Natural Frequency Analysis Research Articles

Experimental parametric study on hydroelastic behaviour of a 15000-TEU container ship based on segmented ship model

ABSTRACT Large-scale ships with high elasticity and low natural frequency, behave high dynamic response amplitude under impulsive wave loads (whipping) and short period waves (springing), which could result in serious ultimate loads and fatigue damage. The segmented model test is a more powerful approach for the ship hydroelastic analysis compared with ship seakeeping test. However, the effect of some test parameters on the hydroelastic responses is still not a clear statement. Therefore, the number of segments, propulsion mode and backbone form are chosen for the parametric study on ship hydroelastic behaviour. A three-dimensional (3-D) nonlinear time-domain hydroelastic method is developed, in which the nonlinearity of instantaneous wetted surface and slamming force are considered. Through the analysis of natural frequencies and vertical bending moments (VBM), the impact on hydroelastic behaviour is discussed. Results show that self-propelling models with variable cross-section backbones are more suitable and reliable in studying nonlinear hydroelastic behaviour.

Dynamic calculation and optimization design of arbitrary planar branch piping system

The absorbing transfer matrix method (ATMM) is applied to dynamics calculation and optimization design of planar branch piping systems combined with the response surface model or method (RSM) and a new proposed hybrid RSM (HRSM). A main path is chosen to absorb the influences of sub-branches, and the branch point transfer matrix in the main transfer path is established and proved by the ANSYS simulation and experimental results. It shows that the errors between the ATMM and the finite element method are less than 0.36% in the calculation of the natural frequencies of the two-branch piping system, and the ATMM also agrees well with the dynamics response experimental results of the cross-branch piping system. Then, based on the initial design model of a double-branch piping system, first order natural frequency analysis samples are selected for the branch point positions optimization using the uniform design method (UD) and calculated by the ATMM; the minimum value of the RSM, obtained by fitting the samples with a second-order polynomial (SOP) function, is solved as the best design scheme using the genetic algorithm (GA). Finally, for the problem of supporting positions optimization of a T-branch piping system, a HRSM using the SOP function to fit the variation law with different supporting positions in the samples of the dynamics response optimization target, which is the total x-directional vibration acceleration level (TAC) of three supporting points in the frequency 1–300 Hz and the Fourier basis function to fit the relationship of SOP function error with independent variables is proposed combining the Minimize Prediction (MP) adding point criterion to gradually update the samples, until the HRSM reaches stability and obtains the wanted design solution.

Natural Frequency Analysis of Horizontal Piping System Conveying Low Viscosity Oil–Gas–Water Slug Flow

The water cut (WC) has a significant effect on the flow parameters, such as liquid holdup, liquid phase velocity, and flow regimes of the low-viscosity oil–gas–water slug flow, and it can change the vibration characteristics of piping systems. To study the effect of water cut on the vibration characteristics of piping systems conveying such internal flow, a new dynamic model is developed. Galerkin’s method is used to discretize the equation and determine the natural frequencies by solving for the eigenvalues of the equation coefficient matrix. The results show that in the range of 10–90% WC, the natural frequency increases and then decreases, and the turning point occurs near the phase inversion region (WC = 40–60%). The main reason is the highly effective viscosity in the phase inversion region, which leads to an increase in the liquid holdup. The natural frequency increases and then decreases with superficial gas velocity, and the inflection point decreases with the increase in water cut in the oil-based flow regime and increases with the increase in water cut in the water-based flow regime. The critical gas velocity is lowest near the phase inversion region, but it should be noted that the presence of the critical gas velocity is related to the pipe length and superficial liquid velocity. The results of the study provide a reference for the design of safe pipeline operation.

An analysis and experimental validation of natural frequencies of elastic ellipsoids with the Rayleigh–Ritz method

The Rayleigh–Ritz method is widely employed to analyze free vibrations of elastic solids and structures. For a simple formulation and efficient evaluation of vibrations of elastic ellipsoids, which also include spheres, the Cartesian coordinate system is utilized. It is hoped that the formulation with lengthy expressions can be solved with fewer terms of displacement functions in Chebyshev polynomials for simple evaluations of stiffness and mass matrices of the elastic ellipsoids with the procedure. The vibrations of elastic ellipsoids are calculated with geometric parameters for the validation of the procedure and formulation with known results and the analysis from this study.

