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The purpose of this paper is to derive linear modal equations describing the forced liquid sloshing in a rigid truncated (tapered) conical tank, as well as to show how to couple these modal equations with “global” dynamic equations of a complex mechanical system carrying this tank.

Derivation of the modal equations can be based on the Trefftz variational method developed by the authors in a previous paper. Describing the coupled dynamics utilizes Lukovsky' formulas for the resulting hydrodynamic force and moment due to liquid sloshing.

The so‐called Stokes‐Joukowski potentials can be found by using the Trefftz method from the authors' previous paper with the same polynomial‐type functional basis. Coupling the modal equations with the global dynamic equations becomes a relatively simple task facilitated by Lukovsky's formulas. Using the linear multimodal method can be an efficient alternative to traditional numerical and analytical tools employed for studying the coupled vibrations of a tower with a conical rigid tank on the tower top.

The derived modal equations are equipped by tables with the computed non‐dimensional hydrodynamic coefficients. Interested readers (engineers) can incorporate the modal equations into the global dynamic equations of a whole mechanical system without new computations of these coefficients.

The multimodal method can be an alternative to traditional numerical tools. Using the derived modal equations simplifies analytical studies and provides efficient calculations of the coupled dynamics of a mechanical system carrying a rigid tapered conical tank with a liquid.

The purpose of this paper is to design a component synthesis method to suppress the vibration of the flexible spacecraft, which has the constant amplitude force/moment actuator.

The authors proposed a method to construct constant amplitude of time delay and composite coefficient sequences based on the principles of the component synthesis vibration suppression (CSVS). The associated design strategy of the CSVS torque control is also developed. The dynamic model consisting of a single axis rotating rigid central body and a fixed flexibility panel is used to validate the proposed method. Constraint modal and free modal method are both tested to analyse the natural frequencies of the panel and dynamic properties of rigid–flexible decoupling system, under the conditions of known and unknown frequencies. The feasibility of constructing CSVS control force based on the constraint modal frequency is also analysed.

The proposed method can suppress multistage vibration and has arbitrary order robustness for each order frequencies simultaneously. Simulation results show that only the duration time of the actuator has to be set for the proposed method, reasonable vibration suppression effect can be achieved.

The method can be used in spacecraft, especially flexible spacecraft to suppress the vibration; the approach is convenient for engineering application and can be easily designed.

The authors proposed a method to construct constant amplitude of time delay and composite coefficient sequences based on the principles of the CSVS.

The finite element method (FEM) is used to calculate the two-dimensional anti-plane dynamic response of structure embedded in D’Alembert viscoelastic multilayered soil on the rigid bedrock. This paper aims to research a time-domain absorbing boundary condition (ABC), which should be imposed on the truncation boundary of the finite domain to represent the dynamic interaction between the truncated infinite domain and the finite domain.

A high-order ABC for scalar wave propagation in the D’Alembert viscoelastic multilayered media is proposed. A new operator separation method and the mode reduction are adopted to construct the time-domain ABC.

The derivation of the ABC is accurate for the single layer but less accurate for the multilayer. To achieve high accuracy, therefore, the distance from the truncation boundary to the region of interest can be zero for the single layer but need to be about 0.5 times of the total layer height of the infinite domain for the multilayer. Both single-layered and multilayered numerical examples verify that the accuracy of the ABC is almost the same for both cases of only using the modal number excited by dynamic load and using the full modal number of infinite domain. Using the ABC with reduced modes can not only reduce the computation cost but also be more friendly to the stability. Numerical examples demonstrate the superior properties of the proposed ABC with stability, high accuracy and remarkable coupling with the FEM.

A high-order time-domain ABC for scalar wave propagation in the D’Alembert viscoelastic multilayered media is proposed. The proposed ABC is suitable for both linear elastic and D’Alembert viscoelastic media, and it can be coupled seamlessly with the FEM. A new operator separation method combining mode reduction is presented with better stability than the existing methods.

As a practical engineering method, earthquake response spectra play an important role in seismic hazard assessment and in seismic design of structures. However, the computing scale and the efficiency of commercial software restricted the solution of complex structures. There is a clear need of developing large-scale and highly efficient finite element procedures for response spectrum analysis.

In this paper, the kernel theories for earthquake response spectra are deduced and the corresponding parallel solution flow via the modal superposition method is presented. Based on the algorithm and the parallel data structure of JAUMIN framework, a parallel finite element (FE) solution module is established. Using the solution procedure on a supercomputer equipped with up to thousands of processors, the correctness and parallel scalability of the algorithm are evaluated via numerical experiments of typical engineering examples.

The results show that the solution module has the same precision as the commercial FE software ANSYS; the maximum solution scale achieves 154 million degrees of freedom (DOFs) with a favorable parallel computing efficiency, going far beyond the computing ability of the commercial FE software.

The solution scale in this paper is very challenging for the large-scale parallel computing of structural dynamics and will promote the dynamic analysis ability of complex facilities greatly.

This paper aims to present a fast and effective approach to tackle complex fluid structure interaction problems that are relevant for the aeronautical design.

High fidelity computer-aided engineering models (computational fluid dynamics [CFD] and computational structural mechanics) are coupled by embedding modal shapes into the CFD solver using RBF mesh morphing.

The theoretical framework is first explained and its use is then demonstrated with a review of applications including both steady and unsteady cases. Different flow and structural solvers are considered to showcase the portability of the concept.

The method is flexible and can be used for the simulation of complex scenarios, including components vibrations induced by external devices, as in the case of flapping wings.

The computation mesh of the CFD model becomes parametric with respect to the modal shape and, so, capable to self-adapt to the loads exerted by the surrounding fluid both for steady and transient numerical studies.

