Range of applicability of real mode superposition approximation method for seismic response calculation of non-classically damped industrial buildings

An industrial building is a non-classically damped system due to the different damping properties of the primary structure and equipment.The objective of this paper is to quantify the range of applicability of the real model superposition approximation method to the seismic response calculation of industrial buildings.The analysis using lumped mass-and-shear spring models indicates that for the equipment-to-structure frequency ratiosγf>1.1 orγf<0.9,the non-classical damping effect is limited,and the real mode superposition approximation method provides accurate estimates.For 0.9<γf<1.1,the system may have a pair of closely spaced frequency modes,and the non-zero off-diagonal damping terms have a non-negligible effect on the damping ratios and mode shape vectors of these modes.For 0.9<γf<1.1 and the equipment-to-structure mass ratiosγm<0.07,the real mode superposition approximation method results in large errors,while the approximation method can provide an accurate estimation for 0.9<γf<1.1 andγm>0.07.Furthermore,extensive parametric analyses are conducted,where both steel structures and reinforced concrete structures with equipment with various damping ratios are considered.Finally,the finite element analysis of a five-story industrial building is adopted to validate the proposed range of applicability.

Numerical Calculation Methods for Wavemaking Response Induced by Explosion in Harbour

Using the axial symmetry results of marker and cell (MAC) method as initial value in this paper, two numerical calculating methods are presented for the late wavemaking response induced by explosion in harbour. One of the methods is the superposition method of the vibration mode based on fluid slosh in container. Another one is the joining method of the MAC results with the shallow wave theory calculation in time domain. As a practical example, it is conducted to the numerical calculation about 1000 ton TNT equivalent explosion within touch of water surface. The results show that it can be rationally described with the methods to the wavemaking progress and character. The numerical results are identical with the observed scene on the spot experiment. The methods are simple and applicable in the engineering design.

ELASTIC IMPACT ON FINITE TIMOSHENKO BEAM

In this paper the analytical solutions of the impact of a particle on Timoshenko beams with four kinds of different boundary conditions are obtained according to Navier's idea, which is further developed. The initial values of the impact forces are exactly determined by the momentum conservation law. The propagation of the longitudinal and transverse waves along the beam, especially, the effects of boundary conditions on the characteristics of the reflected waves, are investigated in detail. Some results are compared with those by MSC/NASTRAN.

Dynamics of structural systems with various frequency-dependent damping models

The aim of this paper is to present the dynamic analyses of the system involving various damping models. The assumed frequency-dependent damping forces depend on the past history of motion via convolution integrals over some damping kernel functions. By choosing suitable damping kernel functions of frequency-dependent damp- ing model, it may be derived from the familiar viscoelastic materials. A brief review of literature on the choice of available damping models is presented. Both the mode superposition method and Fourier transform method are developed for calculating the dynamic response of the structural systems with various damping models. It is shown that in the case of non-deficient systems with various damping models, the modal analysis with repeated eigenvalues are very similar to the traditional modal analysis used in undamped or viscously damped systems. Also, based on the pseudo-force approach, we transform the original equations of motion with nonzero initial conditions into an equivalent one with zero initial conditions and therefore present a Fourier transform method for the dynamics of structural systems with various damping models. Finally, some case studies are used to show the application and effectiveness of the derived formulas.

线性动力系统的模态叠加方法与时间积分方法相结合的求解策略

本文将模态叠加法与梯形法则等时间积分法相结合, 以提高线性动力系统的求解精度. 在这种组合策略中, 最基本的工作是将一个动力系统分解为两个子系统, 即一个小规模含有低频成分的系统和一个含有高频成分的系统. 前者可以用模态叠加解析方法有效地求解, 后者则通过时间积分法(如纽马克法)进行求解. 这两个子系统的响应之和就是原始动力系统的响应. 结果表明, 在几乎不牺牲效率的情况下, 基于该策略生产的组合方法比被组合的时间积分方法更精确, 但组合方法的精度阶次与被组合的时间积分方法相同. 数值实验验证了该组合策略的有效性.