Mode Synthesis Method Research Articles

Vibration and stability of axially loaded cracked beams

Structural defects such as cracks are the source of local flexibilities and cause deficiencies in structural resistance. In the engineering constructions, structural elements sometimes are subjected to axial loading. Therefore, besides crack ratios and locations, influence of applied load on the stability and dynamical characteristics should also be explored. This study offers a numerical technique for the vibration and stability analysis of axially loaded cracked beams. The model merges finite element and component mode synthesis methods. Initially, stability analysis is completed and then dynamical characteristics of beams are found. Very good conformities between outcomes of the current study and those in literature, give the confidence that proposed method is reliable and effective.

Computational Aeroelastic Simulation of Rapidly Morphing Air Vehicles

A new approach for CFD-based aeroelastic simulation of rapidly morphing flight vehicles is presented is presented. The morphing vehicle consists of a number of components interconnected by actuators and contact constraints. Due to aerodynamic, inertial and actuation loads the overall structure undergoes large-displacement morphing. The method assumes that each component experiences large rigid-body displacements and small elastic deformations that are linear combinations of the individual normal modes. The structural equations of motion are based on a substructure modal synthesis method which applies fictitious masses at the interface coordinates. The modal synthesis method is expanded to allow large rotations between the structural components while keeping displacements and rotation compatibility at the interface coordinates. The compatibility equations are timedependent, and the inclusion of their time derivatives in the equations of motion brings introduces non-linear dynamic effects. The resulting generalized-coordinate nonlinear matrix equations of motion are embedded in a time-accurate CFD code. The vector of generalized forces includes aerodynamic forces from the CFD solution, inertial forces due to the modal accelerations and the relative component rotational velocities, and actuation forces. The computational process is demonstrated by two models: a two-wings-and-body configuration, where the wings are rotated rapidly from parallel position along a fuselage to perpendicular position; and a wing-body configuration where the wing is rotating about a hinge attached to a slender body from a parallel position to a perpendicular one. The morphing simulations demonstrate a robust and stable computational process that exhibits significant aeroelastic effects.

고속 전력선통신 모뎀용 수신단측 전류모드 대역통과 필터 설계

본 논문에서는 저전압 저전력 필터 설계에 적합한 전류모드 방식을 이용하여 고속 전력선통신(PLC)모뎀 수 신단의 1MHz~30MHz 차단주파수를 갖는 6차 대역통과 필터를 설계하였다. 3차 바터워스 고역통과 필터와 3차 체비세프 저역통과 필터를 종속연결로 구성하여 대역통과 필터를 설계하였다. 필터를 구성하기 위한 핵심로써 기존의 전류미러형 적분기에 비하여 증가된 이득 및 차단주파수를 가지는 새로운 전류모드 적분기를 설계하였다. 설계된 전류모드 적분기의 이득과 차단주파수는 각각 32.2dB 및 247MHz이였다. 설계된 6차 대역통과 필터의 차단주파수는 제어전압에 따라서 200KHz에서 50MHz까지 조정이 될 수 있으며 소비전력은 공급전압 1.8V에서 2.85mW이였다. 설계된 대역통과 필터는 1.8V, <TEX>$0.18{\mu}m$</TEX> CMOS 공정파라메터를 사용하여 검증되었다. In this paper a <TEX>$6^{th}$</TEX> 1MHz~30MHz bandpass filter for Power line communication(PLC) modem receiver is designed using current mode synthesis method which is good to design the low-voltage and low-power filter. The designed bandpass filter is composed of cascade connecting between <TEX>$3^{rd}$</TEX> Butterworth highpass filter and <TEX>$3^{rd}$</TEX> Chebychev lowpass filter. As a core circuit in the current-mode filter, a current-mode integrator is designed with new architecture which can improve gain and unity gain frequency of the integrator. The gain and the unity gain frequency of the designed integrator is each 32.2dB and 247MHz. And the cutoff frequency of the designed <TEX>$6^{th}$</TEX> bandpass filter can be controlled to 50MHz from 200KHz according to controlling voltage and the power consumption is 2.85mW with supply voltage, 1.8V. The designed bandpass filter was verified using a <TEX>$0.18{\mu}m$</TEX> CMOS parameter.