Free Vibration Analysis of Anisotropic Composite Materials of a Fixed-Wing

Nowadays, the availability of composite materials and their acceptable manufacturing cost, in addition to their high strength-to-weight ratio, has shifted the use of the materials from metal alloys to composite materials in the aircraft industry. In this paper, a comprehensive analysis of wing natural frequencies and deflection with regard to three different composite materials - carbon fiber, glass fiber, and Kevlar fiber - was conducted, and the results were compared with conventional metal alloys aluminum2024 and 7075-T6, while taking into account the anisotropic behavior of the composite materials. The results indicate that the metal alloys aluminum 2024 and 7075-T6 have the best properties, and consists of the most suitable materials for aircraft wings compared with other composite materials. In addition, the deflection of the wing using AL2024 was about 0.549 unit length and for 7075-T6 was about 0.547 unit length, which was almost less than half of the deflections of other proposed composite materials which are 1.252, 1.389, 1.293 unit length for glass fiber, Kevlar fiber and carbon fiber, respectively.

Impact of calibrated soil-monopile-interaction model on resonance frequencies

Offshore wind turbines (OWTs) are sensitive, dynamic structures that require accurate estimation of the natural frequency of the support structure. This requires an integrated analysis of the wind turbine structure, including a realistic representation of the foundation response. This paper studies how the natural frequency analysis is influenced by the soil-monopile interaction model following the PISA guidance. A case study of an instrumented OWT at a Belgian offshore wind farm is presented. Comparing results between the calculated and monitored natural frequencies clearly demonstrates that a realistic representation of the foundation stiffness is crucial for accurate calculation of the OWT dynamics. The integrated analysis of the OWT based on the calibrated foundation model yields very accurate results.

Deformations and natural vibration frequency of a three-dimensional truss in a multi-storey building

Introduction. The analysis of deformations arising under the action of various loads and natural vibration frequencies is an integral part of the structural analysis of a multi-storey building. As a rule, this analysis is performed numerically in various systems using the finite element method and specialized software programmes. Analytical solutions are rare, but they are needed to evaluate the numerical ones and calculate simplified models of structures. The task is to find the analytical dependence of the frame deflection in a multi-storey building and its first natural frequency on the number of panels. The mass of the truss model is assumed to be distributed uniformly over the nodes. Only horizontal displacements of masses are taken into account.
 Materials and methods. To calculate the forces arising in the rods of a statically determinate truss using the method of joint isolation in the alphameric form, the software compiled in the Maple math system is applied. The calculation of displacements of nodes is performed using the Mohr integral. The Dunkerley method allows finding the analytical form of the lower estimate of the first frequency of natural vibrations for an arbitrary number of storeys in a building. The analysis of a series of solutions, made in the alphameric form for trusses with a successively growing number of panels allows deriving the final vibration frequency formula. When determining the natural vibrations of the characteristic matrix, the Eigenvalues operator from the LinearAlgebra package was used.
 Results. The resulting formulas used to analyze the deflection (horizontal displacement) of a structure under the action of a horizontal lateral load and the formula for estimating the first vibration frequency have simple forms, convenient for the quick verification of numerical solutions and preliminary evaluation of the behaviour of a designed structure.
 Conclusions. The proposed spatial statically determinate model of a multi-storey building allows deriving formulas for the analysis of deformations and natural frequencies of a structure with an arbitrary number of storeys. Resulting formulas can be applied to solve optimization tasks and serve as the basis for calculating a more complex statically indeterminate model of a structure.

