relative orientation of the fluctuating forces that are exerted on the cylinder due to the shedding of vortices in its wake with respect to its oscillation path.

Synergistic Hybrid Marine Renewable Energy Harvest System

This paper proposes a novel hybrid marine renewable energy-harvesting system to increase energy production, reduce levelized costs of energy and promote renewable marine energy. Firstly, various marine renewable energy resources and state-of-art technologies for energy exploitation and storage were reviewed. The site selection criteria for each energy-harvesting approach were identified, and a scoring matrix for site selection was proposed to screen suitable locations for the hybrid system. The Triton Knoll wind farm was used to demonstrate the effectiveness of the scoring matrix. An integrated energy system was designed, and FE modeling was performed to assess the effects of additional energy devices on the structural stability of the main wind turbine structure. It has been proven that the additional energy structures have a negligible influence on foundation/structure deflection (<1%) and increased system natural frequency by 6%; thus, they have a minimum influence on the original wind system but increased energy yield.

Vibration analysis of FGM anisogrid lattice plates with one width fold based on the continuous model using the GDQE method

This research tests the idea of folding on the free vibration response of anisogrid lattice plates. It is assumed that the oblique and straight ribs with functionally graded materials (FGMs) construct the lattice plate. The stiffness and mass of the whole plate are computed by employing the global continuous model based on the shear deformable orthotropic plates. Then a width fold is created in the plate to check its effect on improving the system's natural frequencies. An element-based 2D generalized differential quadrature method recently developed solves this problem. This method divides the physical domain into simple domains (patching) and distributes a series of nodes on each patch (quadrature scheme). The motion equations of each patch are derived using Hamilton's principle. Next, the displacement and stress resultant continuity conditions are satisfied between common nodes. After that, the obtained global equations are solved, and the natural frequencies of such structures are calculated. After validating the response with the available literature, the influence of composite characteristics and geometry on the folded FGM lattice plate is distinguished.

Hydrodynamic performance of wave energy converter integrated with pile restrained floating structure near a partially reflecting seawall

The integration of a Wave Energy Converter (WEC) with a Pile-Restrained Rectangular Floating Breakwater (PRFB) in the presence of a partially reflecting vertical seawall is analysed to enhance the hydrodynamic performance and WEC efficiency of the integrated breakwater-WEC device based on small amplitude wave theory using the Boundary Element Method (BEM). The rectangular floating breakwater is designed to have heave motion with a pile-restrained floating structure placed in a position to attenuate the incoming wave in the transmitted region and the linear power take-off (PTO) damping is employed to calculate the absorbed power. The study is performed to understand the effectiveness of wave energy conversion and its hydrodynamic performance due to changes in the seawall's porosity, relative structural width, relative structural draft, wave energy conversion power take-off damping coefficients, and the relative gap of the WEC integrated with PRFB from the seawall. The study demonstrated that in the presence of a fully reflecting seawall, the wave energy extraction is enhanced for the integrated WEC system without compromising the defined threshold wave reflection coefficient but at the expense of a constrained range of wavenumbers that correspond near the system's fundamental natural frequency. Moreover, the capture width ratio is noted to be higher for relatively smaller structural drafts, while the wave reflection coefficient shows precisely the reverse trend. However, under such circumstances, the integrated WEC system operates as a motion-trapping structure, especially when the reflection coefficient of the seawall, CR≥0.75. Thus, the present study will assist the designer in determining the appropriate degrees of efficiency of the WEC device without sacrificing hydrodynamic performance by fine-tuning the hybrid floating breakwater system's geometrical parameters.

Adaptive input shaper for payload swing control of a 5-DOF tower crane with parameter uncertainties and obstacle avoidance

This paper proposes an adaptive input shaper for swing control of a five degrees of freedom tower crane under various parameter uncertainties together with payload hoisting and simultaneous motions. The real-time adaptive mechanism is designed using neural network and the shaper parameters can be updated based on current crane's parameters. This approach avoids the requirement for re-design of controllers as in the conventional technique. Experiments are conducted to assess effectiveness of the controller under challenging scenarios up to 100% changes in the system's natural frequency. These involve different speeds and payload masses, payload hoisting, and distances of trolley and jib. Results demonstrate that the shaper is robust against parameter uncertainties and its superiority is confirmed with an improvement of at least 50% as compared to a comparative robust shaper. The shaper also provides a satisfactory performance under obstacle avoidance where payload lifting and lowering are performed within a single manoeuvre.

Analytical 2D model for the liquid storage rectangular tank

This work aims to evaluate the free vibration of deformable fluid-filled rectangular tanks in two dimensions. These tanks are surrounded by soil, and consequently, the soil-fluid-structure interaction is taken into account. Here, the fluid is supposed to be compressible, non-rotational, and non-viscous. And, the soil is presumed to be cohesive. Besides the analytical solution, the formulation using finite elements to solve the problem is presented. For validating the suggested analytical solution, several numerical examples are examined. Additionally, a sensitivity analysis is performed to examine how various parameters affect the fluid–structure-soil system's natural frequencies and mode shapes. Findings have proven the correctness of the proposed solution.