Finite Element Modal Analysis Research Articles

Influence Prediction of Tissue Injury on Frequency Variations of the Lumbar Spine under Vibration

A three-dimensional finite element model of the spine T12-S1 segment was developed and used to investigate biodynamics characteristics of the human lumbar spine. The T12-S1 model was carefully built including spinal vertebrae, intervertebral discs, and ligaments so as to approach the real human spine. Finite element modal analysis was carried out to obtain vibration modes and resonant frequencies of the spine. The analytical results indicate that the vertical resonant frequency of the spinal T12-S1 segment with a mass of 40 kg on the top vertebra is 7.68 Hz. The vertical resonant frequencies of spine motion segments decrease with the number of spine motion segments increasing. The tissue injury, such as disc denucleation and removal both of facet articulations and their capsular ligaments may decrease the resonant frequencies of spine in different extent. The denucleation makes larger influence on vertical resonant frequencies than facetectomy does. The denucleation is more harmful to the facet articulations under whole body vibration. The dynamic characteristics of the T12-S1 model accords with the actual human spine, and it is useful for the relative studies of the human spine, such as biomechanical characteristics, vibration-related injury mechanism of the human spine, and development of vibration-related mechanical products.

Modal analysis of cold-formed pallet rack structures with semi-rigid connections

The three dimensional (3D) model of conventional pallet racking systems were prepared using the finite element program ANSYS and free vibration modal analysis carried out on conventional pallet racks with the 18 types of column sections developed along with semi-rigid connection. The stiffness of the connector was tested using the conventional cantilever method and also using a double cantilever method. Non-linear finite element analysis of both the tests was carried out. From the experimental study on connection and finite element modal analysis, a simple analytical model that captures the seismic behavior of storage racks in their down aisle direction is proposed. The model is aimed at developing simplified equation for the fundamental period of storage racks in their down aisle direction. A parametric study was carried out to find out fundamental mode shape and time period. Finite element method is used for the accuracy and appropriateness of cold-formed steel frame.

Dynamic Response Analysis of Working Device of Hydraulic Excavator under Working Impact Loading

A there-dimensional finite element model of the working device of a single backhoe-bucket hydraulic excavator was developed to analyze and evaluate the rationality of structure design of the working device in this study. By finite element modal analysis, the resonant frequencies and vibration modes of the working device system were obtained. By dynamic response analysis, the changing trends of stress and strain of the device were obtained. In addition, the influence of different excavating resistance forces to the working device on dynamic response of the device system was compared for large and small resistance forces at the beginning excavation moment. The results show that a large resistance force at the initial excavating moment may result in the device vibrating with large vibration amplitude at the beginning excavation moment. These results might provide useful reference on design improvement of the excavator working device.

Anomaly of mode field in multistep index profile multimode fiber

A remarkable anomaly of a mode field in multistep-index multimode fibers was observed. It is demonstrated by a finite-element modal analysis that the highest field peak locations of guided modes with the anomaly shift toward the core-cladding boundary drastically.

Modal contribution analysis of an operating complete flexible HDD affecting the head-disk motion due to shock

This paper proposes a finite element modal and shock analysis of an operating complete flexible hard disk drive (HDD). It develops a finite element model of a complete flexible HDD including the spinning disk-spindle system with fluid dynamic bearings, the head-suspension-actuator with pivot bearings and air bearings, the base plate and cover with complicated geometry. The finite element model also includes a mounting table, which is a tetrahedron element with big mass, to simulate the shock to the HDD from the exciter. It performs the modal analysis to calculate the natural frequencies and mode shapes as well as the mode superposition to calculate the motion between head and disk. It proposes a method to determine the contribution of each superposed vibration mode to the head-disk motion of an operating complete flexible HDD due to shock. It also proposes the numerical criterion to determine the head crash due to shock, and it is applied to investigate the contribution of each vibration mode to the head-disk motion when the head-crash occurs. It shows that the coupled (0,0) disk modes play the dominant role on the head-disk motion and that the pure disk modes have no effect on the head-disk motion under the axial shock. The proposed method can be effectively applied to investigate the dynamics of a HDD and to design a robust HDD against shock to prevent the head-crash.