Numerical and Experimental Modal Analyses of Inclined Supported Bridge Wing Structures

This paper studies ship bridge extensions called "bridge wings", which are one of the most critical areas of importance in ship vibration. These extensions, which have been modeled at the laboratory scale, have been analyzed using both experimental and finite element analysis methods. Bridge wing models have been constructed with varying inclination angles, and the natural frequencies and mode shapes obtained, both experimentally and numerically, have been compared. In this way, the effects of design properties on the results have been emphasized. Besides, the natural frequency discrepancies between the experimental and finite element analyses have been found to be very low. Another important result of this study has been obtained such that a certain support angle has been detected which the mode shape transition occurs in resonance. Natural frequency and mode shape analyses of the plates which have been supported with beams with varying inclination angles and achievement of mode shape transition phenomenon can be considered as the novelty about the contribution of this study to the state-of-the-art.

Welding Residual Stress Distribution of U-Rib Stiffened Plates of Steel Box Girders and its Influence on Structural Natural Frequencies

This paper mainly explores the distribution of welding residual stress of U-rib stiffened plates of steel box girders and examines the influence of welding residual stress over the natural frequencies of these plates. The research focuses on two aspects, namely, the distribution of welding residual stress, and the dynamic behavior of U-rib stiffened plates in the context of that distribution. Firstly, we build two finite element models to analyses the welding process and study the dynamic behavior. Next, the authors discussed how different geometric parameters, as well as welding parameters, affect the residual stress distribution. In addition, the welding residual stress curves were fitted for steel box girders of varied sizes, and a simplified formula was deduced for the distribution of welding residual stress. After that, the simplified formula was applied to analyze the natural frequencies of stiffened plates in multiple sets of models. Through the analysis of natural frequency under different boundary conditions, it was learned that the welding residual stress has a remarkable influence on the natural frequencies of stiffened plates.

Magnetoelastic nonlinear free vibration of an annular plate under a nonuniform magnetic field of the long straight current‐carrying wire

AbstractIn this article, the magnetoelastic nonlinear free vibration of a thin conductive annular plate under the nonuniform toroidal magnetic field is investigated, where the magnetic field is generated by a long straight current‐carrying wire. Based on electromagnetic theory, expressions of the nonuniform magnetic field, electromagnetic forces are deduced. The nonlinear free vibration equation of plate is derived by using the Hamilton principle. Considering different boundary conditions, the axisymmetric vibration differential equation is achieved by the Galerkin method. The method of multiple scales is employed to obtain the second‐order approximate analytical solutions and natural frequency. In numerical calculation, the characteristics of nonlinear natural vibration and singular points varying with different parameters, for example, current intensity and plate size, are presented, respectively. The results indicate that, with the increase of current, natural frequency increases and then stabilizes in the inner‐clamped and out‐free (C‐F) boundary, but decreases and stabilizes in the cases of the inner‐clamped and out‐clamped (C‐C) boundary or inner‐simply and out‐simply (S‐S) boundary. Moreover, when wire current is off, natural frequency maintains a constant, where the equilibrium solution of the system is a center. In addition, for all boundary conditions, natural frequency increases significantly with increase of internal radius and thickness, but decreases with the increase of outer radius.

Spatial Assessment of Heterogeneous Tissue Natural Frequency Using Micro-Force Optical Coherence Elastography.

Analysis of corneal tissue natural frequency was recently proposed as a biomarker for corneal biomechanics and has been performed using high-resolution optical coherence tomography (OCT)-based elastography (OCE). However, it remains unknown whether natural frequency analysis can resolve local variations in tissue structure. We measured heterogeneous samples to evaluate the correspondence between natural frequency distributions and regional structural variations. Sub-micrometer sample oscillations were induced point-wise by microliter air pulses (60–85 Pa, 3 ms) and detected correspondingly at each point using a 1,300 nm spectral domain common path OCT system with 0.44 nm phase detection sensitivity. The resulting oscillation frequency features were analyzed via fast Fourier transform and natural frequency was characterized using a single degree of freedom (SDOF) model. Oscillation features at each measurement point showed a complex frequency response with multiple frequency components that corresponded with global structural features; while the variation of frequency magnitude at each location reflected the local sample features. Silicone blocks (255.1 ± 11.0 Hz and 249.0 ± 4.6 Hz) embedded in an agar base (355.6 ± 0.8 Hz and 361.3 ± 5.5 Hz) were clearly distinguishable by natural frequency. In a beef shank sample, central fat and connective tissues had lower natural frequencies (91.7 ± 58.2 Hz) than muscle tissue (left side: 252.6 ± 52.3 Hz; right side: 161.5 ± 35.8 Hz). As a first step, we have shown the possibility of natural frequency OCE methods to characterize global and local features of heterogeneous samples. This method can provide additional information on corneal properties, complementary to current clinical biomechanical assessments, and could become a useful tool for clinical detection of ocular disease and evaluation of medical or surgical treatment outcomes.

