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Abstract A dynamic model to study the coupled longitudinal and transverse vibrations of a submarine elastic propeller-shaft-hull system is developed using the FRF-based substructuring method (FBSM). The total system is firstly modeled as two substructures: the elastic propeller-shaft subsystem and the hull shell. For the former substructure, the elastic propeller is modeled by using harmonic blade array elements and the shafts are assumed to be Timoshenko beams, while the latter one is modeled using traditional finite element method. After that, the two substructures are synthesized using FBSM. The modes, the natural frequencies and the coupled longitudinal and transverse vibration characteristics of the propeller-shaft subsystem, the hull shell, and the total system are analyzed. An experiment studying the dynamic characteristics of a large-scale submarine experimental setup is processed and compared with the numerical results, which shows great consistency. Finally, a further discussion is carried out focused on how the bearing stiffness affects the coupled vibration characteristics of the total system. Highlights • The dynamic model of an elastic propeller-shaft-hull system is developed using FBSM. • The elastic propeller is modeled by using harmonic blade array elements. • The vibration behaviors of the substructures and total system are simulated and compared. • Experiment is performed to validate the coupled vibrations of the substructures and total system. • Coupled vibration analysis using FBSM is of reasonable accuracy and high efficiency. [ABSTRACT FROM AUTHOR]

Based on the Balanced Truncation approach, a novel methodology for the construction of a superelement for the dynamic analysis of elastic structures made with viscoelastic materials is presented. Contrary to classical modal reduction techniques (Craig-Bampton, MacNeal) where the normal modes basis must be enriched to account for damping effects, the methodology presented here takes advantage of the Golla–Hughes–McTavish rheological model (GHM) before reducing the system via the Balanced Proper Orthogonal Decomposition (BPOD). The Lagrange multipliers are finally employed to couple the reduced system to a host structure, as made in popular dynamic substructuring techniques. This method has two major advantages. First, substantial savings are achieved by the judicious combination of GHM and POD techniques. Second, the reduced system takes the form of a constant matrix of small size which permits to preserve confidentiality. [ABSTRACT FROM AUTHOR]

A numerical approach is proposed to compute the dynamic response of periodic structures with cyclic symmetry, and assemblies made up of these periodic structures. The wave finite element (WFE) method is used to describe the wave modes which occur around the circumferential direction of these periodic structures. Emphasis is placed on assessing the dynamic flexibility modes of a periodic structure by considering unit forces which are successively applied to the boundary degrees of freedom. It is shown that the matrices of dynamic flexibility modes can be quickly computed. This yields an efficient dynamic substructuring technique to analyze the dynamic behavior of assemblies made up of several periodic structures. Numerical experiments are carried out which concern the analysis of a single periodic structure as well as assemblies made up of two and three structures. [ABSTRACT FROM AUTHOR]

A nonlinear signal-based control (NSBC) method utilises the ‘nonlinear signal’ that is obtained from the outputs of a controlled system and its linear model under the same input signal. Although this method has been examined in numerical simulations of nonlinear systems, its application in physical experiments has not been studied. In this paper, we study an application of NSBC in physical experiments and incorporate an error feedback action into the method to minimise the error and enhance the feasibility in practice. Focusing on NSBC in substructure testing methods, we propose nonlinear substructuring control (NLSC), that is a more general form of linear substructuring control (LSC) developed for dynamical substructured systems. In this study, we experimentally and numerically verified the proposed NLSC via substructuring tests on a rubber bearing used in base-isolated structures. In the examinations, NLSC succeeded in gaining accurate results despite significant nonlinear hysteresis and unknown parameters in the substructures. The nonlinear signal feedback action in NLSC was found to be notably effective in minimising the error caused by nonlinearity or unknown properties in the controlled system. In addition, the error feedback action in NLSC was found to be essential for maintaining stability. A stability analysis based on the Nyquist criterion, which is used particularly for linear systems, was also found to be efficient for predicting the instability conditions of substructuring tests with NLSC and useful for the error feedback controller design. [ABSTRACT FROM AUTHOR]