Updating component reduction bases of static and vibration modes using preconditioned iterative techniques

Although component mode synthesis (CMS) methods for structural dynamic analysis were introduced in the 1960s, one of the current challenges is to apply the methodology in a practical design process in which (parametric) modifications are applied to the component(s). For every design change, these components need to be remodeled and their reduction bases recomputed, thereby seriously hindering the effectiveness of the CMS approach. To overcome this, we propose in this work an approach based on preconditioned iterative methods to efficiently update the reduction basis.For the updating of the static modes, we use the well known preconditioned conjugate gradient (CG) method applied in a block form and combined with the projection and reconjugation technique. The updating of vibration modes is achieved using the recent inverse-free preconditioned Krylov subspace (IFPKS) method, while techniques for extending its preconditioning and enhancing its initial guess are also proposed. Both algorithms are started from the nominal solutions and preconditioned using the factorization of the nominal stiffness matrix. As a result, no factorization of the modified stiffness matrix is needed and optimal use is made of the available information. The effectiveness of the proposed updating strategy will be illustrated by an industrial case study.

Non-linear flexible body analysis for mechanical systems

Component mode synthesis method considers only small deformation problems and cannot handle large deformation problems. This paper presents an improved mode synthesis method. Mild geometric nonlinear problems have been solved by considering nonlinear effects in the stiffness matrix.

Alternating Stress Dynamics Analysis of Harmonic Gear Flexible Wheel

This article is the study of alternating stress of flexible wheel in harmonic gear drive system. Firstly, according to elasticity theory to theoretically analyze flexible wheel stress; then, based on the basic principle of sub-structure modal synthesis method , use the software of UG、PATRAN and ADAMS to carry out co-simulation; Finally, based on the dynamics simulation, to analyze the alternating stress simulation results of flexible wheel and compare theoretical results and simulation results to come conclusion. The results show that: altering stress simulation results of flexible wheel are coincident with theoretical simulation results, have a deeper understand the stress change trend in the drive process of flexible wheel, lay a foundation for further carrying out dynamics simulation of harmonic gear drive system.

Effects of Machine Tool Configuration on Its Dynamics Based on Orthogonal Experiment Method

In order to analyze the influence of configuration parameters on dynamic characteristics of machine tools in the working space, the configuration parameters have been suggested based on the orthogonal experiment method. Dynamic analysis of a milling machine, which is newly designed for producing turbine blades, has been conducted by utilizing the modal synthesis method. The finite element model is verified and updated by experimental modal analysis (EMA) of the machine tool. The result gained by modal synthesis method is compared with whole-model finite element method (FEM) result as well. According to the orthogonal experiment method, four configuration parameters of machine tool are considered as four factors for dynamic characteristics. The influence of configuration parameters on the first three natural frequencies is obtained by range analysis. It is pointed out that configuration parameter is the most important factor affecting the fundamental frequency of machine tools, and configuration parameter has less effect on lower-order modes of the system than others. The combination of configuration parameters which makes the fundamental frequency reach the maximum value is provided. Through demonstration, the conclusion can be drawn that the influence of configuration parameters on the natural frequencies of machine tools can be analyzed explicitly by the orthogonal experiment method, which offers a new method for estimating the dynamic characteristics of machine tools.

The Application of Modal Synthesis Method in the Processing Center Dynamics Analysis

Modal synthesis method is a method which can reduce structural degrees of freedom, it is applicable for analysis and calculations of Machining centers and other large-scale structure. In this paper, the dynamical performance of Five-axis boring and milling processing center was studied with component mode synthesis technology . Compared with full model FEM, component mode synthesis technology could meet the accuracy requirements and have higher computational efficiency. Modal characteristics of processing center in different positions was studied, the result showed that each frequency of processing center in different position was different while the vibration mode remained unchanged.

