Mode Natural Frequencies Research Articles

Isomap-Based Three-Dimensional Operational Modal Analysis

In order to identify the modal parameters of time invariant three-dimensional engineering structures with damping and small nonlinearity, a novel isometric feature mapping (Isomap)-based three-dimensional operational modal analysis (OMA) method is proposed to extract nonlinear features in this paper. Using this Isomap-based OMA method, a low-dimensional embedding matrix is multiplied by a transformation matrix to obtain the original matrix. We find correspondence relationships between the low-dimensional embedding matrix and the modal coordinate response and between the transformation matrix and the modal shapes. From the low-dimensional embedding matrix, the natural frequencies can be determined using a Fourier transform and the damping ratios can be identified by the random decrement technique or natural excitation technique. The modal shapes can be estimated from the Moore–Penrose matrix inverse of the low-dimensional embedding matrix. We also discuss the effects of different parameters (i.e., number of neighbors and matrix assembly) on the results of modal parameter identification. The modal identification results from numerical simulations of the vibration response signals of a cylindrical shell under white noise excitation demonstrate that the proposed method can identify the modal shapes, natural frequencies, and ratios of three-dimensional structures in operational conditions only from the vibration response signals.

Vibration and dynamic behavior of electrostatic size-dependent micro-plates

The recent trend of using thin micro-plate structures in severe operational conditions caused the classical theory (CT) to be no longer suited in analyzing the dynamic characteristics of them. For this study, the modified version of the couple stress theory (MCST) is adopted. Then, using Hamilton’s principle and Kirchhoff plate theory, the dynamic form of the size-dependent equation of motion for micro-plates stimulated by electrostatic dynamic excitation is acquired. The mixed extended Kantorovich and differential transformation methods on partial differential equations are applied to obtain the mode shapes and natural frequencies. The mode shapes from the linear free vibration solution are used as the mode shapes of the assumed multi-mode displacement field. The displacement field is required to solve the dynamical equation of motion. The equations are subsequently solved by the fourth-order Runge–Kutta method. Some universal graphs are also presented using the MCST to predict the effects of the size effect, tensile and compressive residual stresses, and aspect ratio of micro-plate on the free vibration and dynamic behaviors of micro-plates around their static configuration. It is found that the non-dimensional natural frequency parameter varies linearly versus the other non-dimensional parameters of the micro-plate. Various interesting phenomena are observed from the current simulations of the dynamic response of micro-plates to both DC and AC excitation, as well as the boundary of the frequency behavior conversion. A comparison is drawn between the responses of the micro-plate based on the modified couple stress and CT taking the size dependency into account. To facilitate understanding of the physical phenomena observed in the results, a simple physical analog to the micro-plates is suggested. This physical analog, which describes the boundary of frequency behavior conversion, is the linear relationship between the non-dimensional parameters of the system. The study of this model can help to realize some of the complex responses of the micro-plates.

Higher mode elliptical integral solution for the large amplitude free vibration of a rectangular plate backed by a cavity

In this article, the elliptic integral solution form is adopted to obtain the higher mode natural frequencies of the large amplitude rectangular plate backed by a cavity. The main advantage of the proposed method is the concise acoustic structural modal formulation which do not require heavy computation effort. A set of numerical results are presented for studying the higher mode natural frequencies.

Dynamic load test analysis of upper bearing arch bridge

The bridge load test is an important means to evaluate the completed performance, construction quality and structural bearing capacity of the bridge structure, including determining the dynamic load test to determine the natural frequency, damping ratio and vibration mode of the bridge structure or structure, so as to determine the structural rigidity. The quality is an important factor to determine the basis. However, for the dynamic characteristics measurement method of the upper bearing arch bridge, the specification does not give a detailed detection method or recommendations. Combining with the analysis results of the field test data of the upper bearing arch bridge, this paper obtains a more accurate arrangement of test points.

Modeling analysis and lightweight design for an axle hub considering stress and fatigue life.

