Modal Analysis Approach Research Articles

Vibration and radiation from capped cylindrical shells in water

Extensive experimental results will be presented of the vibration and radiation from shaker-driven, cylindrical shells with enclosed ends. Through the past 3 years, a great deal of knowledge about these shells has been gained through the use of nearfield acoustical holography to probe the vibration and radiation fields. These fields are represented globally over the shell, with the help of color displays, and from these pictures the mechanisms involved in vibration and radiation become apparent. Furthermore, with the help of thin shell theory these results are interpreted so that some generalizations can be made about the physics. The importance of a thorough understanding of the theory of vibration and radiation from an infinite cylindrical shell is demonstrated in comparisons of the dispersion relations to the measured data. Also the spatial filtering effect of the fluid on the modes of vibration is shown. This filtering effect is shown to retain the modal nature of the surface vibration leading to a powerful new approach for modal analysis. Also, the effects of the spherical-like endcaps on the vibration and radiation will be discussed.

Seismic response analysis of a multi-walled coaxial cylindrical tank under vertical excitation.

The seismic response under vertical excitation of the large-sized, multi-walled coaxial cylindrical tank filled with liquid is investigated theoretically. In this paper, the bulging motion which occurs in the relatively high frequency region due to the flexibility of the shell is analyzed by means of the finite element method. The natural frequency, the time history of the displacement response of the shell and the dynamic pressure response of the liquid are derived by the modal analysis approach.

Seismic Reliability of Rigid Frame Structures

A reliability analysis method has been developed for plane‐frame structures with shear walls subjected to earthquake ground accelerations. The structural reliability is measured in terms of the probability that throughout the structure's lifetime, its response will remain linear. The earthquake ground acceleration is assumed to be a stationary and Gaussian random process with mean zero and a Kanai‐Tajimi spectrum. To describe the statistical variation of an individual earthquake's intensity, an extreme value distribution of Type II is employed, while the Poisson arrival law is used to model the earthquake occurrences. The modal analysis approach is taken to map the safe domain associated with individual critical member forces in the (transformed) generalized coordinate vector space. Then, the global reliability is obtained by estimating the probability that fhe generalized coordinate vector will remaifn in the domain representing the interaction of these safe domains throughout the structure's lifetime. N...

Selective modal analysis of power system oscillatory instability

The dimensionality problems posed by the analysis of the oscillatory stability of large power systems remains an open issue. An extension to the original selective modal analysis (SMA) approach that has been inspired by the oscillatory stability problem is presented. SMA is a physically motivated framework for understanding, simplifying and analyzing complicated linear time-invariant models of dynamic systems. The proposed method avoids dealing with the large system matrix and shows significant reductions in storage and computation requirements as compared to straight eigenanalysis. It can also exploit a priori knowledge on the potential instability case to be studied. This reduced-order eigenanalysis approach has been checked for examples of realistic size and can be used as a basis for an efficient production-grade code for analysis of oscillatory stability in large power systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

有限共振原理に基づく偏心構造物の極限応答解析 : 1. モード分離応答解析法

In order to make clear the ultimate states of asymmetric structures under earthquake excitations, an approximate analysis approach for evaluating modal responses (response displacement amplitude, absorbed energy) of torsionally coupled systems by using FINITE RESONANCE RESPONSE ANALYSIS (F.R.R.A.) is proposed. In this paper, Finite Resonance Capacity Vectors and Finite Resonance Capacity Spectra of the torsionally coupled system are defined. And according to their characteristics that they depend on the equivalent-elastic-natural-period, the modal response analysis approach is devoloped. To verify the method described in this paper, an example of earthquake response analysis for a mono-eccentrical structure subjected to an unidirectional earthquake excitation is performed.

On the coupling measures between modes and state variables and subsynchronous resonance

Abstract In a previous paper we related the participation factors of the selective modal analysis approach to MacFarlane's modal energies and we called them coupling measures between modes and state variables. In this paper we relate them to newly suggested measures of modal controllability and observability. We use the coupling measures to select an easily measurable signal, which is the line current, to feed back through the excitation loop to stabilize a single-machine system with subsynchronous resonance. We also show that a dynamic controller designed by classical frequency response methods changes the eigenstructure of the closed-loop system, so as to decouple the mechanical mode from the electrical variables. This links the work to some recent results on eigenstructure assignment by dynamic output feedback.

A New Time Domain Multiple Input Modal Analysis Method

A time domain approach for multiple input modal analysis of oscillatory systems is proposed. The mathematical foundation for the approach is given along with its applications to a simulated lumped parameter system and the structural dynamics analysis of a milling machine. It has been shown that the proposed multivariate time series models are able to identify the complex mode shapes from multiple input structural test data. The advantages of the proposed method in comparison to existing methods are also highlighted.

