Dynamic Substructure Method Research Articles

Analysis of the influence of clamp installation position on vibration stress for spatial pipeline

In aero-engines, small changes in the clamp position can sometimes significantly alter the vibration stress of the pipeline system, so there is an urgent need to study the influence of clamp position on pipeline vibration stress. Firstly, a dynamic modeling method of spatial pipeline system is proposed based on the finite element method, the modeling method can more accurately simulate the complex boundary constraints caused by multiple clamps and pipe fittings. Then, an improved dynamic substructure method (reduced-order method) is developed by combining the dynamic substructure method with the clamp position parametric model to improve the efficiency of the subsequent clamp position parameters influence analysis. Further, the rationality and efficiency of the reduced-order modeling approach are verified by numerical and experimental studies. Finally, the influence of the clamp position and the key parameters of different components (pipe body, clamps, fittings) on the pipeline vibration stress is investigated. The results show that when the main vibration region of the pipeline system coincides with the installation region of the clamp, the vibration stress can be significantly reduced by installing the clamp in the maximum modal displacement region of the corresponding pipe segment. The related modeling methods and conclusions can provide valuable references for the dynamics design of pipeline system in engineering practice.

Another explicit forms of dynamic substructuring approaches using dynamic constraints at joint nodes

ABSTRACT The dynamic substructuring design describes the dynamic responses in the modal, frequency and physical domains using coupling methods at joint nodes. This paper presents dynamic structuring methods to modify existing substructuring methods by merging the concept of interfacial forces in the satisfaction of compatibility conditions at joint nodes. The algorithms correspond to a type of model reduction approaches that use a few modes of substructures with the assumption of pseudo-masses at the joint nodes of the substructures. It was verified through numerical examples that the pseudo-masses rarely affected the dynamic responses of the synthesized structure. A frequency response function-based substructuring method was derived by applying interface forces at joint nodes to frequency response function (FRF). The proposed dynamic substructuring methods are expressed in explicit forms for synthesizing substructures without any numerical schemes. The validity of the proposed method was illustrated using two numerical examples. The limitations of this study are evaluated using numerical examples.

Dynamic modeling and analysis of fluid-delivering cracked pipeline considering breathing effect

Crack is the most common failure mode of the pipeline system, which may lead to high-speed and high-pressure hydraulic oil leakage. In this paper, the dynamic modeling and model order reduction methods for the fluid-delivering cracked pipeline (FDCP) considering the breathing effect are proposed, and the structural intensity method (SIM) is introduced to visualize the vibration transmission and breathing effect of FDCP. The fluid, solid, and coupling elements are constructed to establish the dynamic model of FDCP, the spring element is used to simulate the breathing effect, the dynamic substructure method is extended to perform the model order reduction of FDCP, and the rationality of the modeling method is verified by experiments. SIM and energy principles are used to visualize and analyze the vibration transmission of FDCP. The analysis results show that the natural frequencies are sensitive to the cracks in the maximum modal displacement and stress regions, and the fluid velocity and pressure (FVAP) will enhance the breathing effect of FDCP. In addition, the vibration transmission analysis can accurately detect the crack with different damage degrees, and FVAP do not influence the vibration transmission laws. The modeling and analysis method in this paper can provide a theoretical reference for fault diagnosis of FDCP.

A general structural design method, dynamics modeling and application study for built-in sandwich annular traveling wave piezoelectric transducers

This study first summarized a piezoelectric excitation source arrangement guideline for sandwich annular traveling wave transducers, which can excite ideal traveling waves for driving while ensuring consistent circumferential stiffness of the annular transducer. Consequently, a general structural design method was proposed for annular sandwich traveling wave piezoelectric transducers operating with out-of-plane traveling waves based on the above-mentioned arrangement guideline. Moreover, to study the vibration characteristics of the designed transducer based on the proposed method, an electromechanical coupled dynamics model was developed using the dynamic substructure method combined with the Lagrange equation. This model is universal and has guiding significance for the design and optimization of the same type of annular traveling wave piezoelectric transducers. Thereafter, the feasibility of the transducer structure design method and the correctness of the developed dynamics model were verified through appropriate vibration measurement experiments on the transducer prototype. The measured ideal mode shape and regular elliptical motion verified the feasibility of the transducer design method, and the comparison between the vibration measurement and theoretical model calculation results confirmed the correctness of the developed dynamic model. Finally, an application study of the proposed built-in sandwich traveling wave transducer was conducted to investigate its driving characteristics. The proposed transducer was used to drive a rotor to build a traveling wave piezoelectric motor. In addition, output performance experiments of the motor prototype were conducted. The experimental results indicated that under the driving conditions of 300 N pre-pressure, 500 Vpp voltage, and 19 kHz exciting frequency, the no-load speed of the motor was 19.04 RPM, its stall torque was 1.2 N·m, the maximum output power of the entire machine reached 0.6453 W, and its maximum output efficiency was 15.87%. Moreover, the normal operation of the rotating motor further verified the feasibility of the transducer structure design approach and the reliability of the drive application. The structural design method and the corresponding dynamic model proposed in this study are expected to have important guiding significance for the design and optimization of sandwich-type annular traveling wave transducers. Furthermore, the application investigation in this study provides a typical example for the traveling wave transducer.