The combination of experimental and numerical data is a typical challenge in complex vibro-acoustic problems. Rather than employing model-updating techniques, we combine the modal substructuring technique with non-conforming grids in order to be able to directly employ experimental and numerical modes for the description of weakly coupled vibro-acoustic systems. By incorporating Delaunay triangulation in the process, mechanical modes of any origin and discretized in terms of point clouds can be coupled with computational acoustic modes. The method is validated using a two-sided vibro-acoustic box. It is demonstrated that, by employing suitable interpolation techniques, systems based on coarsely discretized experimental modes can be used analogously to computational modes. The approach makes it straightforward to take into account modal damping and to fit numerical modes via experimental modal parameters, such as eigenfrequency, modal mass and damping. • Structural modes from modal analysis can be coupled with computational acoustic modes. • Simple implementation for complex grids by employing point clouds and Delaunay triangulation. • Interpolation techniques allow to use low-res scattered measurement points. • Coupled vibro-acoustic modes can be derived from uncoupled modes. • Thin-plate spline interpolation significantly reduces coupling errors. [ABSTRACT FROM AUTHOR]

• Polynomial and interpolation models allow for interface displacement reconstruction. • Complex polynomial models outperform the rigid model using the same indicators. • The proposed approaches can be combined for an extended capability. • The method is numerically validated in the context of substructuring. Frequency response functions (FRF) are valuable structure characterizations that are used for the study of noise and vibration, load identification, modal analysis or model updating. They are usually estimated as mobilities by exciting the structure and measuring the normalized response for each frequency. However, rotational degrees of freedom (DOF) are typically difficult or impossible to measure directly. Previous studies have shown that rotational DOFs can be critical for the successful application of different techniques, such as dynamic substructuring. Consequently, different approaches have been proposed to take them into account, such as the finite differences method. Frequency Based Substructuring (FBS) is a dynamic substructuring technique that allows for the coupling of the frequency response functions of separate subsystems in order to synthesize the coupled system's FRFs without the physical assembly. This technique can be sensitive to inconsistencies between the substructures or incomplete information in the interface characterization. The inclusion of rotational degrees of freedom in the FRFs of the interfaces for the application of substructuring has been extensively discussed in literature, but there are still some limitations in frequency due to the assumptions that are required, especially the rigidity assumption of the interfaces. The goal of this paper is to present an experimental approach to relax the rigidity assumption and increase the complexity of the force and displacement field characterization of interfaces. This would extend the value of the estimated FRFs to higher frequency ranges, in which the local deformations start to have an important effect. To particularize the general approach, different possible models are proposed and discussed, highlighting their benefits and disadvantages. Some of these models are validated numerically and experimentally. Finally, the performance of the approach for substructuring applications is also analyzed on a numerical model. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper we outline the basic theory of assembling substructures for which the dynamics are described as Impulse Response Functions. The assembly procedure computes the time response of a system by evaluating per substructure the convolution product between the Impulse Response Functions and the applied forces, including the interface forces that are computed to satisfy the interface compatibility. We call this approach the Impulse Based Substructuring method since it transposes to the time domain the Frequency Based Substructuring approach. In the Impulse Based Substructuring technique the Impulse Response Functions of the substructures can be gathered either from experimental tests using a hammer impact or from time-integration of numerical submodels. In this paper the implementation of the method is outlined for the case when the impulse responses of the substructures are computed numerically. A simple bar example is shown in order to illustrate the concept. The Impulse Based Substructuring allows fast evaluation of impact response of a structure when the impulse response of its components is known. It can thus be used to efficiently optimize designs of consumer products by including impact behavior at the early stage of the design, but also for performing substructured simulations of complex structures such as offshore wind turbines. [Copyright &y& Elsevier]

