Dynamic Response Of Linear Structures Research Articles

Fluid Structure Interaction Using Modal Superposition and Lagrangian CFD

This study investigates the impact of fluid loads on the elastic deformation and dynamic response of linear structures. A weakly coupled modal solver is presented, which involves the solution of a dynamic equation of motion with external loads. The mode superposition method is used to find the dynamic response, utilizing predetermined mode shapes and natural frequencies associated with the structure. These essential parameters are pre-calculated and provided as input for the simulation. Integration of the weakly coupled modal solver is accomplished with the Lagrangian Differencing Dynamics (LDD) method. This method can directly use surface mesh as boundary conditions, so it is much more convenient than other meshless CFD methods. It employs Lagrangian finite differences, utilizing a strong formulation of the Navier–Stokes equations to model an incompressible free-surface flow. The elastic deformation of the structure, induced by fluid forces obtained from the flow solver, is computed within the modal coupling algorithm through direct numerical integration. Subsequently, this deformation is introduced into the flow solver to account for changes in geometry, resulting in updated flow pressure and velocity fields. The flow particles and vertices of the structure are advected in Lagrangian coordinates, resulting in Lagrangian–Lagrangian coupling in spaces with weak or explicit coupling in time. The two-way coupling between fluid and structure is successfully validated through various FSI benchmark cases. The efficiency of the LDD method is highlighted as it operates directly on surface meshes, streamlining the simulation setup. Direct coupling of structural deformation eliminates the conventional step of mapping fluid results onto the structural mesh and vice versa.

Damage detection of moment frames using ensemble Empirical Mode Decomposition and clustering techniques

Most of the damage detection methods implement dynamic response of linear structures for indication of damage. Time-frequency methods employ signal processing techniques to detect temporal changes in frequency characteristics of vibration response of the system. However, most of these techniques fail facing with nonlinear systems due to consecutive changes in stiffness that lead to fake damage indications. This study is divided into two parts. First, the Empirical Mode Decomposition method (EMD) is compared to Ensemble EMD (EEMD) to clarify the capability of these methods as signal processing tools. For this reason, the acceleration responses of a nonlinear steel moment frame are extracted by EMD and EEMD. Second, Hilbert transform based on EEMD is employed in conjunction with a density-based clustering technique to classify the changes in frequency and amplitude patterns to identify and estimate the extent of damage. Simulation results demonstrate that frequency is not an appropriate parameter to determine the extent of damage for nonlinear systems.

An evolutionary stochastic ground-motion model defined by a seismological scenario and local site conditions

This paper is concerned with modeling earthquake-induced ground accelerations and the simulation of the dynamic response of linear structures through the principles of stochastic dynamics. A fully evolutionary approach, with nonstationarity both in amplitude and in frequency content, is proposed in order to define the seismic action, based on seismological information in the form of a small number of input parameters commonly available in deterministic or probabilistic seismic design situations. The signal is obtained by filtering a Gaussian white-noise. The finite duration and time-varying amplitude properties are obtained by using a suitable envelope function. By utilizing a subset of the records from the PEER-NGA strong-motion database, and time-series analysis tools extended to nonstationary processes, the key transfer-function properties, in terms of circular frequency, damping ratio and spectral intensity factor, are identified. A regression analysis is conducted for practical and flexible application of this model, in order to empirically relate the identified time-varying parameters of the filter to the characteristics defining earthquake scenarios such as magnitude, rupture distance and soil type. A validation study and a parametric investigation using elastic response spectra is also included. Results show that the final seismic model can reproduce, with satisfactory accuracy, the characteristics of acceleration records in a region, over a broad range of response periods.