The lightweight of axle hub has been recognized as a typical representative of reducing the quality of vehicles for energy saving and emission reduction. Therefore, a modeling analysis and lightweight design based on ANSYS for axle hub is proposed. Firstly, design dimensions and structural parameters of axle hub are modeled. The hub model is imported into workbench software to simulate the static analysis. The stress and deformation of the axle hub are obtained by mesh element division, boundary condition constraints and loading conditions, and the modal and fatigue strength of the hub are simulated to obtain the modal natural frequency and life data. Then, from the point of view of reducing the quality and safety of the hub, the structure of the hub is changed, the model is compared again, and the lightweight design scheme can be obtained. The results show that the weight of a hub decreases by 5.537% after lightening. This method can improve the structure, save materials, reduce production costs, and shorten the design cycle. This lightweight design method has important reference and practical significance for the lightweight design of axle wheels and similar products.

Crack Identification and Localization In Structural Beams Using Numerical and Experimental Modal Analysis- A Review

This article presents a critical review of recent research done on crack identification and localization in structural beams using numerical and experimental modal analysis. Crack identification and localization in beams are very crucial in various engineering applications such as ship propeller shafts, aircraft wings, gantry cranes, and Turbo machinery blades. It is necessary to identify the damage in time; otherwise, there may be serious consequences like a catastrophic failure of the engineering structures. Experimental modal analysis is used to study the vibration characteristics of structures like natural frequency, damping and mode shapes. The modal parameters like natural frequency and mode shapes of undamaged and damaged beams are different. Based on this reason, structural damage can be detected, especially in beams. From the review of various research papers, it is identified that a lot of the research done on beams with open transverse crack. Crack location is identified by tracking variation in natural frequencies of a healthy and cracked beam

Markers tracking and extracting structural vibration utilizing Randomized Hough transform

The structural vibrations data may be used for health-monitoring of structures, determination of the structural characteristics, or up-date the structural analysis model. Therefore, accuracy in the measurement of these vibrations is crucial. Extracting the structural vibrations by utilizing accelerometers or LVDT11Linear Variable Differential Transformer sensors has different limitations, such as wiring restrictions, accessibility, and sometimes a change in the mass and stiffness of the structure. In recent years, we have witnessed an increase in the use of remote sensing. One of these methods is the use of camera and image processing. In this paper, a new algorithm is used to track marker points, which are attached to the object to extract structural dynamic characteristics like mode shapes and natural frequencies. For this purpose, the Randomized Hough detection algorithm is used to observe the ellipse markers movement on the structure. So, a three-story frame was considered and the vibration, mode shape and the natural frequency were derived from the new algorithm. The results have been compared with other measurement techniques like the Lucas-Kanade algorithm, the accelerometer sensors, and finite element method. The consequences indicate that the new algorithm improves computer vision in tracking points for extracting structural dynamic properties.

Axial force measurement of the bolt/nut assemblies based on the bending mode shape frequency of the protruding thread part using ultrasonic modal analysis

Abstract Bolt/nut assemblies are commonly used in machines and structures to enable easy assembly and disassembly. However, the axial force (i.e. the fastening force) of such assemblies decreases due to recursive external loading on the bolt/nut assemblies or chronic progressive wearing of the assemblies. Consequently, axial force monitoring is essential in preventing serious failure due to loss of functions in the assembly or fatigue. This study proves that the axial force on bolt/nut assemblies can be measured by investigating changes in the bending mode natural frequency of the bolt's threaded portion that protrudes from the nut (hereinafter referred to as the “protruding thread part“). This method is postulated on the observation that a reduction in the axial force decreases the joint stiffness of the bolt/nut assembly at the protruding thread part, leading to a shift in the characteristic peak frequency of the bending mode. A bolt/nut assembly is formed and its bending mode shapes and bending mode frequencies are obtained by impact tests. A series of tests are performed to define a quantitative measure of the correlation between the shift in the bending mode frequency and the axial force on the bolt/nut assembly. This method enables to perform measurement of the axial force on the bolt/nut assembly of −40 to −50% in the frequency range between 25 and 35 kHz. Dependency of the accuracy of this method on bolt aspect ratio (protruding length/nominal diameter) shows that lower aspect ratios are better suited for measuring axial force via bending mode frequency variation.

