Use of dynamic influence coefficients in forced vibration problems with the aid of fast fourier transform

The use and importance of dynamic stiffness influence coefficients in flexural forced vibrations of structures composed of beams are described. The dynamic forces can be either harmonic or general transient forces. The dynamic influence coefficients are defined in the Fourier transform plane, are computed there and are given in Table form for a uniform free-free beam. The dynamic problem formulated in terms of these coefficients is reduced to a static form. The dynamic response is obtained, in general, by a matrix inversion in the Fourier transform plane and a numerical inversion, based on the Cooley-Tukey algorithm, of the transformed solution. Structural examples of forced vibrations of a simple beam and a rigid frame illustrate the use of dynamic coefficients and demonstrate their advantages over other known methods in accuracy, simplicity of formulation and speed of computation.     

Use of dynamic influence coefficients in forced vibration problems with the aid of Laplace transform

The use and importance of dynamic stiffness influence coefficients in flexural forced vibrations of structures composed of beams are described. The dynamic forces can be either harmonic or general transient forces. The dynamic influence coefficients are defined in the Laplace transform plane, are computed there and are given in tables for uniform beams under various end conditions. The dynamic response is obtained, in general, by a matrix inversion in the Laplace transform plane and a numerical inversion, based on interpolation concepts, of the transformed solution. Structural examples of forced vibrations of a simple beam and a rigid frame illustrate the use of dynamic coefficients and demonstrate their advantages over other known methods in accuracy, simplicity of formulation and speed of computation.     

Automated structural design and analysis of advanced composite wing models

The design of a composite wind tunnel model has demonstrated the ability to tailor the response of a composite structure to provide desired static and dynamic characteristics. This was possible because the strength and stiffness properties of composite structures can be controlled through selection of materials and lamination patterns. To take maximum advantage of the capability, efficient computer procedures are being developed for the design and analysis of composite structures. A finite element procedure and a direct Rayleigh-Ritz procedure, specialized for the preliminary analysis of wing-type structure, are discussed. The use and accuracy of these procedures have been demonstrated on a low cost, low risk basis in the design and analysis of a composite wind tunnel model and in test-theory correlation for static and dynamic response. Material selection, intermediate design decisions, fabrication, testing for natural modes and frequencies, and testing for influence coefficients for the wind tunnel model are discussed.     

Thermally induced vibrations of beam structures

A general numerical method is developed for determining the dynamic response of beam structures to rapidly applied thermal loads. The method consists of formulating and solving the dynamic problem in the Laplace transform domain with the aid of dynamic stiffness influence coefficients defined for a beam element in that domain and of obtaining the response by a numerical inversion of the transformed solution. Thus, the solution of the associated heat conduction problem, usually obtained by Laplace transform and needed for the computation of the thermal load, can be used in its transformed form. The effects of damping and of axial compressive forces on the structural response are also studied. Three examples are presented in detail to illustrate the proposed method and demonstrate its advantages.     

Adaptive differential dynamic programming for multiobjective optimal control

An efficient numerical solution scheme entitled adaptive differential dynamic programming is developed in this paper for multiobjective optimal control problems with a general separable structure. For a multiobjective control problem with a general separable structure, the “optimal” weighting coefficients for various performance indices are time-varying as the system evolves along any noninferior trajectory. Recognizing this prominent feature in multiobjective control, the proposed adaptive differential dynamic programming methodology combines a search process to identify an optimal time-varying weighting sequence with the solution concept in the conventional differential dynamic programming. Convergence of the proposed adaptive differential dynamic programming methodology is addressed.     