Dynamic response of linear structures to a random stream of pulses

The vibration of a linear structure caused by a random series of pulses is considered. Some different aspects of a point stochastic process characterizing a stream of pulses are taken into account. It is assumed that the occurrence process may be a general point stochastic process, a Poisson process, a renewal process, or a double point stochastic process. The case of loading of the structure by two streams of pulses is also considered. An analytical technique is developed to determine the probabilistic characteristics: i.e., the response of the structure as the expected value, the covariance, the cumulants, the characteristic function and the probability density function of the response. One general conclusion follows from these results: the variance of the response is smaller in the case of a general point stochastic process and a renewal process than for a Poisson process.

Using Lanczos vectors and Ritz vectors for computing dynamic responses

The Lanczos vectors and the Ritz vectors have been used for computing the dynamic response of linear structures. Although the procedures of using these two sets of vectors appear similar to the procedure of using the eigenvectors to find an approximate solution, the fundamental mechanisms of the three are different. We compare the three sets of vectors in detail to show some of the important differences in the hope that this comparison will be helpful to the use of the Lanczos vectors or the Ritz vectors for computing dynamic responses.

Dynamic response of linear structures to random streams of arbitrary impulses in time and space

The dynamic response of continuous structures to a stream of arbitrary impulses is considered. The impulses commence at random times and are located at random points on the surface of the structure. The shapes of the impulses can be arbitrary and can have a deterministic or stochastic nature, both in time and in space. The respective time durations and amplitudes of the impulses are also random. An analytical technique is developed to determine the response of the structure, and explicit expressions are provided for the expected value and covariance of the structure deflection. The results presented in the work can be used, for example, in estimating the reliability of bridge loading by traffic flow.

Dynamic Analysis of Structures by the DFT Method

Following a brief review of the Discrete Fourier Transform (DFT) method of analyzing the dynamic response of linear structures, the limitations and principal sources of potential inaccuracies of this approach are identified, and an evaluation is made of the nature and magnitudes of the errors that may result. Two versions of a modification are then presented which dramatically improve the efficiency of the DFT procedure, and the relative merits of the two techniques are examined. The concepts involved are developed by reference to single‐degree‐of‐freedom systems, and they are illustrated with the aid of judiciously selected numerical solutions.

Dynamic response of linear structures to a stream of random impulses in a “space-time” system

The dynamic response of continuous structures subjected to a stream of random impulses in a “space-time” system is considered. The impulses reach the structure at random points on the surface and at random time intervals. It is assumed that the stream can be correlated in respect to space and time. Explicit expressions are provided for the expected value and covariance of the structure deflection.

Dynamic response of linear structures to correlated random impulses

A systematic analysis of the dynamic response of linear continuous structures to randomly arriving impulses is presented. A counting (or point) process characterizing the considered stream of impulses is described by the product density functions of degree one and two. By making use of a normal mode approach and assuming specific forms for the product densities (characterizing the expected arrival rate of the impulses and their correlation) the formulae for the variances and cross-covariances of modal responses are derived. The variance of the plate response is obtained and discussed for different practical situations and the results are shown graphically.

Dynamic Response of Linear Structures With Large Parameters

The response of a linear structure with large stiffness parameters is shown to behave as a rigid object under sufficiently smooth and bounded excitations.

Dynamic behaviour of building‐foundation systems

AbstractA discussion of the effects of soil‐structure interaction on the dynamic response of linear structures which respond as single‐degree‐of‐freedom systems in their fixed‐base condition is presented. The structures are presumed to be supported at the surface of a homogeneous, elastic halfspace and to be excited at the base. The free‐field ground motions investigated include a harmonic motion, a relatively simple pulse‐type excitation and an actual earthquake record. Comprehensive response spectra are presented for a range of the parameters defining the problem, and the results are used to assess the accuracy of a simple, approximate method of analysis in which the system is represented by a viscously damped, simple oscillator. Special attention is given to defining the conditions under which the interaction effect is of sufficient importance to warrant consideration in design. The method of analysis used to obtain the numerical data reported herein is reviewed only briefly, the emphasis of the paper being on the interpretation of the results.