A modal synthesis method for the elastoacoustic vibration problem

For large and complex structures with repetitive characteristics, a multi-stage substructure dynamic analysis method based on modal synthesis is proposed to effectively improve the efficiency of simulation calculation. First, the repetitive components are taken as the primary substructure, and the components that produce local modes in the primary substructure are taken as the secondary substructure. The modal synthesis method is used to truncate all modal characteristics of the secondary substructure, and the constrained modal parameters and main modal parameters of the primary substructure are obtained. Then, according to the spatial coordinates, the primary substructure stiffness matrix and mass matrix are repeatedly assembled to obtain the condensation model of the whole structure. The condensation model is used for dynamic simulation to obtain the acceleration load of the substructure installation interface. Finally, the internal dynamic response of the substructure at all levels is obtained by using the super-element method. The simulation analysis of space-borne phased array synthetic aperture radar antenna shows that the multi-stage substructure dynamic simulation analysis results are highly consistent with the traditional analysis results, and the calculation efficiency is increased by more than four times. The substructure dynamic analysis method is reasonable and reliable.

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.

MODELLING AND CONTROL OF A TWO-AXIS ROBOT WITH FLEXIBLE LINKS

This study describes the rotordynamics analysis of the Space Shuttle Main Engine (SSME) high-pressure oxidizer turbopump. Modal synthesis methods were used to account for the complex coupling of the pump and engine structure. Cross-coupling elements effecting rotor stability were included in the analysis. Results of the analysis indicated that smaller bearing clearances and a smooth turbine interstage seal would result in longer bearing life and improved stability. Subsequent testing with these design features has shown the same results.

The large flexible solar array for the satellite will deploy when it reaches the scheduled orbit by the space rocket, which is key for the normal running of the satellite. However, undesirable and unpredicted frequency vibration may be resulted from the flexibility of elements of the solar array. In this paper, the dynamic model of the solar panel was firstly developed based on the modal synthesis method. Moreover, the stretchable mechanism in the solar array was introduced by applying Euler-Bounerlli beam theory. Also, guide ropes, hinges and electric cables were considered in the proposed model. It was found the proposed model could achieve a higher accuracy of simulation compared to the traditional method with the coordinate method. Especially, the dependence of the guide rope tension on the deployment dynamic behavior of the solar array was explored by this model. Results showed that vibrations of the solar array could be reduced by improving the guide rope tension, which could be used in design and operation of the solar array.

The free vibrations of a complex system with a natural frequency identical to that of one of its subsystems is discussed. Such eigenvibrations need special consideration in many modal synthesis methods as the characteristic matrix (equation) does not exist. Particular emphasis has been placed on the case where a resonating subsystem is subjected to forces from other subsystems, which has not received sufficient attention in the literature on substructure synthesis methods. Examples of such eigenvibrations for two simple systems are given. A general equation for system eigenfunctions corresponding to eigenfrequencies of the isolated subsystems is presented and discussed.

The concrete pump truck’s boom system of 5 booms is taken as the research object in this paper. Combined with finite element theory and multi-body dynamics theory, a rigid-flexible coupling model of concrete pump truck’s boom system is established by modal synthesis method. With the measured displacement-time curve of turntable as the excitation, the booms’ pumping process in horizontal mode is simulated by the dynamic simulation software ADAMS. Through the field experiment results, the rationality of the modal is verified. It provides an effective method for dynamics analysis and structure improve of the concrete pump truck’s boom system.

<div class="htmlview paragraph">Disc brake squeal is a complicated dynamic problem confronting automobile manufacturer for decades. A squealing disc brake is studied and a closed-loop coupling model with 128 degrees of freedom is established on the basis of Finite Element Method and Modal Synthesis Method. Based on the system model, calculation and analysis are performed to find which structure factors affect squeal phenomenon greatly. At last, it is found that some of the <i>mounting bracket</i> modes dominate the appearance of the squeal. According to that, possibly the structure modification of the <i>bracket</i> is an accessible way to eliminate the brake squeal.</div>

<div class="section abstract"><div class="htmlview paragraph">Nowadays, the design and development of the sliding door has been gained great attention for its easy egress and ingress. However, most studies on the kinematic and dynamic characteristics of sliding doors were based on the commercial code ADAMS, while the accuracy of flexibility in modal synthesis method and the ability of complex contact condition may not be guaranteed. Thus, a new dynamic analysis method by using the commercial code LS-Dyna was proposed in this paper to take into account the complex deformation and boundary conditions based on the finite element model. The impact force obtained from the Ls-dyna was compared with that from ADAMS when their monitoring points speed and closing time maintained the same during the sliding process. The impact force between the rollers and the guides was employed as evaluation criterion for different methods because of its effect on the roller wear and the moving smoothness in the sliding process. To validate the results, the impact force was measured by using the strain gauges and optical fibers measure. It turned out that the impact force from LS-Dyna agrees better with the experimental test than that from ADAMS. LS-dyna outperforms ADAMS, in terms of modeling method, dynamic analysis theory and boundary condition. In addition, the dynamic analysis based on finite element method in LS-Dyna environment can simulate the structural deformation and the motion space coupling boundary condition during the sliding process of door better.</div></div>