Abstract: Traditional model updating of large-scale structures is usually time-consuming because the global structural model needs to be repeatedly re-analyzed as a whole to match global measurements. This paper proposes a new substructural model updating method. The modal data measured on the global structure are disassembled to obtain the independent substructural dynamic flexibility matrices under force and displacement compatibility conditions. The method is extended to the case when the measurement is carried out at partial degrees-of-freedom of the structure. The extracted substructural flexibility matrices are then used as references for updating the corresponding substructural models. An orthogonal projector is employed on both the extracted substructural measurements and the substructural models to remove the rigid body modes of the free–free substructures. Compared with the traditional model updating at the global structure level, only the sub-models at the substructural level are re-analyzed in the proposed substructure-based model updating process, resulting in a rapid convergence of optimization. Moreover, only measurement on the local area corresponding to the concerned substructures is required, and those on other components can be avoided. The effectiveness and efficiency of the proposed substructuring method are verified through applications to a laboratory-tested frame structure and a large-scale 600m tall Guangzhou New TV Tower. The present technique is referred to as the inverse substructuring model updating method as the measured global modal data are disassembled into the substructure level and then the updating is conducted on the substructures only. This differs from the substructuring model updating method previously proposed by the authors, in which the model updating is still conducted in the global level and the numerical global modal data are assembled from those of substructures. That can be referred to as the forward substructuring model updating method. [Copyright &y& Elsevier]

Abstract: When testing to identify an experimental model of a substructure, it is often beneficial to exercise the interface by attaching a fixture such as a rigid mass. An analytical representation of the fixture must then be used to subtract its effects from the assembly. However, this can cause the mass and stiffness matrices to become indefinite in some situations. This paper presents two new metrics that can be used by the analyst to determine the cause of indefinite mass or stiffness matrices after substructure uncoupling. The metrics rank the experimental and fixture modes based upon their contribution to offending negative eigenvalues. Once the troublesome modes have been identified, they can be inspected and often reveal why the mass has become negative. Two examples are presented to demonstrate the metrics and to illustrate the physical phenomena that they reveal. [Copyright &y& Elsevier]

Abstract: In this paper, a novel inertia-capacitance (IC) beam substructure formulation based on the IC-field presentation from the bond graph method is developed. The IC beam provides a modular, systematic and graphical approach to beam modeling. These features allow the modeler to focus more on the modeling and less on the mathematics. As such, the IC beam is proposed as an alternative to the many existing types of beam models available in the literature. The IC beam is formulated in the center of mass body fixed coordinate system allowing for easy interfacing in a multibody system setting. This floating frame approach is also computationally cheap. Elastic deformations in the IC beam are assumed to be small and described by modal superposition. The formulation couples rigid body and elastic deformations in a nonlinear fashion. The formulation is also compact and efficient. Detailed derivations for a two-dimensional planar IC beam with bending modes are presented. A modal acceleration method based on the decoupling of bending modes is proposed for use in the IC beam. The rotating beam spin-up maneuver problem is solved. The Karnopp–Margolis method is applied to ensure complete integral causality for an efficient numerical system. Geometric substructuring technique is applied to model large deflections. The IC beam is shown to be capable of solving the rotating beam problem accurately and efficiently. [Copyright &y& Elsevier]

Abstract: This article presents a technique for modelling the coupled dynamics of a railway vehicle and the track. The method is especially useful for simulating the dynamics of high speed trains running on nonlinear tracks. The main hypothesis is a cyclic system: an infinite track on which there is an infinite set of identical vehicles spaced at a regular interval of distance. Thus the main problems of the finite-length track models (e.g. the waves that reflect at the end of the track and interact with the vehicle; and the time interval of integration must be shorter than the track length divided by the velocity) are avoided. The flexibility of the method can be observed from the case studies presented in the present work: a vehicle passing over a hanging sleeper, and the vehicle–track dynamics for different ballast compaction cases. The results show the influence of the hanging sleeper gap on the wheel–rail contact forces, and the bending moment at the sleeper for different ballast compaction cases. [ABSTRACT FROM AUTHOR]

Abstract: The substructuring technology possesses much merit when it is utilized in model updating or damage identification of large-scale structures. However, the conventional substructuring technologies require the complete eigensolutions of all substructures available to obtain the eigensolutions of the global structure, even if only a few eigensolutions of the global structure are needed. This paper proposes a modal truncation approximation in substructuring method, in which only the lowest eigensolutions of the substructures need to be calculated. Consequently, the computation efficiency is improved. The discarded higher eigensolutions are compensated by the residual flexibility. The division of substructures and the selection of master modes in each substructure are also studied. The proposed substructuring method is illustrated by a frame structure and a practical bridge. The two case studies verify that the proposed method can improve the original substructuring method significantly. [Copyright &y& Elsevier]