Parametric model order reduction and vibration analysis of pipeline system based on adaptive dynamic substructure method

In the dynamics topology optimization process of the pipeline system, the parametric model order reduction (PMOR) method is needed to improve the efficiency of model reconstruction and vibration analysis. In this paper, the general PMOR and vibration analysis methods of pipeline system based on adaptive dynamic substructure method are innovatively proposed. Based on the spatial 8-node conforming solid element, a spatial 8-node nonconforming solid (Solid-NC) element with high accuracy is obtained by introducing the node-free displacement items. The node coordinates of the finite element models corresponding to the straight-line and curved arc segments of the pipeline system are obtained based on the direction vector method and the vector decomposition method respectively, thus the parametric finite element model of the pipeline system is established. The pipeline body is divided into single interface substructures and double interface substructures based on the dynamic substructure method, thus the PMOR method that can change the number of substructures or elements contained in the substructure with the pipeline shape or mesh density is obtained, and then the natural characteristic and vibration response solutions of the pipeline system are performed. Finally, the rationality and efficiency of the proposed PMOR method are verified by an example.

Investigating the use of dynamic sub-structuring methods in predicting floating floor performance.

Floating floors are a common means of reducing airborne and structure-borne noise, however, prediction of in-situ performance remains a challenge for many consultants. The specification of such floors, usually based on single degree of freedom assumptions, does not account for the influence of floating floor dynamics, dynamics of host structures or interplay/power flow between the two via the isolating mounts. Reliance on single degree of freedom systems tend to over-predict the performance of the floating floor element, often leading to noise/vibration issues in the finished construction. A more robust approach is needed, though is challenging due to complexities in characterising large-scale constructions, where source-to-receiver Frequency Response Functions (FRFs) must account for multiple points of contact between floating and structural elements. This paper first presents a hybrid method for evaluating the source-receiver FRF of a simple floating floor via a sub-structured approach, and confirms the validity of the method to that of the source-receiver FRF measured directly. Efforts to simplify the analysis to a set of engineering-grade operations is also presented, the aim being movement towards a methodology that can be more readily utilised by practitioners, without the need for expensive modelling software or high end hardware setups.

Evaluation of Different Contact Assumptions in the Analysis of Friction-Induced Vibrations Using Dynamic Substructuring

Dynamic substructuring methods are initially developed for time-invariant systems to evaluate the dynamic behavior of a complex structure by coupling the component substructures. Sometimes, the component substructures change their position over time, affecting the dynamics of the entire structure. This family of problems can be tackled using substructuring techniques by isolating the time dependency in the coupling conditions among the time-invariant substructures. Mechanical systems, composed of subsystems in relative motion with a sliding interface, can be analyzed using this approach. In previous work, the authors proposed a solution method in the time and frequency domain using this approach under the assumption that the relative sliding motion at the contact interfaces is a-priori known, at least approximately. This assumption implies that the perturbation generated by the friction-induced vibration is neglected. In subsequent work, a more realistic contact assumption was considered to account also for the local vibration of the contact point and the geometric nonlinearity due to the elastic deformation. In this paper, a simplification with respect to the realistic contact assumption is introduced, which neglects the angular variation of the direction normal to the contact interface. The simplified approach is advantageous because it is equally able to highlight the occurrence of friction-induced instabilities, and it reduces the computational burden. The results of the substructuring methods using different contact assumptions are compared with those of a reference numerical method to show how the choice of the contact algorithm allows for tackling a wide range of operating conditions, from simple position-dependent problems up to complex friction-induced vibration phenomena.