In this paper, contact modeling technique and dynamics analysis of piston and cylinder system are presented by using modal synthesis method. It is very important to select mode shapes representing a global or local behavior of a flexible body due to a specified loading condition. This paper proposes a technique to generate the static correction modes which are nicely representing a motion by a contact force between a piston and cylinder. First normal modes of piston and cylinder under a boundary condition are computed, and then static correction modes due to a contact force applied at contacted nodes are added to the normal modes. Also, this paper proposes an efficient dynamics analysis process while changing the shape of the piston and cylinder. In optimization process or design study, their geometric data can be changed a bit. The slight changes of their contact surfaces make a high variation of the magnitude of a contact force, and it can yield the different dynamic behavior of an engine system. But, since the variations of the normal and correction modes are very small, the re-computation of their normal and correction modes due to the change of contact surfaces can be useless. Until now, whenever their contact surfaces are changed at a design cycle, the modes have been recomputed. Thus, most engineers in industries have been spent many times in very tedious and inefficient design process. In this paper, the normal and correction modes from the basic geometry of the piston and cylinder are computed. If the geometry shape is changed, nodal positions of the original modal model are newly calculated from an interpolation method and changed geometry data. And then the updated nodes are used to compute a precise contact force. The proposed methods illustrated in this investigation have good agreement with results of a nodal synthesis technique and proved that it is very efficient design method.

During the morphing process, the dynamic modeling of the morphing wing aircraft presents the characteristics of rigid‐elastic coupling effects, moving boundaries, and low computational efficiency. Meanwhile, parameters such as aerodynamic forces/moments, center of pressure, center of mass, and moment of inertia would also change significantly, which would seriously affect the flight stability. Therefore, this paper mainly focuses on the rigid‐elastic coupling dynamic modeling of morphing wing aircraft. Based on the virtual power principle, a floating coordinate system and the modal synthesis method are adopted to establish a rigid‐elastic coupling dynamic model that accounts for the elasticity of the wings, which can accurately capture the cross‐scale coupling effects between the rigid‐body motion and the elastic deformation of the wings during the continuously morphing process. Considering the moving boundary problem between the fuselage and the wings during the continuously morphing process, a dynamic constraint modeling technique based on the Craig‐Bampton method and a node's life and death technique describing the constraint states are proposed, which can avoid the complex operations of reestablishing the finite element model of the elastic bodies for traditional methods. Moreover, a method of smoothing model for the rigid–elastic coupling system is developed, which can significantly improve the computational efficiency for the dynamic equation of the morphing wing aircraft. And by changing the value of the smoothing factor, preservation of specific high‐frequency components can be controlled. Finally, the numerical examples are carried out to verify the proposed rigid‐elastic coupling dynamic model for the morphing wing aircraft.

<div class="htmlview paragraph">This paper adopts a method of tire modeling which uses tire experimental modal parameters which are obtained by means of radial and tangential excitation. The action force from ground to tire are treated as inputs for model. Calculations of static properties are dealt with transfer functions at 0 frequency. An iterative algorithm is used to work out the vertical properties, contact length and vertical and frictional force distribution in longitudinal direction. The vertical vibration characteristics under 300Hz of a pre-loaded tire are given, and that of the system composed of wheel, suspension and car body are analyzed by using modal synthesis method. The study shows the feasibility and advantages of this method.</div>

<div class="section abstract"><div class="htmlview paragraph">This paper presents CAE method enhancement which realizes time domain gear noise simulation to practical use for AISIN AW automatic transmission assembly model.</div><div class="htmlview paragraph">Today, vehicle electrification has been accelerating due to severe fuel consumption regulations. Furthermore, as quietness of interior noise of vehicle is improving, further gear noise reduction of A/T is imperative. Currently, as one of the countermeasures for realizing lightweight and NV reduction, we apply elongate holes in gear flange. Although the effect of gear noise reduction is confirmed in evaluations, the mechanism for this gear noise reduction by the elongate holes has not been clarified completely and the current simulation based on modal analysis with static condition cannot replicate actual NV phenomena of A/T assy. Furthermore, it takes an enormous amount of time and cost since the design study for elongate holes is based on the evaluation results. Therefore, clarification of the mechanism and development of NV simulation enhancement which can replicate NV phenomena is required for efficient design study. As a result of evaluation for verifying NV phenomena by elongate holes, we confirmed gear noise level reduction because a resonance frequency of the gear is fluctuated owing to the stiffness difference between hole part and lib part of the gear.</div><div class="htmlview paragraph">This time, in order to replicate the NV phenomenon with above mentioned mechanism by CAE method, we apply time domain simulation for gear noise to practical use for A/T assy model by using “multibody dynamic simulation” based on modal synthesis method. As a consequence, we present that validity of time domain NV simulation was confirmed by the evaluation for gear noise of A/T assy.</div></div>

Since the noise generated by mechanical structures affects the merchantability, it is important to predict the noise and vibratory characteristics at the first design stage. The frames and panels or trim parts in automobiles are coupled systems of the rigid and flexible substructure. In these systems, vibration of the flexible structures often becomes one of the major noise sources when the excitation force is applied to the rigid structure. FEM and modal analysis technique are not sufficient to carry out the effective low noise design in higher frequency because of high modal density and complexity of mode shape. Modal energy propagation method, proposed in this paper, is based on the mode synthesis method and the vibration power flow between the eigen modes of the rigid and flexible structures. Previous studies have verified that the vibration level can be reduced by extracting modes that contribute highly to the vibration power flow between subsystems and changing their characteristics. In this report, we present the results of applying this method to a coupled system of a body and panel structures in automobiles and verifying its validity. The structural modifications obtained from this analysis method were verified for their effectiveness in decreasing vibration.

A Finite element discretization of the streamfunction formulation of the stationary quasi-geostrophic equations of the ocean