The component mode synthesis (CMS) method is widely used to establish reduced dynamic models of complex structures so that iterative problems such as flutter analyses can be efficiently analyzed with reasonable cost and time. In the present study, a structural coupling method is developed for the dynamic analysis of a nonlinear structure consisting of substructures connected by nonlinear interfaces such as nonlinear hinge joints or sliding mode conditions. In order to verify the coupling method extended to consider the hinge joints, a numerical plate model consisting of two substructures and torsional springs is synthesized, and its modal parameters are compared with analysis data. The extended coupling method is further improved to consider the sliding mode condition. The improved coupling method is applied to a three-substructure-model with nonlinearity of sliding lines between the substructures. Finally, using the proposed coupling method, a dynamic model of a tilting structure consisting of two substructures with sliding line conditions is synthesized, and its dynamic characteristics are investigated. The analysis results show that the improved coupling method is effectively applicable to the dynamic analysis of a nonlinear structure with the sliding mode condition. [Copyright &y& Elsevier]

An iterated improved reduced system (IIRS) procedure combined with substructuring scheme for both undamped and nonclassically damped structures is presented. Iterated IIRS method is an efficient reduction technique because the highly accurate eigenproperties from the repeatedly updated condensed matrices can be obtained without consuming expensive computational cost. However, single domain direct approach of this method to large structures requires much computational resources and even makes analysis intractable in the case only limited computer storage is available. These problems can be overcome by combining the substructuring scheme with IIRS procedure. The newly developed IIRS method combined with a substructuring scheme can provide an efficient methodology for large-scale eigenvalue problems. The validation of the present method and the evaluation of computational efficiency are demonstrated through the numerical examples. [Copyright &y& Elsevier]

Modeling of vibro/acoustic systems with embedded acoustic components of complex geometries is a challenging task. In particular, the presence of irregular-shaped acoustic modules, which are usually treated by finite element (FE) method, increases system complexities and makes the use of existing sub-structuring modeling techniques cumbersome. To tackle the problem, an efficient three-dimensional sub-structuring modeling method is proposed in this paper. As an important sub-structural module, a dedicated coordinate transformation technique is established to cope with polygon acoustic components. The embodiment of the technique into the existing sub-structuring framework avoids the use of conventional FE modules, thus increasing the flexibility and the efficiency of the simulation, conducive to system optimization. As an example, noise reduction in a duct, comprising a Micro-Perforated Panel (MPP) liner and a trapezoidal expansion chamber, is examined. The accuracy of the proposed model is firstly validated against both FE simulations and experiments. Numerical results uncover a dual hybrid sound reduction process, namely sound absorption of the MPP and wave reflection due to the geometry changes of the duct. Optimizations based on the proposed sub-structuring technique allow one to balance the hybrid reflective-absorptive effects through proper parameter tuning to maximize the sound attenuation within a prescribed frequency range. [ABSTRACT FROM AUTHOR]

This paper considers distributed model predictive control (DMPC) for the vibrations of smart tensegrity structures with input saturation. A distributed control strategy is necessary to enable the autonomy in the individual subsystems, reduce the computational burden of centralized control, and enhance the fault tolerance of control systems. In this work, the dynamic model for smart tensegrity structures equipped with active piezoelectric actuators is generated first by the finite element method. Then, based on the substructuring technique, the entire tensegrity structure system is decomposed into a series of multilevel subsystems. For each subsystem, the continuous-time predictive model equations are discretized by the explicit form of the Newmark-β algorithm. Finally, based on the parametric variational principle, the DMPC problem with input saturation is transformed into a series of linear complementarity problems. The proposed method provides a simple, unified and flexible multilevel distributed control framework for solving the vibration control problems of smart tensegrity structure systems. Numerical experiments illustrate that the proposed DMPC method is effective and exhibits performance comparable to that of a typical centralized model predictive control (CMPC) method. In addition, the constraints of the control input saturation for the proposed DMPC method can be satisfied. [ABSTRACT FROM AUTHOR]