HDDにおけるサーボの高性能化を目指したスマート構造の最適設計(<特集>D&D 2008)

The head positioning accuracy of the hard disk drive (HDD) should be improved to meet today's increasing performance demands. Vibration suppression of the arm in the hard disk drive is very important to enhance the servo bandwidth of the head positioning system. In this study, the smart structure is introduced into the hard disk drive to suppress the vibration. It has been expected that technology of smart structure will contribute to the development of small and light-weight mechatronics devices with the required performance. First, modeling of the system is conducted with finite element method (FEM) and modal analysis. Next, the actuator location and the control system are simultaneously optimized using genetic algorithm (GA). Vibration control effect with the proposed vibration control mechanisms has been evaluated by some simulations.

Optimization of Smart Structure for Improving Servo Performance of Hard Disk Drive

Head positioning accuracy of the hard disk drive should be improved to meet today's increasing performance demands. Vibration suppression of the arm in the hard disk drive is very important to enhance the servo bandwidth of the head positioning system. In this study, smart structure technology is introduced into the hard disk drive to suppress the vibration of the head actuator. It has been expected that the smart structure technology will contribute to the development of small and light-weight mechatronics devices with the required performance. First, modeling of the system is conducted with finite element method and modal analysis. Next, the actuator location and the control system are simultaneously optimized using genetic algorithm. Vibration control effect with the proposed vibration control mechanisms has been evaluated by some simulations.

Application of Experimental and Finite Element Modal Analysis in Development of a Novel Solder Joint Inspection Systems

Inspection of flip chip solder joints has been a crucial process in the electronics manufacturing industry to reduce manufacturing cost, improve yield, and ensure product quality and reliability. New inspection techniques are urgently needed to fill in the gap between available inspection capabilities and industry requirements of low-cost, fast-speed, and highly reliable inspection systems. The laser ultrasound inspection system under development aims to provide a solution that can overcome some of the limitations of current inspection techniques. This research project is based on laser ultrasound and interferometric techniques. A pulsed laser generates ultrasound on the chip's surface, and the entire chip is excited into structural vibration. An interferometer is used to measure the vibration displacement of the chip's surface at several points, and solder joints with different qualities cause different vibration responses. By analyzing the surface vibration responses, defects in solder joints may be detected and/or classified. In this paper, a broadband laser pulse is used for dynamic excitation of the chip before its vibration signature is analyzed. Experimental modal analysis extracts and estimates the modal information (mode frequencies and mode shapes) from raw vibration signals. Multiple-point surface responses are scanned with an interferometer under repeated laser pulse excitation. Spectral estimation on the raw vibration signals gives dominant-mode frequencies. The corresponding vibrational patterns are obtained by reconstructing the scanned grids using the decomposed signals at each mode frequency. Because we are interested only in the transverse vibration on the chip's surface, and because the chip's length and width are much larger than its thickness, it can be modeled as a rectangular plate with pin supports. Modal analysis by finite element modeling is applied to devices with and without defects. The objectives are to identify the differences of mode frequencies and mode shapes between good chips and chips with defects and to identify measurement points that show maximum difference in the presence and absence of defects.

Modal Parameter Extraction of a Turboset From High Speed Balance Data

Turbosets used in power generation industry are frequently placed on flexible foundations, which significantly influence the overall dynamics. Establishment of structural models that capture the rotor and foundation effects reliably using finite element modeling or modal analysis is difficult because of model complexity and/or costs involved. This paper presents a method to extract modal parameter information of a turboset using frequency response function data recorded during high speed balancing. The main advantage of the present method over the others is the low cost and small effort involved, so that it is of practical use in an industrial setting. A real life example dealing with parameter extraction for a large generator rotor is presented to demonstrate its implementation.