Seismic response analysis of a multi-walled coaxial cylindrical tank.

The large-sized, multi-walled coaxial cylindrical tank has been studied in recent years because various kinds of oil can be stored in one tank It is important to design such tanks considering seismic response. This paper describes theoretical studies of the coupled vibration of the contained liquid and the shell plate of the cylindrical tank in response to lateral earthquake excitation, by the finite element method. In this paper, the bulging motion which occurs in the relatively high frequency region due to the flexibility of the shell is analyzed. The natural frequency the time history of the displacement response of the shell and the dynamic pressure response of the liquid of the actual tank are derived by the modal analysis approach.

The coupled oscillations of a liquid and the elastic side walls of a rectangular tank.

The hydroelastically coupled oscillations of a liquid and the elastic side walls of a rectangular tank partially filled with a liquid, in response to the lateral excitation, are investigated. It is well-known that there are tow types of liquid motion, i.e., sloshing and bulging. In the present paper, the sloshing motion, in which the liquid surface oscillation may be of finite amplitude, is analyzed taking the nonlinearity into account. The time histories of the liquid surface displacement and the wall deformation are calculated to the harmonic, and earthquake excitations by the modal analysis approach. An experiment was conducted using a model tank, and the vibration responses of a liquid and the walls were measured. A good agreement was found between the theoretical and experimental results.

Numerical noise in ocean and estuarine models

Approximate methods for solving the shallow water equations may lead to solutions exhibiting large fictitious, numerically-induced oscillations. The analysis of the discrete dispersion relation and modal solutions of small wavelengths provides a powerful technique for assessing the sensitivity of alternative numerical schemes to irregular data which may lead to such oscillatory numerical noise. For those schemes where phase speed vanishes at a finite wavenumber or there are multiple roots for wavenumber, oscillation modes can exist which are uncoupled from the dynamics of the problem. The discrete modal analysis approach is used here to identify two classes of spurious oscillation modes associated respectively with the two different asymptotic limits corresponding to estuarine and large scale ocean models. The analysis provides further insight into recent numerical results for models which include large spatial scales and Coriolis acceleration.

Modal Analysis of Machine Tool Structures Based on Experimental Data

The basic problem in modal analysis of machine tool structures is the extraction of modal parameters from the measured transfer function data. Conventionally this task is performed in two steps. The transfer function is determined using a Digital Fourier Analyzer followed by a suitable curve fitting procedure. In order to avoid the inherent problems associated with these procedures a new approach for modal analysis is proposed in this paper. Anticipating the stochastic nature of the systems excitation and response Modified Autoregressive Moving Average Vector models (MARMAV) are proposed. The modeling procedure yields a parametric representation of the structural behavior allowing the extraction of the modal information in one step, directly, rather than in two as in the conventional approaches. The mathematical foundation for the approach is given along with its application to a simulated three-degree-of-freedom system and a knee type milling machine. The newly proposed procedure is commensurate to the existing ones in light of the computational efforts involved; however, it eliminates the subjective judgment of the analyst since the modeling procedure is based on rigorous statistical adequacy checks. Finally, the proposed approach is amenable for implementation in a computer-based machine tool structural dynamics analyzer.

Pseudo bond graphs of circulating Fluids with application to solar Heating design

Two different bond-graph schemes for the modeling of circulating fluids are discussed and compared. The first uses a heuristic approach wherein the flow path is broken into segments. Each segment has separate hydraulic and thermal submodels which are linked with active bonds. The model is general enough to handle natural convective flows, heat storage, conduction, forced convective heat transfer and heat energy sources. The second method, applicable to pumped flows, uses a modal analysis approach to derive state equations for the modal temperatures, the time varying coefficients of the spatially varying mode shapes in a separation of variables solution for the temperature partial differential equation. Two examples are worked to illustrate the models. Numerical simulation results are presented using the first method and a simple analytic solution given to illustrate the second.

Seismic Response by SRSS for Nonproportional Damping

A method is presented to obtain seismic design response of linearly behaving structures with nonproportional damping characteristics. For such systems, time history analyses are usually performed to obtain accurate seismic response. To obtain design response, such procedures can become expensive and cumbersome as an ensemble of time histories may have to be considered as seismic input. Other procedures have been developed to ascertain appropriate values of modal dampings so that modal analysis approach and thus commonly adopted square-root-of-the-sum-of-the-sqaures (SRSS) procedures can be used. The approach presented here considers nonproportional damping effects exactly in analytical sense. It uses state-vector formulation and is based on random virbration priciples. The approach is similar to conventional SRSS approach and thus ground response spectrum can be directly used to obtain designd respose.