This paper discusses advances in interactive discrete element simulation for use in computer‐aided concurrent design. We highlight the computational problems of creating a ‘virtual world’ populated by objects which behave much as real world objects and propose a system based on a new class of volumetric models, called superquadrics. These functions have significant advantages for calculating multibody interactions, and by coupling volumetric representation to a modal decomposition method for the physical dynamics we have been able to gain up to two orders of magnitude in efficiency. The modal method allows us to trade off high order modes for improved stability, time step magnitude, temporal aliasing and speed of response, and so provide almost real time feedback to the designer. We believe that virtual manufacturing systems will be especially useful in conceptual design, in design for manufacture and in the new thrust in concurrent design.

The purpose of this paper is to present an application of the Generalized Finite Element Method (GFEM) for modal analysis of 2D wave equation.

The GFEM can be viewed as an extension of the standard Finite Element Method (FEM) that allows non-polynomial enrichment of the approximation space. In this paper the authors enrich the approximation space with sine e cosine functions, since these functions frequently appear in the analytical solution of the problem under study. The results are compared with the ones obtained with the polynomial FEM using higher order elements.

The results indicate that the proposed approach is able to obtain more accurate results for higher vibration modes than standard polynomial FEM.

The examples studied in this paper indicate a strong potential of the GFEM for the approximation of higher vibration modes of structures, analysis of structures subject to high frequency excitations and other problems that concern high frequency oscillatory phenomena.

The purpose of this paper is to contribute to the solution of the fatigue damage problem of reinforced concrete frames in bending.

The problem of fatigue damage is formulated based on the rheological–dynamical analogy, including a scalar damage variable to address the reduction of stiffness in strain softening. The modal analysis is used by the finite element method for the determination of modal parameters and resonance stability of the selected frame cross-section. The objectivity of the presented method is verified by numerical examples, predicting the ductility in bending of the frame whose basic mechanical properties were obtained by non-destructive testing systems.

The modal analysis in the frame of the finite element method is suitable for the determination of modal parameters and resonance stability of the selected frame cross-section. It is recommended that the modulus of elasticity be determined by non-destructive methods, e.g. from the acoustic response.

The paper presents a novel method of solving the ductility in bending taking into account both the creep coefficient and the aging coefficient. The rheological-dynamical analogy (RDA) method uses the resonant method to find material properties. The characterization of the structural damping via the damping ratio is original and effective.

In this paper, the aim is to present a modeling strategy for a flexible rotor/active magnetic bearing (AMB) system with non‐collocation. Special attention is paid to the vibration reduction and the stable passage through the first critical speed.

The finite element method based on Euller‐Bernoulli beam theory is applied in the formulation of the rotor model. Since rotor/AMB systems are complex mechatronic systems, reduced order approach is used in the control system design. This study applies the modal decomposition method and the modal truncation method, thus retaining the lower order bending modes. The obtained numerical results are compared with the measured open loop frequency responses and the existing differences are compensated in order to obtain accurate numerical model.

Frequency response of the entire system model (flexible shaft, actuators, power amplifiers and sensors) with amplitudes expressed in rotor lateral displacements can be verified by the measured frequency responses. The deviations in the amplitude and phase diagrams are then successfully corrected using the appropriate model modifications.

The results of this research find direct applications in flexible rotors supported by AMBs, e.g. high speed spindles, turbo molecular pumps, flywheel energy storage systems, etc. The presented procedure can be especially valuable in the design of model based controllers.

An AMB system model is developed and presented in this paper, in conjunction with a systematic description of an efficient procedure for the elimination of the typical mismatches between the simulation and experiment. Firstly, rotor/AMB test rig is stabilized with an appropriately tuned PID controller and an open loop frequency response is obtained for such a system. This response is then compared to corresponding simulation results for which mismatches are identified and eliminated thus yielding an accurate model of the system.

The purpose of this paper is to examine the cross‐coupled responses of a coupled rotor‐fuselage flight dynamic simulation model, including a finite‐state inflow aerodynamics and a coupled flap‐lag and torsion flexible blade structure.

The methodology is laid out based on model development for an articulated main rotor, using the theories of aeroelastisity, finite element and finite‐state inflow formulation. The finite‐state inflow formulation is based on a 3D unsteady Euler‐based concepts presented in the time domain. The most advantages of the model are the capability of modeling dynamic wake effects, tip losses and skewed wake aerodynamics. This is, in fact, a special type of the inflow model relating inflow states, to circulatory blade loadings through a set of first‐order differential equations. A non‐iterative solution of the differential equations has practically altered the model into a simple and direct formulation appending properly to the rest of the helicopter mathematical model. A non‐linear distribution of the induced velocity over the rotor disc is finally obtained by the use of both Legendre polynomials and higher‐harmonic functions. Ultimately, validations of the theoretical results show that the on‐axis response, direct reaction to the pilot input, has a good accuracy both quantitatively and qualitatively against flight test data, and the off‐axis response, cross‐coupled or indirect reaction to the pilot input are improved by this approach of modeling.

Improvements in dynamic prediction of both trim control settings and dynamic cross‐coupled responses of helicopter to pilot inputs are observed.

Further work is required for investigation of the augmented finite state inflow model, including the wake rotation correction factors to describe helicopter maneuvering flight characteristics.

The results of this work support the future researches on design and development of advanced flight control system, incorporating a high bandwidth with low‐phase delay to control inputs and also high levels of dynamic stability within minimal controls cross coupling.

This paper provides detailed characteristics on the mathematical integration problems associated with the advanced helicopter flight dynamics research.