Substructure Coupling of Microend Mills to Aid in the Suppression of Chatter

Microend milling offers the ability to machine microparts of complex geometry relatively quickly when compared with photolithographic techniques. The key to good surface quality is the minimization of tool chatter. This requires an understanding of the milling tool and the milling structure system dynamics. However, impact hammer testing cannot be applied directly to the prediction of tool tip dynamics because microend mills are fragile, with tip diameters as small as 10μm. This paper investigates the application of the receptance coupling technique to mathematically couple the spindle/micromachine and arbitrary microtools with different geometries. The frequency response functions (FRFs) of the spindle/micromachine tool are measured experimentally through impact hammer testing, utilizing laser displacement and capacitance sensors. The dynamics of an arbitrary tool substructure are determined through modal finite element analyses. Joint rotational dynamics are indirectly determined through experimentally measuring the FRFs of gauge tools. From the FRFs, chatter conditions are predicted and verified through micromilling experiments.

An approach to design a high power piezoelectric ultrasonic transducer

Application of ultrasonic waves has been considerably progressed during the last decade and piezoelectric ceramics have had a common use as the driving source of such waves. However, there is not enough documented information on design and technology of manufacturing a high power ultrasonic transducer. In this paper, an attempt has been made to analyze the stress produced along the oscillating PZT employed ultrasonic head by applying the principles of acoustic wave propagation. Then, based on such analysis, general principles of PZT transducer design, excited by a DC-biased alternating electrical source, has been derived and finally a typical such transducer has been designed, manufactured and tested. By employing finite element modal analysis, the resonance frequency of the transducer was determined and compared with the experimental results. It was concluded that, the constitutive piezoelectric equations referred to in most sources and books are not valid for analyzing the acoustical dynamic stress in ultrasonic transducers. Instead, the analysis should be done with considering the dynamic behavior (elastic, damping and Inertia factors) of the problem.

Fatigue crack growth regular tests for engine crankshaft and analysis on the mechanism

The crack propagation characteristics of a kind of diesel crankshaft are studied by measuring the crack growth rate using the frequency sweep method. This method is based on resonant fatigue test rig. According to the regularity that the resonance frequency will drop as the crankshaft’s crack growth, the method tracks the crack size’s growth rate dynamically by scanning the spectra of the resonant system. After the crankshaft is broken and actual shape and size of the crack are available, finite element modal analyses are conducted to accurately calculate the crack size at various test-cycle time point. The frequency sweep method is a more capable method than normal methods. It can be directly applied to a component even with complex structure and has been treated by all kinds of technology processing. As a corresponding result, the crack growth rate curve plotted herein would synthetically reflect many influence factors on the crack propagation behavior, such as geometric parameters, precision of machine tooling and reinforcing treatments, etc. 4 crankshaft specimens are tested and the result shows that a 3-section feature exists in the Paris region of the curve. According to the specimens’ fracture surface profile, it is concluded that the feature’s formation is chiefly due to the stress ratio’s sudden change during crack propagating, which is caused by surface residual stress of the .

Failure analysis of a second stage blade in a gas turbine engine

The failure of a second stage blade in a gas turbine was investigated by metallurgical and mechanical examinations of the failed blade. The blade was made of a nickel-base alloy Inconel 738LC. The turbine engine has been in service for about 73,500 h before the blade failure at 5:50 PM on 14 August 2004. Due to the blade failure, the turbine engine was damaged severely. The investigation was started with a thorough visual inspection of the turbine and the blades surfaces, followed by the fractography of the fracture surfaces, microstructural investigations, chemical analysis and hardness measurement. The observation showed that a serious pitting was occurred on the blade surfaces and there were evidences of fatigue marks in the fracture surface. The microstructural changes were not critical. It was found that the crack initiated by the hot corrosion from the leading edge and propagated by fatigue and finally, as a result of the reduction in cross-section area, fracture was completed. An analytical calculation parallel to the finite element method was utilized to determine the static stresses due to huge centrifugal force. The dynamic characteristics of the turbine blade were evaluated by the finite element modal and harmonic analyses. Finally according to the log sheet records and by using a Campbell diagram there was a good agreement between the failure signs and FEM results which showed the broken blade has been resonated by the third vibrational mode occasionally before the failure occurred.