Natural frequency analysis of FG-GOP/ polymer nanocomposite spheroid and ellipsoid doubly curved shells reinforced by transversely-isotropic carbon fibers

This investigation aims to determine the frequency responses associated with three-phase nanocomposite polymer-Graphene Oxide Powder (GOP)-carbon fiber spheroid and ellipsoid doubly-curved shells. In detail, the GOP nano-material is engaged to increase polymeric matrix mechanical features and form Crossbreed Matrix (CM) as well. For this reason, the rule of the mixture and the Halpin-Tsai schemes are recruited to pick up mechanical features associated with CM material. Next, carbon fibers are used to enhance mechanical criteria CM material and produce three-phase material as well. Accordingly, the Halpin-Tsai homogenization scheme is devoted to finding mechanical criteria connected to three-phase material. Afterwards, the equations of motion linked to spheroid and ellipsoid shells are mined hiring Hamilton's principle. Then, the compelling method named Generalized Differential Quadrature (GDQ) strategy is allocated to gap the basic motion equations associated with mentioned shells. At next, the standard eigenvalue computation is allocated to extract frequency responses related to the shells. To verify the offered procedure, one example is premeditated and compared with FEM commercial software. At last, various issues are arranged to excavate the trace of material mechanical and geometrical features related to the three-phase nanocomposite spheroid and ellipsoid doubly curved shells.

고유진동수 제한을 갖는 골조구조의 GA 기반 최적설계 시스템

Normal strategy of structure optimization procedure has been minimum cost or weight design. Minimum weight design satisfying an allowable stress has been used for the ship and offshore structure, but minimum cost design could be used for the case of high human cost. Natural frequency analysis and forced vibration one have been used for the strength estimation of marine structures. For the case of high precision experiment facilities in marine field, the structure has normally enough margin in allowable stress aspect and sometimes needs high natural frequency of structure to obtain very high precise experiment results. It is not easy to obtain a structure design with high natural frequency, since the natural frequency depend on the stiffness to mass ratio of the structure and increase of structural stiffness ordinary accompanies the increase of mass. It is further difficult at the grillage structure design using the profiles, because the properties of profiles are not continuous but discrete, and resource of profiles are limited at the design of grillage structure. In this paper, the grillage structure design system under the constraint of high natural frequency is introduced. The design system adopted genetic algorithm to realize optimization procedure and can be used at the design of the experimental facilities of marine field such as a towing carriage, PMM, test frame, measuring frame and rotating arm.

Bridge Natural Frequencies, Numerical Solution versus Experiment

The article is dedicated to a numerical and experimental analysis of the basic natural frequencies of a bridge structure. It presents the results obtained using the finite element method and the frequency response functions applied in two variants, using the lumped mass model and the model with a continuously distributed mass, as well as the results obtained using the energy method. It describes a simple experiment to measure the response of a bridge to random excitations from rail traffic, and compares the values of selected natural frequencies obtained by numerical and experimental methods. It offers engineers alternative solutions for their applications in engineering practice. It tries to bring a complicated theory closer to engineering practice in the simplest possible way and, at the same time, arouses interest in its deeper study.