Identifying financial time series with similar dynamic conditional correlation

One of the main problems in modelling multivariate conditional covariance time series is the parameterization of the correlation structure. If no constraints are imposed, it implies a large number of unknown coefficients. The most popular models propose parsimonious representations, imposing similar correlation structures to all the series or to groups of time series, but the choice of these groups is quite subjective. A statistical approach is proposed to detect groups of homogeneous time series in terms of correlation dynamics for one of the widely used models: the Dynamic Conditional Correlation model. The approach is based on a clustering algorithm, which uses the idea of distance between dynamic conditional correlations, and the classical Wald test, to compare the coefficients of two groups of dynamic conditional correlations. The proposed approach is evaluated in terms of simulation experiments and applied to a set of financial time series.     

Conceptual design of aeroelastic structures by topology optimization

A topology optimization methodology is presented for the conceptual design of aeroelastic structures accounting for the fluid–structure interaction. The geometrical layout of the internal structure, such as the layout of stiffeners in a wing, is optimized by material topology optimization. The topology of the wet surface, that is, the fluid–structure interface, is not varied. The key components of the proposed methodology are a Sequential Augmented Lagrangian method for solving the resulting large-scale parameter optimization problem, a staggered procedure for computing the steady-state solution of the underlying nonlinear aeroelastic analysis problem, and an analytical adjoint method for evaluating the coupled aeroelastic sensitivities. The fluid–structure interaction problem is modeled by a three-field formulation that couples the structural displacements, the flow field, and the motion of the fluid mesh. The structural response is simulated by a three-dimensional finite element method, and the aerodynamic loads are predicted by a three-dimensional finite volume discretization of a nonlinear Euler flow. The proposed methodology is illustrated by the conceptual design of wing structures. The optimization results show the significant influence of the design dependency of the loads on the optimal layout of flexible structures when compared with results that assume a constant aerodynamic load.     

Soil-structure interaction and effect of axial force on the dynamics of offshore structures

The offshore structures are flexible systems subjected to various types of loadings. The heavy gravitational loads on the top decks, wind and water wave pressures acting on the platforms are transferred to the soil through the piles or mat foundations. Under the vibration, the variation in the pore pressures induces additional effects on the embedded part of the piles. The effect of the soil-structure interaction on the dynamics of the structure is taken into account as the deformations of the soil caused by the motion of the structure which in turn modify the response of the structure. The effect of the axial forces, within the individual members, on the vibration of the structure is included in the formulation. The dynamic stiffness matrix of the members are developed by considering the actual mass distribution and the effect of the axial force of the members. For the members embedded into soil, the soil reactions and the skin frictions are also considered as continuously varying over the members. Therefore, the equations of motion are satisfied along any infinitesimal element of the members. The new formulation is introduced in the general purpose computer code STDYNL, then the sensitivity of the overall dynamic response of the deep water platforms to the variation of the soil characteristics and to the effect of the axial forces of the members are investigated.     

A disturbance model for control/structure optimization with output feedback control

This paper deals with a technique for the integrated optimization of structure and control in the design of flexible systems. The current approach uses the concept of response to dynamic constraints to establish a concise variational methodology to total system optimization, and eliminates the need to specify rather arbitrary trade-offs between control energy and structural mass. Results give an explicit dependency between structural stiffness (hence mass), disturbance magnitude, available control energy, and deflection constraints. The current paper presents results for direct output feedback and dynamic filter compensation with optional positive real constraints on the filters. The key element of the design approach is to formulate a set of response constraints that bound the allowable deflections and a set of constraints that bound the allowable control energy. The results for model structures indicate the importance of the control-structure interaction in a light-weight structure and the trade-offs between controller complexity, energy and structural mass.     