Determinantal method for locally modified structures. Application to the vibration damping of a space launcher

In order to improve the dynamic behaviour of an existing or already designed structure, local modifications can be performed by taking advantage of the relative displacement between two points of the structure. A stiffner, damper or viscoelastic rod may be added and its effect on the initial structure must be assessed. A new formulation is developed, based on the response of the initial structure at the attachment points of the local modification. A determinantal equation results, whose roots are the eigenvalues of the modified structure. The equation is solved numerically with a dedicated algorithm and it is shown that this is faster than performing an eigenvalue problem reanalysis. The method is able to deal with both undamped and damped systems, and can handle several modifications simultaneously. It is applied on the last stage of a space launcher, along with a double modal synthesis method.

Design for a New Type of Powder Molding Equipment Based on Multibody Dynamics Simulation

A new compaction powder metallurgy equipment integrated with the mould and the frame is introduced to substitute the traditional powder metallurgy equipment (P/M). During the design and manufacture, finite element method is used to analyze the motion of the equipment. The Lagrange equation and modal synthesis method for flexible body are constructed, and then the cooperative simulation method using ADAMS and MARC is present for solving flexible multibody dynamics of flexible body. Results show that the design of the structure of the powder metallurgy equipment is feasible and the low cost and the simple structure are its merits compared to the traditional equipment.

Performance evaluation of a 3-D kinetic model for CANDU reactors in a closed-loop environment

Abstract The performance of a newly developed three dimensional (3-D) reactor kinetic model for CANDU reactor is evaluated in this paper. The evaluation is carried out in a closed-loop environment with the help of an existing reactor regulating system (RRS). The 3-D model is obtained based on a modal synthesis method, which represents the neutron flux distribution inside the reactor in both time and space. Throughout this paper, a special attention has been paid to compare the performance of the developed 3-D model with that of traditional coupled point kinetic models. The dynamic behavior of the reactor model in a practical load-following mode has also been examined. The accuracy of the model has been validated against actual plant measurements under both transient and steady-state conditions. Through the analysis and the simulation studies, it has convincingly demonstrated that the developed 3-D model has significant advantages over traditional coupled point kinetic models in terms of the improved accuracy and the higher resolution in modeling the reactor internal dynamics.

On a component mode synthesis on multi-level and its application to dynamics analysis of vehicle system supported with spring-stiffness damper system

The component mode synthesis (CMS) method on multi-level, called as recursive component mode synthesis (RCMS) method, is implemented for the free vibration analysis of a vehicle system supported on damper-controlled spring-stiffness suspension. The nonproportional damping is considered to describe the suspension system. The focus of the RCMS method is the out-of-core concept that uses disk space rather than memory when computing large scale vehicle FE models. After the eigensolutions are obtained, the mode superposition method is used to compute the dynamic response in the frequency domain. The proposed method can deal with a damped structural system with a general damping system. The performance and accuracy of the proposed method compared to the Lanczos method are demonstrated through an example FE model.

Model-Based Fault Diagnosis Approach for Rotor System with Unidentified Supporting Parameters

The model based diagnosis method can detect both the fault location and the fault extent of the rotating machinery at the same time as it can combine the dynamics and fault diagnosis method together. However, the modal test of the supporting part is necessary when using the existing model based method, and the precision of the modal test results make a strong impact on the diagnosis results. In order to improve this case, an improved model based diagnosis method is presented herein by combining the fixed-interface modal synthesis method with the traditional model based diagnosis method. The DOF of the unidentified parameter due to the supporting parts are partitioned to interface DOF, and the displacement information of the supporting parts can be measured by the mounted sensors. Therefore, the model based diagnosis method can be carried out by only using the parameters of the rotor without considering the effects from the supporting, which can greatly improve the diagnosis precision and efficiency. This method is fit for the rotor systems with unidentified supporting parameter, and the rotor systems with unknown nonlinear supporting parameter. Both the numerical simulation results and the experiment results in the example proved the efficiency of this method.