Experimental and Simulation Modal Analysis of a Prismatic Battery Module

The battery pack is the core component of a new energy vehicle (NEV), and reducing the impact of vibration induced resonance from the ground is a prerequisite for the safety of an NEV. For a high-performance battery pack design, a clear understanding of the structural dynamics of the key part of battery pack, such as the battery module, is of great significance. Additionally, a proper computational model for simulations of battery module also plays a key role in correctly predicting the dynamic response of battery packs. In this paper, an experimental modal analysis (EMA) was performed on a typical commercial battery module, composed of twelve 37Ah lithium nickel manganese cobalt oxide (NMC) prismatic cells, to obtain modal parameters such as mode shapes and natural frequencies. Additionally, three modeling methods for a prismatic battery module were established for the simulation modal analysis. The method of simplifying the prismatic cell to homogenous isotropic material had a better performance than the detailed modeling method, in predicting the modal parameters. Simultaneously, a novel method that can quickly obtain the equivalent parameters of the cell was proposed. The experimental results indicated that the fundamental frequency of battery module was higher than the excitation frequency range (0–150 Hz) from the ground. The mode shapes of the simulation results were in good agreement with the experimental results, and the average error of the natural frequency was below 10%, which verified the validity of the numerical model.

Vibration analysis of a rotating cantilever double-tapered AFGM nanobeam

Nano-structures such as carbon nanotube, nanobeams, nanorods, nanoplates, nanowires, and nanorings are tremendously used in various small-scale devices and investigating their dynamical behavior has been a hot research topic and can be beneficial in manufacturing and designing new devices. Therefore, free vibration analysis of a rotating cantilever double-tapered axially functionally graded material nanobeam is presented in this work. Due to the nano-scale dimension, classical beam theories are incompetent at describing the behavior of nanobeams. Thus, the nonlocal Eringen elasticity theory is adopted which considers the nonlocal scale effect for the small dimension effect of the structure of a nano-scale mechanism. The proposed nanobeam structure is assumed to taper linearly in two different axes, and its material is changing nonlinearly along its length. The equation of motion of the proposed system is found utilizing the nonlocal Eringen theory, and it is solved using a semi-analytical technique, differential transform method. Mode shapes and natural frequencies are extracted as the solution of the equation of motion of the system. Furthermore, the effects of several parameters such as nonlocal scale effect, rotational speed, hub radius, and taper ratios on the natural frequencies are investigated. Finally, a comparison between the presented work and other reported results show an excellent agreement.

Nonlocal vibration of carbon/boron-nitride nano-hetero-structure in thermal and magnetic fields by means of nonlinear finite element method

Abstract Hybrid nanotubes composed of carbon and boron-nitride nanotubes have manifested as innovative building blocks to exploit the exceptional features of both structures simultaneously. On the other hand, by mixing with other types of materials, the fabrication of relatively large nanotubes would be feasible in the case of macroscale applications. In the current article, a nonlinear finite element formulation is employed to deal with the nonlocal vibrational behavior of carbon/boron-nitride nano-hetero-tubes in the presence of magneto-thermal environment. Euler–Bernoulli beam model in conjunction with the Eringen’s nonlocal theory of elasticity is adopted to derive the governing equation of motion. In order to conduct a nonlinear frequency analysis, the von-Kármán nonlinearity associated with moderate rotations is also considered. It is well known that temperature gradients can significantly change the dynamic behavior of nanotubes. On the other hand, the coefficients of thermal expansions of carbon and boron-nitride nanotubes are quite different that may affect the structural stability of hybrid nanotubes. Hence, to explore the vibration characteristic of such composite structures, the influence of magneto-thermal environment is also taken into account. Finally, the eigenvalue analysis is performed to exhibit the nonlinear mode shapes and natural frequencies of the system due to initial displacement. It is expected that the recognition of dynamic behavior of such hybrid nanotubes may open the doors to the creative design of next-generation nano-devices.