Direct identification of structural parameters from dynamic responses with neural networks

A novel neural network-based strategy is proposed and developed for the direct identification of structural parameters (stiffness and damping coefficients) from the time-domain dynamic responses of an object structure without any eigenvalue analysis and extraction and optimization process that is required in many identification algorithms for inverse problems. Two back-propagation neural networks are constructed to facilitate the process of parameter identifications. The first one, called emulator neural network, is to model the behavior of a reference structure that has the same overall dimension and topology as the object structure to be identified. After having been properly trained with the dynamic responses of the reference structure under a given dynamic excitation, the emulator neural network can be used as a nonparametric model of the reference structure to forecast its dynamic response with sufficient accuracy. However, when the parameters of the reference structure are modified to form a so-called associated structure, the dynamic responses forecast by the network will differ from the simulated responses of the associated structure. Their difference can be assessed with a proposed root mean square (RMS) difference vector for both velocity and displacement responses. With the associated structural parameters and their corresponding RMS difference vectors, another network, called parametric evaluation neural network, can be trained. In this study, several 5-story frames are considered as example object structures with simulated displacement and velocity time histories that mimic the measured dynamic responses in practice. The performance of the proposed strategy has been demonstrated quite satisfactorily; the error for the estimation of each stiffness or damping coefficient is less than 10% even in the presence of 7% noise. Numerical simulations show that the accuracy of the identified parameters can be significantly improved by injecting noise in the training patterns for the parametric evaluation neural network. The proposed strategy is extremely efficient in computation and thus has potential of becoming a practical tool for near real time monitoring of civil infrastructures.     

双向地震激励下隔震结构抗倾覆特性的数值分析

为研究叠层橡胶支座隔震建筑的抗倾覆性能,建立隔震结构在双向地震激励下倾覆力矩时域响应动力分析模型.在对该模型进行简化的基础上,利用结构设计反应谱探讨结构高宽比和结构基本周期等因素对隔震结构抗倾覆力矩与倾覆力矩比值的影响.给出多层和小高层隔震结构在双向地震作用下的抗倾覆安全因数随地震烈度、场地土类别的变化规律.利用本课题...     

Topology optimization of dynamic stress response reliability of continuum structures involving multi-phase materials

This paper proposes a methodology for maximizing dynamic stress response reliability of continuum structures involving multi-phase materials by using a bi-directional evolutionary structural optimization (BESO) method. The topology optimization model is built based on a material interpolation scheme with multiple materials. The objective function is to maximize the dynamic stress response reliability index subject to volume constraints on multi-phase materials. To solve the defined topology optimization problems, the sensitivity of the dynamic stress response reliability index with respect to the design variables is derived for iteratively updating the structural topology. Subsequently, an optimization procedure based on the BESO method is developed. Finally, a series of numerical examples of both 2D and 3D structures are presented to demonstrate the effectiveness of the proposed approach.

     

Inverse response problem (control) of dynamic systems via Hamilton's law

By using Hamilton's law (of varying action) directly, the solution of a control problem becomes one of solving a set of algebraic equations only; no differential equations are needed. The approach specifies the response as a polynomial in power series of time, the coefficients of which are chosen to yield the desired behavior of the dynamic system. The unknown control inputs are assumed to be also polynomials in power series of time with unknown coefficients. The inverse response (control) problem is solved by finding these unknown input coefficients by an application of Hamilton's law which must always be satisfied by the dynamic system. The feasibility of the method is demonstrated for the control of a spatially discrete nonlinear dynamic system.     

Investigations on characteristics of micro/meso scale gas foil journal bearings for 100–200 W class micro power systems using first order slip velocity boundary conditions and the effective viscosity model

In this paper, a modified compressible Reynolds equation for micro/meso scale gas foil journal bearings considering first order slip and effective viscosity under rarefied flow conditions is presented. The influence of rarefaction effect on the load carrying capacity, attitude angle, speed and frequency dependent stiffness and damping coefficients, modal impedance, natural frequencies and unbalance response is studied. From numerical analysis, it has been found that there is significant change in all the static and dynamic characteristics predicted by the no-slip model and model with effective viscosity. There is also a considerable difference between the values predicted by a model with effective viscosity and a model without effective viscosity. For a given eccentricity ratio, the influence of effective viscosity on load carrying capacity and attitude angle is more significant for the typical operating speed range of micro/meso scale gas turbines. The influence of effective viscosity decreases with increase in compliance of bearing structure. Similarly, the influence of effective viscosity on frequency dependent stiffness and damping coefficients increases with excitation frequency ratio. Significant change in natural frequency, modal impedance and unbalance response for model with no slip and slip with effective viscosity is observed. The influence of effective viscosity is found to be significant with increase in Knudsen number.     