Response of composite plates to blast loading

The transient response of composite plates, with and without central circular holes, to blast loading is studied. The modal-analysis approach has been used in the computation of numerical results, which have been obtained for isotropic and orthotropic plates, with and without holes. In order to verify the theoretical results, experiments have been conducted on aluminum and unidirectionally reinforced E-glassepoxy plates, using a shock tube as the loading device. The experimental peak dynamic strains (normalized with respect to the pressure) are compared with the theoretical values. The strain-time history is also shown for a particular gage location in the composite plate. Finally, a comparison of dynamic-amplification factors, defined as the ratio of the peak dynamic strains to the static strains, has been made between the isotropic and the composite plates.

Dynamic response of single span highway bridges

AbstractThe dynamic response of single span simply supported bridge decks subjected to the passage of vehicles is examined. A modal analysis approach is adopted that is based upon a finite strip idealization of the deck. The vehicle is modelled as a rigid body supported at two points by a suspension idealization that accounts for the effect of tyre stiffness and the frictional nature of real suspension systems.Results are presented for an orthotropic slab deck and a box girder deck that illustrate the effects of (i) the initial precompression of the suspension system as the vehicle enters the span, (ii) the ratio of the vehicle's natural frequency to that of the bridge deck and (iii) a bridge deck surface profile that is not perfectly horizontal.

Applications of GIFTS III to structural engineering problems

The paper describes the latest version of the GIFTS system (Graphics Oriented Interactive Finite Element Package for Time-Sharing), due for release at the end of March 1976. The paper gives a description of the program modules available in the GIFTS library and the options available within its framework. Examples are given to demonstrate the use of GIFTS in design-oriented applications. Some performance measurements are included. Amongst the GIFTS features described are: 1. 1. Automatic model and load generation. 2. 2. Generation and display of higher order elements. 3. 3. Display of model, loads, boundary conditions, deflections and stresses. 4. 4. Suitability for use as a pre- and post-processor for large batch programs. 5. 5. Static analysis capabilities for trusses, frames, membranes, plates and shells. 6. 6. Vibrational mode computation for complex structures. 7. 7. Transient response analysis using either direct integration or a modal analysis approach. 8. 8. Substructuring and constrained substructuring. 9. 9. Mixed boundary conditions. 10. 10.Thermal stresses. Three examples have been chosen for inclusion in the paper. They illustrate some of the more important aspects of the GIFTS III system. These examples include the analysis of a three-dimensional framework, vibrational mode computation of an aircraft wing and the analysis, using substructures, of a bulk-ore carrier.

Propagation of a Gaussian Beam in Planar and Cylindrically Inhomogeneous Media: Comparison of Modal Analysis and Approximate Approaches

This work presents a study on the propagation of electromagnetic waves in media, characterized by k = k0 m k2 y 2 and k = k0 m k2 r2. A vector theory based on Maxwell's equations is used to derive linear homogeneous second-order equations satisfied by the transverse electric and magnetic field components. The various modes of propagation and the corresponding propagation constants have been determined. These are used to study the propagation and focusing of waves which have an intensity distribution along their wavefront. An alternative method for the study of the propagation and focusing of electromagnetic waves has been discussed. This is based on an approximate solution of the wave equation given in previous communications. For parameters of interest, the results obtained from the approximate solution are in excellent agreement with the solution obtained from the modal analysis of the problem. The present study should be of relevance in tropospheric communication and focusing of laser beams in selfoc f...

The launching of surface waves by a magnetic line source

The paper deals with the idealized problem of the excitation of surface waves along two infinite, identical, separate and parallel dielectric slabs by a magnetic line source (slot). The problem is reduced to a superposition of simpler ones, namely two parallel slabs with symmetrical excitation and two parallel slabs with antisymmetrical excitation.The simplified problems are solved by the modal-analysis approach, and the synthesis of the modal components is carried out to obtain the far fields excited by the magnetic line.Radiation pattern, total power of the surface waves, total radiation loss and the efficiency of launching the surface wave are derived and computed numerically for various thicknesses of the slabs, various air-gaps between the slabs and different positions of the magnetic line source. The theoretical results indicate that, for each thickness of the slabs, high efficiency is obtained with an optimum location of the source and an optimum air-gap. Moreover, the thicker the slabs, the higher is the maximum efficiency. The thickness of the slabs and the air-gap are ultimately limited by the requirement that only one surface wave should exist for the structure.