Dynamic characteristics and experiment of push–pull high-power ultrasonic consolidation resonance system for metal foil

To realize metal foil consolidation, a push–pull high-power ultrasonic consolidation resonance system is designed. Firstly, the structure of a high-power piezoelectric transducer was designed and calculated, the push–pull ultrasonic consolidation resonance system was designed according to requirements of ultrasonic consolidation. Secondly, the finite element modal analysis of the ultrasonic consolidation resonance system was carried out, the natural frequency and vibration mode were obtained. The dynamic simulation of the ultrasonic consolidation resonance system was carried out based on the four-terminal network method and MATLAB/Simulink, the displacement of piezoelectric transducer and the resonance system was obtained, the output displacement of piezoelectric transducer and the consolidation sonotrode end surface is 6 μm and 20 μm respectively. Thirdly, the dynamic model of the consolidation resonance system was established, according to the transfer function, the root locus method and frequency response method were used to analyze the characteristics of the system. Finally, the sweep frequency and impedance measurement of piezoelectric transducer were carried out, and the sweep frequency and fixed frequency measurement of the ultrasonic consolidation resonance system were also carried out. Experimental results show that the resonant frequency of piezoelectric transducer is 19,875 Hz, and the minimum impedance value is 261.43 $$\Omega$$ when the frequency is near 20 kHz. When applying 120 V and 160 V voltage signal, the resonant frequency is 20,039 Hz and 20,055 Hz, the maximum displacement of the sonotrode which is excited by double piezoelectric transducers is about 16 μm. The ultrasonic consolidation machine is fabricated, which can meet requirements of metal foil consolidation, such as high-power and amplitude.

Effect of clay nanoparticles on the mechanical and vibration characteristics of intraply aramid/carbon fiber reinforced epoxy composite

AbstractIn the present contribution, the tensile, flexural, vibration and damping properties of intraply aramid/carbon fiber reinforced epoxy composite with the effect of clay nanoparticles inclusion have been investigated. Seven clay nanoparticles contents of 0, 1, 2, 4, 6, 8, and 10 wt% were used to produce the composite laminates. The samples were produced and experimented in accordance with ASTM standards. The standards ASTM D 638, ASTM D 790, and ASTM E756 were used for tensile, flexural, and vibration tests, respectively. Vibration characteristics were calculated using experimental modal analysis. Half power band‐width method was applied to evaluate damping responses of first natural frequency modes of the composite samples. The results indicated that the high improvement of tensile and flexural strength was obtained at clay nanoparticle contents of 1 and 2 wt% with increment of 13.1% and 28.2%, respectively. The highest values of natural frequency, storage modulus, lost modulus were obtained at clay nanoparticle contents of 10, 1, and 2 wt% with increments of 23.4%, 20.7%, and 11.6%, respectively.

Nonlinear Flight Mode Identification by Applying Modified Ensemble Empirical Mode Decomposition and Hilbert–Huang Transformation