Vehicle Interior Low Frequency Noise Optimum Using Substructure Modal Synthesis Method

Combined with the structural dynamic model of a car set up with the substructure modal synthesis method, body panels acoustic contribution was analyzed to reduce the in-car structural noise in low frequency range. The driver-right-ear position was selected as acoustic response point, with the operational vibration response of the dynamic model as boundary condition for acoustic BEM (boundary element model), the panels that attribute most to the in-car noise were located according to ATV (acoustic transfer vector) results. After the vibrational restraint of the crucial panels by corresponding experimental measurement, in idling, the most decrease of main peaks is 5.7dB; the overall level of in-car noise is reduced by 3.89dB. It indicates that the substructure mode synthesis method can provide proper suggestion for optimizing in-car structural noise.

New strategy of substructure method to model long-span hybrid cable-stayed bridges under vehicle-induced vibration

Hybrid cable-stayed bridges consist of steel and concrete bridge segments, of which steel–concrete joints are of great importance and raise strong research interest. Due to the limitation of the traditional methods, i.e., the member finite element (FE) method and Mixed Dimensional Coupling (MDC) method, the present study proposes a substructure method to model long span bridges. The current application of the substructure method is to extract some specific parts of the whole structure to refine and analyze them. Different from the routine substructure approach, here the entire structure is modeled in detail and divided into many substructures. All the substructures are then condensed into super-elements except the concerned part. The application of the method is then illustrated through numerical studies of the vehicle–bridge coupling vibration of the Jingyue Yangtze River Bridge with a main span of 816 m. The entire bridge is first divided into many substructures with a reasonable length. Among them, the concerned substructure with 23.8 m in length including the steel–concrete joint is modeled in detail but not formed into super-element, while all the other components are modeled in detail and formed into super-elements using the component mode synthesis (CMS) method. All the components including both the super-elements and non-super-elements are then assembled into a complete and fine full bridge model. Finally, the model is used for the vehicle-induced dynamic analysis under deterministic traffic flows. The results show that the joint works well, and the transition between the steel girders and concrete beams is very smooth.

Vibration and stability of multi-cracked beams under compressive axial loading

In this study, a novel technique for the vibration and stability analyses of axially loaded beams with multi-cracks was offered. In the model which combines the finite element and component mode synthesis methods, the cracks were modelled as massless springs. Initially, stability analysis was completed and then three numerical cases were given to explore the effects of axial load levels, crack locations and ratios on the natural frequencies and mode shapes of the beams. Very good conformities between outcomes of the current study and those in literature, gave the confidence that the proposed method which could be used to predict crack positions, crack sizes and critical buckling load of defected structures by using the modal data, was reliable and effective. Key words: Finite element analysis, damage, failure assessment, pressurised components.

Finite-element analysis of unsupported sleepers using three-dimensional wheel–rail contact formulation

Owing to repeated traffic loads, the ballast of a railroad track can become unevenly distributed, resulting in different settlements of adjacent sleepers and possibly to a sleeper–ballast loss of contact. The sleeper–ballast loss of contact can significantly change the stiffness properties and modes of deformation of the track. This in turn can cause damage to the structure and can lead to undesirable dynamic behaviour of the vehicles that negotiate this damaged track. The focus of this investigation is on developing a more comprehensive procedure that can be used to examine the effect produced by unsupported sleepers of a flexible track on the dynamics of railroad vehicle systems. The procedure used in this study is based on a validated non-linear multi-body railroad vehicle system formulation that takes into account the coupling between the elastic deformations of the track, the sleeper movements, and the three-dimensional contact parameters. The method used in this article allows for developing a detailed finite-element track model that accounts for non-periodic and asymmetrical mechanical defects. The finite-element equations of motion of the track that includes unsupported sleepers are integrated with the non-linear constrained dynamic equations of the multi-body railroad vehicle system. Component mode synthesis methods are used to reduce the number of the governing equations of motion and eliminate high-frequency modes. The dynamic coupling between the track modal co-ordinates and the wheel–rail contact parameters is considered in this investigation by using creepage and creep force expressions that depend on the track deformations and sleeper movements. In order to demonstrate the use of the procedure described in this article, a track model which has rails and sleepers modelled as beams rigidly connected at the intersection points is used. The effect of the ballast is considered using an elastic foundation. The results obtained in this investigation are used to compare between the responses of two tracks; one with no sleeper–ballast loss of support and the other with unsupported sleepers. The results are reported for different values of the forward velocities in order to have a better understanding of the effect of the sleeper loss of support on the system dynamics. The creepages that depend on the track deformations as well as the system frequencies are analysed. The results obtained in this investigation are found to be in good agreement with the results reported in the literature on unsupported sleepers.