Resonant metamaterial designs for a broadband mitigation of flow-induced vibrations

Resonant metamaterials have recently emerged as lightweight and performant noise and vibration solutions for the hard-to-address low-frequency ranges. These engineered materials are made by an assembly of resonant elements onto a host structure. Their interaction leads to tuneable frequency ranges, known as stop bands, in which they can outperform classical noise control measures. However, these stop bands have a limited frequency range effect. To broaden the noise and vibration performance also outside the stop band, this paper presents a design approach for a finite resonant metamaterial plate. Two regularly spaced grids of resonant elements are both added to a plate. In the first grid, the resonant elements are tuned to the same nominal frequency and stop band behaviour is achieved. In the second grid, the tuned frequency of each resonant element is found through an optimisation procedure, with the goal of minimising the dynamic response of the plate outside the stop band. To speed up the optimisation, model order reduction and a dynamic sub-structuring method are employed. The performance of this finite resonant metamaterial plate design is validated by evaluating its vibration response due to a broadband grazing flow excitation and comparing it to a plate with equivalent mass additions.

Analysis and Experimental Study on Dynamic Behavior of Stepper-Actuated Dual-Axis Data Transmission Antenna

The satellite-borne data transmission antenna is the main disturbing source of low-frequency microvibration of spacecraft, which immensely affects the image quality of remote sensing satellite. In this paper, the dynamic characteristics of flexible load driven by stepping motor on flexible boundary are studied. The dynamic equation of the stepping motor driven by current subdivision is simplified by linearization method. The dynamic model of flexible load driven by stepping motors on flexible boundary is established by using the Dynamic Substructure Method, and the analytical expression of microvibration of the data transmission antenna is given. The coupling relationship between the stepping motors and the flexible structure is analyzed by modal coordinate transformation. The microvibration model is verified by simulation and experiment, and the main causes and coupling factors of microvibration are explained. The results show that the model can accurately predict the microvibration of the satellite antenna and can be applied to the microvibration prediction in orbit. The reasonable selection of the working velocity of the stepping motors can effectively reduce the microvibration, which provides the basis for the design of the antenna control system.

A simplified iterative approach for testing the pulse derailment of light rail vehicles across a viaduct to near-fault earthquake scenarios

Near-fault (NF) earthquakes cause severe bridge damage, particularly urban bridges subjected to light rail transit (LRT), which could affect the safety of the light rail transit vehicle (“light rail vehicle” or “LRV” for short). Now when a variety of studies on the fault fracture effect on the working protection of LRVs are available for the study of cars subjected to far-reaching soil motion (FFGMs), further examination is appropriate. For the first time, this paper introduced the LRV derailment mechanism caused by pulse-type near-fault ground motions (NFGMs), suggesting the concept of pulse derailment. The effects of near-fault ground motions (NFGMs) are included in an available numerical process developed for the LRV analysis of the VBI system. A simplified iterative algorithm is proposed to assess the stability and nonlinear seismic response of an LRV-reinforced concrete (RC) viaduct (LRVBRCV) system to a long-period NFGMs using the dynamic substructure method (DSM). Furthermore, a computer simulation software was developed to compute the nonlinear seismic responses of the VBI system to pulse-type NFGMs, non-pulse-type NFGMs, and FFGMs named Dynamic Interaction Analysis for Light-Rail-Vehicle Bridge System (DIALRVBS). The nonlinear bridge seismic reaction determines the impact of pulses on lateral peak earth acceleration (Ap) and lateral peak land (Vp) ratios. The analysis results quantify the effects of pulse-type NFGMs seismic responses on the LRV operations' safety. In contrast with the pulse-type non-pulse NFGMs and FFGMs, this article's research shows that pulse-type NFGM derail trains primarily via the transverse velocity pulse effect. Hence, this study's results and the proposed method can improve the LRT bridges' seismic designs.

Stability and Accuracy Analysis of Real-Time Hybrid Simulation (RTHS) with Incomplete Boundary Conditions and Actuator Delay

The main purpose of this paper is to examine the effects of incomplete boundary conditions and actuator delay on the dynamic responses of seismically excited civil structures. A set of constraint equations representing the reserved interface degrees-of-freedom (DOFs) and the delay are introduced to form a mechanical model of real-time hybrid simulation (RTHS) (referred to as RTHS-I&A) for a multi-degree-of-freedom (MDOF) system based on dynamic substructure method (DSM). Then, the RTHS-I&A system is modeled by a discrete closed-loop transfer function based on discrete control theory, using a selected integration algorithm, and the stability of the system is investigated by examining the poles of the function. Three typical cases with different structural properties are utilized to investigate the effects of incomplete boundary conditions and actuator delay. The results show that both incomplete boundary conditions and actuator delay greatly affect the dynamic responses of structures, and the combination of the two factors will amplify their influence especially on the nodes at the interface. The numerical model of RTHS-I&A proposed in this paper is quite useful for evaluating the responses of structures with different interface conditions and loading schemes that are preliminarily designed before a physical testing is conducted, and provides guidance for future relevant researches.