Identification of the “aircraft dynamic modes” is one of the researchers’ favorite subjects in the flight mechanics field to study the behavior of airplane in maneuvers and nonlinear regime. Technically, by measuring the flight test parameters, the flight dynamic modes could be estimated. Although several approaches calculate precisely the linear flight dynamic modes, there is not a known standard procedure to calculate the nonlinear flight dynamic modes. In this paper, identification of the flight dynamic modes in highly nonlinear maneuver conditions and particularly in the coupled dynamic spin maneuvers is investigated. A new approach based on Hilbert–Huang Transform (HTT) for identification of the flight dynamic modes is presented in this paper. To overcome the mode mixing problem during decomposition which leads to imprecise results in the estimation of the flight dynamic modes, a Modified Ensemble Empirical Mode Decomposition (MEEMD) algorithm for processing of the complex signals that originate from FDR is presented in this research. This new algorithm is able to make a precise reconstruction of the original signal and it performs the task of signal decomposition with fewer iterations and so with less complexity order rather than the competitor approaches. An innovative algorithm for calculating flight dynamic modes natural frequencies and the damping ratios which uses the IMFs produced by MEEMD is presented. The obtained approach was applied to flight data, which belong to spin maneuvers. The results show the correct performance of the presented technique in the nonlinear flight regime.

Analysis of the Composite Boring Bar Dynamic Characteristics Considering Shear Deformation and Rotational Inertia

A boring bar is a tool used to install cutters and transfer power during boring. Because the boring bar in a narrow workspace is usually slender, chatter often occurs in the boring process. To improve the chatter stability of the boring bar, researchers have designed composite material boring bars with high dynamic stiffness to meet the requirements of high-speed boring. However, the effect of the shear deformation and rotational inertia were ignored. In this paper, a model of a composite boring bar considering shear deformation and rotational inertia is established based on the Adomian Modified Decomposition Method (AMDM). The dynamic characteristics, such as the vibration mode shapes, natural frequency, and chatter stability of the composite boring bar considering the shear deformation and rotational inertia, are analyzed comprehensively. The analysis results show that, when the shear deformation and rotational inertia are considered, the composite boring bar can exhibit different vibration mode shapes. Moreover, the natural frequencies and the cutting depth will be reduced. The results are helpful to improve the understanding about dynamic characteristics of the composite boring bar, and to provide guidance for designing of boring bars. Moreover, accurate adjustment of the cutting speed and depth in CNC boring can be based on the analysis results.

Modal Analysis of Four Layered Composite Cantilever Beam with Lay-Up Sequence and Length-To-Thickness Ratio

Abstract Composites are well known for their specific strength and specific modulus and therefore finding lots of engineering applications now a day. In this study, a first order shear deformation theory is used to describe mathematical procedure for the free vibration analysis of layered composite cantilever beam. The finite element (FE) model is prepared by using 281 Shell element having 8 nodes with six degrees of freedom at each node for the modal analysis. The detailed effect of lay-up sequence and length-to-thickness ratio with lay-up angle on natural frequencies of various modes are studied by considering four layered composite cantilever beam. Four different lay-up sequences and five different length-to-thickness ratios are considered to study their effect on bending, transverse and torsional modes of vibration. The results obtained are compared with the previously published literature to validate the efficacy and accuracy of the model. The analysis results show distinct modal characteristics due to change in lay-up sequence and length-to-thickness ratio. This study could be used for proper selection of the lay-up sequence and length-to-thickness ratio to adjust modal parameter like natural frequency of the cantilever beam in order to avoid resonance. The parametric study using analytical model would be highly complex and thus FE model is used for the purpose. Natural frequency of all the modes is observed to be highly sensitive to lay up sequence and the effect of length-to-thickness ratio also needs to be considered. Bending mode natural frequency is higher with antisymmetric lay up sequence whereas transverse mode is with symmetric layup sequence for entire range of layup angles. The torsional mode natural frequency is higher with symmetric layup sequence upto the layup angle 450

Semi-Analytical Solution of In-Plane Vibrations of Circular Arches Carrying Added Point Masses