Reduction of system matrices of planar beam in ANCF by component mode synthesis method

A method of reducing the system matrices of a planar flexible beam described by an absolute nodal coordinate formulation (ANCF) is presented. In this method, we focus that the bending stiffness matrix expressed by adopting a continuum mechanics approach to the ANCF beam element is constant when the axial strain is not very large. This feature allows to apply the Craig–Bampton method to the equation of motion that is composed of the independent coordinates when the constraint forces are eliminated. Four numerical examples that compare the proposed method and the conventional ANCF are demonstrated to verify the performance and accuracy of the proposed method. From these examples, it is verified that the proposed method can describe the large deformation effects such as dynamic stiffening due to the centrifugal force, as well as the conventional ANCF does. The use of this method also reduces the computing time, while maintaining an acceptable degree of accuracy for the expression characteristics of the conventional ANCF when the modal truncation number is adequately employed. This reduction in CPU time particularly pronounced in the case of a large element number and small modal truncation number; the reduction can be verified not only in the case of small deformation but also in the case of a fair bit large deformation.

A High-Accuracy Model Reduction for Analysis of Nonlinear Vibrations in Structures With Contact Interfaces

A highly accurate and computationally efficient method is proposed for reduced modeling of jointed structures in the frequency domain analysis of nonlinear steady-state forced response. The method has significant advantages comparing with the popular variety of mode synthesis methods or forced response matrix methods and can be easily implemented in the nonlinear forced response analysis using standard finite element codes. The superior qualities of the new method are demonstrated on a set of major problems of nonlinear forced response analysis of bladed disks with contact interfaces: (i) at blade roots, (ii) between interlock shrouds, and (iii) at underplatform dampers. The numerical properties of the method are thoroughly studied on a number of special test cases.

Structural optimization of an automobile transmission case to minimize radiation noise using the model reduction technique

Vehicles should provide a comfortable environment for passengers. The noise from the transmission case is one of the causes of an uncomfortable environment. The transmission is composed of gears, shafts, bearing and cases. When transmission activity occurs, noise is transferred to the passengers through the transmission case. Design of the transmission case is performed in order to reduce the transmission noise. Acoustic analysis is carried out and structural optimization is utilized for the design to reduce the noise. Generally, the boundary element method (BEM) has been utilized for acoustic analysis. However, it is difficult to utilize the boundary element method in structural optimization because the cost to calculate the sensitivity information is fairly expensive. Instead, the finite element method (FEM) is employed for calculating the radiation noise of the transmission. Radiation noise is considered as the total noise from the transmission. Radiation noise is calculated at the outside of the transmission case and it can be expressed indirectly by multiplication of the velocity in the normal direction of the finite elements, the radiation efficiency and the characteristic acoustic impedance. The high frequencies are dominant for the transmission noise and the radiation efficiency is 1 at the high frequency range. Since the characteristic acoustic impedance has a constant value, the noise is the same as the norm of the velocity. The velocity of each finite element is calculated from modal analysis and the noise is expressed based on the average velocity of the vibrating structure. However, a long computation time is required to calculate the noise in a large scale structure such as a transmission. Thus, the entire model of transmission is condensed into the reduced model by the model reduction technique. The component mode synthesis (CMS) method is employed for the model reduction technique. The CMS method is an effective method for dynamic analysis of large and/or complex structures. The reduced model keeps the dynamic characteristics of the entire structure and it is used for structural optimization. In structural optimization, the design variables are the thicknesses of the groups of the transmission cases, the objective function is the mass of the structure and a constraint is imposed on the noise. An alternative formulation is made by exchanging the objective and constraint functions. The optimization results are discussed in terms of practical application.