Influence of anteroposterior shifting of trunk mass centroid on vibrational configuration of human spine

This study attempts to determine the influence of anteroposterior (A-P) shifting of trunk mass from the upright sedentary posture on dynamic characteristics of the human lumbar spine. A three-dimensional finite element (FE) model comprising of the T12–Pelvis spine unit was used to mimic the human spine system. It is not clear how the A-P shifting of the upper part of human upper body affect on vibrational modality of the human lumbar spine under whole body vibration. Five trunk mass point locations were assumed by 2.0 cm anterior, 1.0 cm anterior, 1.0 cm posterior and 2.0 cm posterior to the upright sedentary posture including no shifting posture. FE modal analysis was used to extract the resonant frequencies and vibration modes of the human spine. The analytical results indicate that trunk mass centroid shifting onwards or rearwards may result in a reduction of vertical resonant frequency of the human spine. The human spine has the highest vertical resonant frequency at the normal upright sedentary posture with the trunk mass locating around 1.0 cm anterior to the L3–L4 vertebral centroid. Larger A-P deformations and rotational deformations were also found at the spine motion segments L3–L4 and L4–L5, which imply higher compressive stress and shear stress at the disc annulus of those spinal motion segments. The findings in this study may explain why long-term whole body vibration might induce the degeneration of human spine at the relevant spinal motion segments.

A Novel Radiating Rib Structure in Switched Reluctance Motors for Low Acoustic Noise

Vibration and acoustic noise limit the application of switched reluctance motors (SRMs). Because the radial vibration of the stator is the primary source of the acoustic noise of SRMs, the modal analysis of the stator vibration is an important and effective way to reduce the acoustic noise. In this paper, we construct eight computational models by varying the structural forms, height, quantity, and shape of radiating ribs to investigate the influence of radiating ribs on the mechanical resonant frequencies, under the condition of the same amount of radiating rib material. We apply three-dimensional finite-element modal analysis to accurately analyze these models. Finally, we derive an optimal structure of the radiating rib to lower the acoustic noise level of SRMs and dissipate heat.

Brake squeal: Linear and nonlinear numerical approaches

“Brake squeal” groups a large set of high-frequency sound emissions from brake systems. They are generated during the braking phase and are characterized by a harmonic spectrum. The onset of squeal is due to an unstable behaviour occurring in linear conditions during the braking phase, and a general approach used by several authors to determine the system instabilities is the complex eigenvalues analysis. When the brake begins to squeal, the response of the system reaches a new limit cycle where the linear models cannot be used anymore. This paper presents the integration of two different numerical procedures to identify the mechanism bringing to squeal instability and to analyse its dynamics. The first approach is a finite element modal analysis of the brake system and is used to identify its eigenvalues and to relate them to the squeal occurrence. The second one is a specific finite element programme, Plast3, appropriate for nonlinear dynamic analyses in the time domain and is particularly addressed to study contact problems with friction between deformable bodies. This programme computes the contact stresses and permits to determine the dynamics of the system along the contact surface, both in the linear and nonlinear fields. The two models are compared and the onset of squeal is predicted both in the frequency domain by the linear model and in the time domain by the nonlinear one. The instability predictions, obtained by the two models, are discussed. To simplify the dynamics of its components, the study is carried out on a simple model, made of a disc, a small friction pad and a beam supporting the pad. The geometry of the model is related to an experimental set-up used to validate the models and to compare the numerical results with the experiments.