Effects of gearbox housing flexibility on dynamic characteristics of gear transmission system

The lightweight design of the gear system is the current tendency. The gearbox housing is modeled as a rigid body and is neglected in the gear dynamic analysis. It is of great significance to introduce the gearbox housing flexibility into the dynamic analysis and analyze the influence of the gearbox housing flexibility on the dynamic behaviors of the gear transmission system, as this can provide important instructions for the lightweight structure design of the housing. The gear–rotor–bearing model and the gear–rotor–bearing–housing model are established by the finite element node method. A Timoshenko beam element is used to represent the shafts. To illustrate the housing effect, two kinds of housing model are established: one tends to be rigid and the other to be flexible and lighter. The housings are simplified as a super element obtained by the dynamic substructure method. Natural frequencies and dynamic responses are illustrated to indicate the effects of housing flexibility. Comparisons of numerical results show that the rigid housing can be neglected for its little effect on the dynamic analysis. The flexibility of the housing slightly reduces the natural frequencies of the gear transmission system, and the maximum reduction is 6.05%. Meanwhile, the amplitudes of the first two resonance peaks of the dynamic transmission error decrease by 9.5% and 5.05%. Besides, more response peaks emerge at higher speeds when the flexibility of housing increases. The complete phenomena of dynamic behaviors of the gear transmission system can be obtained by considering the housing flexibility.

A near-fault vertical scenario earthquakes-based generic simulation framework for elastoplastic seismic analysis of light rail vehicle-viaduct system

This paper focuses on the rapid elastoplastic analyses of light rail vehicle (LRV)- benchmark viaduct system to different seismic scenarios considering the dynamic substructuring method (DSM). Combining the energy-variational principle with the vehicle-bridge interaction (VBI) system, a new framework of train-track system space dynamics is constructed. The present study has established the train-track-bridge coupled system (TTBCS) model, calculated the elastic-plastic seismic responses of the light rail transit bridge (LRTB) subjected to the combined effect of vertical and horizontal earthquakes. Considering three ground motion ensembles, i.e. pulse-like near-fault ground motions (NFGMs), non-pulse-like NFGMs, and far-field ground motions (FFGMs). Results indicate that the large vertical ground motions (VGMs) type NFGMs greatly impact the seismic response of the running safety of the LRV in the low-frequency band compared to the non-pulse-like NFGMs and FFGMs. The results underscore the significance of distinguishing velocity pulses of different types when selecting NFGMs for assessing the nonlinear dynamic response of the VBI system.

Including directly measured rotations in the virtual point transformation

Dynamic substructuring methods serve as a powerful tool in the analysis of modern complex systems. The coupling of substructures has been successful with analytically obtained results. However, substructuring with experimentally obtained data remains challenging. One of the main problems associated with experimental substructuring is the coupling of the rotational degrees of freedom (RDoFs). A promising method where RDoFs are included implicitly is the virtual point transformation. Even though the transformation has been successfully used in the substructuring process, it is still highly susceptible to inaccuracies in the sensor sensitivity and positioning. In this paper an expansion to the virtual point transformation is proposed, which enables the projection of a directly measured rotation response on the interface deformation modes. A novel formulation of the weighting matrix is introduced to consistently include the measured rotations in the transformation. The proposed expansion is demonstrated on a numerical model of a simple beam-like structure and compared with the standard transformation. The effects of inaccuracies in the sensor sensitivity and placement on the overall quality of both transformation are analysed with a global sensitivity analysis. Finally, an experimental validation of the proposed expansion is carried out on a steel beam.

A review on dynamic substructuring methods for model updating and damage detection of large-scale structures

Substructuring methods possess many merits in model updating and damage identification of large-scale structures. With substructuring methods, a global structure is divided into a number of independent substructures. Only the substructures are repeatedly analyzed and the re-analysis of the global structure is thereby avoided. This article reviews widely used dynamic substructuring methods for model updating and damage identification of large-scale structures. These methods can be categorized into forward and inverse substructuring approaches. The former is a conventional process that assembles the vibration properties of each substructure to obtain the vibration properties of the global structure. The latter, on the contrary, disassembles the vibration properties of the global structure into those of the substructures. In each category, both frequency and time domain methods have been developed and will be reviewed.

Decentralized simple adaptive control for large space structures

A decentralized simple adaptive control is proposed for the vibration suppression of large space structures (LSS) with distributed actuators and sensors. The LSS is viewed as a set of connected substructures so that the dynamic substructuring method can be applied to establish the equations of motion for the LSS. Then, extraction and contraction of the subsystems are performed to form the perturbed equations of motion for each substructure. An output feedback control law only requiring the information of the local sensors is designed based on the simple adaptive control method. The stability of the overall system is rigorously proven.