In spite of the current use in modern civil engineering of straight structural components made of reinforced concrete, such as beams and slabs, arches still remain quite often adopted in architectural design, due to their interesting mechanical and esthetical properties. Therefore, practical analytical and numerical tools should be available in order to allow designers to ensure the resistance and stability of this type of structures, especially in the dynamic regime and when point masses are added. The sixth degree differential equation of motion of inextensible arches is known to be quite difficult to deal with and is not applicable to the case examined here of arches with added point masses [1]. The procedure adopted in this article consisted on finding relatively easy particular solutions of this equation satisfying the end conditions and using them as trial functions in the Rayleigh-Ritz formulations of the practical cases of interest. Circular arches of different opening angles are examined here under the classical hypotheses: (1) the effect of shear deformation and rotary inertia are neglected (2) the arch axis is inextensible (3) the dimensions of the cross-section are small in comparisons with the radius;(4) the cross-section is uniform. Three different kinds of end conditions are considered: simply supported-simply supported (SS), clamped-simply supported (CS) and clamped-clamped (CC). The Rayleigh-Ritz method allowed in each case to determine, via an algebraic solution of the associated eigenvalue problem, the first seven mode shapes and natural frequencies of arches with different values of the opening angle. The comparison with the results available in the bibliography was satisfactory and the mode shapes were plotted. The second part of this work was devoted to arches with added concentrated masses: likewise, the numerical values found for the natural frequencies compare quite well with the few references available and the mode shapes are plotted showing the effects of the opening angle, the mass and the positions of the added point masses.

Modal analysis of functionally graded piezoelectric material plates

The goal of this research is to execute a modal analysis of the functionally graded piezoelectric material rectangular plate to find the natural frequency with different mode shapes by using the Finite Element (FE) Technique. The functionally graded piezoelectric material plate is considered to be graded along the thickness and follow the simplified power-law. FEM code has been developed in ANSYS 17.2 for modal analysis of the functionally graded piezoelectric material (FGPM) rectangular plate. The FGPM Rectangular plate mode shapes and natural frequencies are observed at varying boundary conditions. The effect of power-law exponent n variation on the natural frequency of the FGPM plate with different boundary conditions are considered, and results are presented.

Adaptive window function and window size based operational modal parameter identification for linear time-varying structure

In order to select the window function and window size adaptively before getting the results, we proposed adaptive moving window principle component analysis (AMWPCA) based OMA method to identify modal shapes and modal natural frequencies of slow LTV structures with weekly damped only from non-stationary vibration response signal online. The adaptive is achieved in two ways: change the window function or window size. We develop an adaptive indicator as the basis for window function and window size changes. Our adaptive approach is to make the difference between adjacent eigenvalues not too small. The operational modal parameter identification results in non-stationarity response signal dataset of a three-degree-of-freedom structure with slow time-varying mass show that comparing with fixed size moving window principle component analysis, our AMWPCA method can identify the modal shapes and modal frequencies better.

Flow control over a square cylinder using attached rigid and flexible splitter plate at intermediate flow regime

A detailed flow field behind a stationary square cylinder with attached rigid and flexible splitter plates has been studied using particle image velocimetry, constant temperature anemometry, and flow visualization techniques. A wide range of lengths of the splitter plate (L/B = 0–8) are considered, and their respective wake interference is reported. The investigation is carried out at an intermediate flow regime at three Reynolds numbers 600, 1000, and 2000 (based on blocking width “B” of the cylinder). The literature seriously lacks the information on a passive flow control of bluff body wakes in this flow regime. This study shows that the wake frequency and mean drag coefficient vary nonmonotonically to splitter plate lengths. The length of the splitter plate is a critical parameter, which, apart from flow control, can also bring a significant wake transition. At L/B > 3 to L/B = 4, strong secondary vortices are shed from the trailing edge. The shedding of the secondary vortex leads to a sudden shrinkage in the recirculation bubble and an increase in the periodicity of the unsteady flow. The onset of high amplitude flapping occurs in a flexible splitter plate (L/B = 3) at Re = 2000. The vortex shedding frequency becomes higher than the first mode natural frequency of the flexible splitter plate for this length and remains in the same regime for L/B > 3. The amplitude of flapping increases up to L/B = 5 and then again recedes. The high amplitude flapping of the flexible splitter plate adversely affects the mean drag coefficient of the bluff body.