Three dimensional free vibration analysis of functionally graded graphene reinforced composite laminated cylindrical panel

In this paper, natural frequency analysis of functionally graded graphene platelet (GPL) reinforced composite cylindrical panel is investigated. Halpin-Tsai equations are employed to obtain the mechanical properties of the structure. The linear three-dimensional elasticity theory based on the Hamilton principle and the numerical finite element method are used for obtaining the governing equations of motion. Four patterns of GPL distributions such as: FG-X, FG-V, FG-O and UD are assumed through the thickness of shell. The effects of various parameters such as different distributions and weight fractions of GPL, zigzag and armchair lay-up, geometry and different boundary conditions on the natural frequencies and mode shapes of shell have been investigated. The results indicate that the maximum and minimum natural frequencies belong to FG-X pattern and FG-O pattern, respectively.

Grey relation analysis of natural frequency and semi-active robust optimal control of a multi-dimensional isolator based on parallel mechanism and magneto-rheological damper

For isolating multi-dimensional vibrations experienced by precise facilities carried on a vehicle, a novel isolator is proposed based on 2-RPC/2-SPC parallel mechanism with magneto-rheological dampers. Kinematics and dynamics of the isolator are analyzed by geometrics and the Lagrange method. Grey relation analysis approach is conducted to determine the contributions of geometric parameters on natural frequency conveniently. Through analysis, the first order natural frequency of the isolator is affected by the length of the fixed platform most significantly. Due to manufacturing and assembling errors which could not be avoided in the isolator, robust optimal control algorithm is conducted to ensure control effect and robustness of the isolator at the same time. The gain of robust optimal control algorithm is obtained by deducing and solving linear matrix inequality. Compared to passive control, velocity root mean square values of robust optimal semi-active control decreased obviously in horizontal, longitudinal, vertical, and roll directions.

Computational and experimental method of accounting for the dewatering system in the analysis of natural frequencies and waveforms

Computational and experimental method of accounting for the dewatering system in the analysis of natural frequencies and waveforms

Dynamic Property Analysis of Orthotropic Bridge Deck with Local Fatigue Crack

With the increase in traffic volume and overweight vehicles, fatigue problems are highlighted. Especially for the orthotropic steel deck, the premature cracks seriously affect the service performance, operation, and service quality of the bridge. In this paper, the steel box‐girder segment model and deck substructure model considering several typical fatigue cracks were established to reveal the variation law of fatigue cracks on vibration frequency and deflection under vehicle traveling load. A natural frequency analysis was performed to evaluate the change in the vibration characteristics due to localized damage, together with a dynamic analysis that considered a vehicle traveling on the bridge. The results show that the initiation and propagation of several typical cracks have little influence on the lower modes of the overall structure and great influence on the high‐order modes of the substructure. The dynamic deflection response of the bridge changed under vehicle load as damage progressed. Therefore, it was possible to identify cracks of the orthotropic steel bridge deck and to provide guidance for fatigue crack detection and repair.

Analysis and Simulation of Natural Frequencies of Slightly Curved Pipes

For the transverse vibration of slightly curved pipe, a dynamic mechanical model based on Timoshenko beam theory is established for the first time. The natural vibration characteristic of slightly curved pipe under the influence of the fluid flow is analyzed. With generalized Hamiltonian principle, the governing equation of the transverse vibration of slightly curved pipe considering the effect of fluid-structure coupling is derived. Based on Galerkin truncation, the natural frequencies of slightly curved pipe are obtained by generalized eigenvalue method. Effects of the fluid velocity and the initial deflection on the natural vibration characteristic of the pipe are studied. The equivalent stiffness and equivalent damping method base on finite element simulation for the natural vibration of the slightly curved pipe are developed. Then through the finite element numerical simulation software, the results of Galerkin truncation method and the effectiveness of the Timoshenko model are verified. The results show that fluid velocity and the initial bending degree both have significant effects on the natural frequencies of slightly curved pipe.

Comparative modal analysis for a twisted beam axle for a hybrid vehicle

In this article it is presented a comparative analysis of natural mode frequencies for a non-powered rear axle used to fit mass production vehicle and for a similar rear axle derived from the first one to be used to fit a hybrid powered vehicle. The CAD model of the axle and the computed natural mode frequencies were realised using CATIA V5. For calculation, finit element method was used.