On objective functions of minimizing the vibration response of continuum structures subjected to external harmonic excitation

This work deals with the topological design of vibrating continuum structures. The vibration of continuum structure is excited by time-harmonic external mechanical loading with prescribed frequency and amplitude. In comparison with well-known compliance minimization in static topology optimization, various objective functions are proposed in literature to minimize the response of vibrating structures, such as power flow, vibration transmission, and dynamic compliances, etc. Even for the dynamic compliance, different definitions are found in literature, which have quite different formulations and influences on the optimization results. The aim of this paper is to provide a comparison of these different objective functions and propose reference forms of objective functions for design optimization of vibration problems. Analytical solutions for two degrees of freedom system and topological design of plane structures in numerical examples are compared using different optimization formulations for given various excitation frequencies. The results are obtained by the finite element method and gradient based optimization using analytical sensitivity analysis. The optimized topologies and vibration response of the optimized structures are presented. The influence of excitation frequencies and the eigenfrequencies of the structure are discussed in the numerical examples.     

Full-scale measurements of dynamic response of suspension bridge subjected to environmental loads using GPS technology

Nowadays, there are many larger and taller engineering structures than in the past. These structures are commonly designed to be more flexible. Thus, they are sensitive to severe wind gust and earthquake tremor. For the dynamic response prediction, finite element (FE) modal updating and structural health monitoring, the dynamic characteristics of a structure are becoming increasingly important. The aim of this paper is to show an emerging tool-the real time kinematic (RTK) global positioning system (GPS), w...     

Energetically consistent simulation of simultaneous impacts and contacts in multibody systems with friction

This paper presents a methodology for treating energy consistency when considering simultaneous impacts and contacts with friction in the simulation of systems of interconnected bodies. Hard impact and contact is considered where deformation of the impacting surfaces is negligible. The proposed approach uses a discrete algebraic model of impact in conjunction with moment and tangential coefficients of restitution (CORs) to develop a general impact law for determining post-impact velocities. This process depends on impulse–momentum theory, the complementarity conditions, a principle of maximum dissipation, and the determination of contact forces and post-impact accelerations. The proposed methodology also uses an energy-modifying COR to directly control the system’s energy profile over time. The key result is that different energy profiles yield different results and thus energy consistency should be considered carefully in the development of dynamic simulations. The approach is illustrated on a double pendulum, considered to be a benchmark case, and a bicycle structure.     

一种具有PID结构的动态矩阵控制

动态矩阵控制（DMC）是基于对象阶跃响应的一种预测控制算法，它具有结构清晰、算法简单、对模型失配适应能力强等优点，适用于纯时滞，开环渐近稳定的线性对象，是一种成功而有效的控制算法。但DMC的输出动态特性受其参数的影响，目前，对DMC参数的选取一般都是采用试凑结合仿真的方法，费时又费力，从而给设计者造成很大的困难。该文提出了一种对DMC的改进方法——DMPIDC，使PID参数整定方法与动态矩阵控制结合起来．用整定出的PID参数作为DMPIDC的加权系数，保证了良好的输出动态特性，仿真结果表明这种方法是可行的。     

Formulation of time variant stiffness matrices due to changing joint properties

Time variant stiffness matrices due to changing joint properties occur in a wide range of structural dynamic response problems. An example is a structure with element forces which can be reacted at a joint in only one direction. Another is one with structural elements which can be alternately attached and detached to an adjacent structure due to joint clearance. A general treatment of stiffness matrices for structures having joints with time dependent properties is presented. Various joints are examined and the approach is demonstrated by deriving time variant stiffness matrices for simple structures which contain each type of joint.