A semi-analytical model of the train-floating slab track–tunnel–soil system considering the non-linear wheel/rail contact

This paper presents a three-dimensional model for the calculation of train-induced vibration of a floating slab track in an underground tunnel based on the integration of a semi-analytical approach and a dynamic substructure method. The methodology for the train-floating slab track–tunnel–soil coupled model is described and validated by comparing the vibration response of the system with that of the Pipe-in-Pipe model. The innovations of the proposed model include the following: (1) it considers all components of the metro train-induced vibration problem including the train, the floating slab track, the tunnel, the soil and the interactions of the subsystems; and (2) it operates in the time domain and thus is capable of modelling the highly non-linear loading behaviours (i.e. the wheel/rail contact relationship). A hypothetical example is presented to illustrate the vibration isolation effect of the floating slab track using the developed model, and the following conclusions can be drawn. Excellent vibration isolation performance is observed for the floating slab track system, especially for vibrations at a high frequency (above 12.5 Hz), whereas the vibration is amplified near the natural frequency of the floating slab (i.e. 8 Hz in this study) because of the resonance effect. The amplitudes of the soil stresses are reduced due to the floating slab track system, especially for the high-frequency soil stresses.

Research on Microvibrations Generated by a Control Moment Gyroscope on a Flexible Interface Based on a Dynamic Substructure Method

Microvibrations generated by a control moment gyroscope (CMG) will couple with a flexible spacecraft structure, and this seriously degrades certain point performances of a spacecraft. This study focuses on investigating the coupled microvibrations caused by a CMG on a flexible interface by using a dynamic substructure method (DSM). First, a DSM based on a frequency response function (FRF) is established, and this method is used to simultaneously synthesize multiple substructures with different coordinates irrespective of whether their connection interfaces are rigid or flexible. Second, the bearings and the gimbal servo system are simplified into linear springs, and therefore the CMG model is equivalent to a mass-spring-damping system with eighteen degrees of freedom (DOFs). Third, the established DSM is employed to deduce the FRF matrix of the CMG-flexible interface coupling system that consists of CMG mounted on an aluminum honeycomb sandwich palate (AHSP). Dynamic responses of the coupling system are calculated by the derived FRF matrix. Finally, MATLAB and multibody dynamics simulations are conducted to analyze and validate the dynamic responses of the coupling system obtained by the DSM. The results indicate that the DSM is appropriate to predict the coupled microvibrations of CMG on a flexible interface and exhibits high prediction accuracy and computational efficiency.

Hybrid dynamic modeling of shearer's drum driving system and the influence of housing topological optimization on the dynamic characteristics of gears

The drum shearer is one of the main equipments of the long-wall mining system that has been widely used in coal mining for decades. Influenced by large fluctuation and intensive impact of drum load, the drum driving system is a weak part of the drum shearer due to the large dynamic deformation on ranging arm housing and the changes of gear meshing state. Since previous studies did not consider the coupling effects of housing and gearing transmission system, this study is concerned with hybrid finite element/lumped parameter dynamic modeling of the housing-transmission coupled system. In order to model the drum driving system, it is subdivided into two substructures: housing and transmission system. The housing is modeled by finite element method while the transmission system is modeled by lumped parameter method. The dynamic sub-structuring method (DSM) is used to develop a hybrid dynamic model, taking elastic coupling between the housing and transmission system into consideration. Then the influence of housing topological optimization on the dynamic characteristics of drum driving system is also analyzed through the hybrid dynamic model. The housing topological optimization is conducted through the Optistruct solver in Hypermesh, aiming at increasing the natural frequency of housing. It can be concluded that the ranging arm housing topological optimization could reduce the dynamic deformation of the housing and thus also reduce the equivalent mesh misalignment. However, the influence of housing topological optimization on the dynamic meshing force is not very significant.

Experimental‐Numerical Substructuring: a Comparison of Assemblies in Primal and Dual Forms

AbstractA hybrid dynamic substructuring method which combines experimentally measured and finite element (FE) modeled substructures in primal and dual form is presented. On the one hand, the model of the FE substructure is reduced to decrease the computational costs in the analysis of the hybrid model. On the other hand, the experimental substructure is measured while an instrumented fixture (known as Transmission Simulator) is assembled to its interface, providing the required interface dynamics for a high quality experimental model. The model of the transmission simulator is decoupled after measurement from the experimental substructure. Both the coupling and decoupling procedures are performed once with interface displacement (primal form) and once with interface forces (dual form). The hybrid substructuring methods are applied on an example and a comparison between both methods are presented. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)