Finite element modal analysis of an HDD considering the flexibility of spinning disk–spindle, head–suspension–actuator and supporting structure

This paper presents a finite element method to analyze the free vibration of a flexible HDD (hard disk drive) composed of the spinning disk–spindle system with fluid dynamic bearings (FDBs), the head–suspension–actuator with pivot bearings, and the base plate with complicated geometry. Finite element equations of each component of an HDD are consistently derived with the satisfaction of the geometric compatibility in the internal boundary between each component. The spinning disk, hub and FDBs are modeled by annular sector elements, beam elements and stiffness and damping elements, respectively. It develops a 2-D quadrilateral 4-node shell element with rotational degrees of freedom to model the thin suspension efficiently as well as to satisfy the geometric compatibility between the 3-D tetrahedral element and the 2-D shell element. Base plate, arm, E-block and fantail are modeled by tetrahedral elements. Pivot bearing of an actuator and air bearing between spinning disk and head are modeled by stiffness elements. The restarted Arnoldi iteration method is applied to solve the large asymmetric eigenvalue problem to determine the natural frequencies and mode shapes of the finite element model. Experimental modal testing shows that the proposed method well predicts the vibration characteristics of an HDD. This research also shows that even the vibration motion of the spinning disk corresponding to half-speed whirl and the pure disk mode are transferred to a head–suspension–actuator and base plate through the air bearing and the pivot bearing consecutively. The proposed method can be effectively extended to investigate the forced vibration of an HDD and to design a robust HDD against shock.

Experimental Investigation of Smart Hull Structures Based on Macro Fiber Composite Actuators

In the present paper, the dynamic characteristics of smart hull structure are investigated for the feasibility of Macro Fiber Composite (MFC) actuator in active vibration control of smart hull structure. MFC is an advanced anisotropic piezoceramic actuator. Finite element technique was used to ensure application to practical geometry and boundary conditions of smart hull structure. Using finite element method, modal analysis and strain distribution were first conducted to investigate dynamic characteristics of smart hull structure. Based on numerical modal analysis, the locations of MFC actuators are determined to achieve maximum control authority. Then, the MFC actuators are attached to the hull structure and natural frequencies and damping coefficients are identified through experimental modal test.

PREDICTION OF RESONANCE CHARACTERISTICS OF THE FOREARM BONES USING FINITE ELEMENT ANALYSIS

Modal analysis is often used as a diagnostic tool for osteoporosis, fracture healing, and dental treatment monitoring by measuring the resonance characteristics of an anatomical structure. The objective of this study was to conduct parametric finite element modal analysis of the forearm bones using geometric models reconstructed from the Visible Human Project datasets in order to gain insights into the structural integrity of the forearm complex and their implications on bone health. The reported fundamental resonant frequency of the ulna was matched to calibrate the material properties of each anatomical component of the ulna, and subsequently sensitivities of each material parameter were assessed. Resonance characteristics of the radius for four vibration modes were then estimated using the calibrated material data from the calibration simulation. The ulna had the fundamental mode in mediolateral bending at 400 Hz, while the radius in anterior–posterior bending at 411 Hz. The axial and torsional modes always had higher fundamental resonant frequencies over 1700 Hz for both bones. It was suggested that the parametric finite element modal analysis in conjunction with in vivo modal testing may be applicable for determining the physical properties of a long bone for quantitative assessment of bone health.

Vibrational analysis of mandible trauma: experimental and numerical approaches

The aim of this study was to evaluate the effectiveness of vibrational assessment of the mandible fracture patterns. Measurement of natural frequencies and associated vibrational mode shapes was performed to determine the relationship between the dynamic behavior of the human mandible and incidence of mandibular fractures using both in vitro modal testing and finite element analysis. Our results show that the natural frequencies of the human mandible in dry and wet conditions are 567 Hz and 501 Hz, respectively. The first vibrational mode of human mandible is a bending vibration with nodes located at the mandibular body where bone fracture is less likely to occur. By contrast, high vibration amplitudes were identified in the symphysis/parasymphysis and subcondyle regions where bone fractures tend occur. These findings indicate that the vibrational characteristics of the mandible are potential parameters for assessment of the mechanisms of injury.