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1.
The paper presents a method for synthesizing the modal properties of substructures to obtain the exact modal properties of a combined structure. Unlike the currently available modal synthesis approaches, the proposed approach does not require the solution of any transformed eigenvalue problem of the combined structure by conventional means. The substructures are assumed to be coupled by connecting elements and the coupling is done sequentially with one element at a time. The eigenvalues at each stage of coupling are obtained by solving a non-linear characteristic equation. A simple Newton-Raphson solution scheme is adequate for this purpose. Once the eigenvalues are determined, the eigenvectors can be calculated in closed form. Several examples demonstrating the applicability of the proposed approach are presented. 相似文献
2.
Lothar Banz Adrian Costea Heiko Gimperlein Ernst P. Stephan 《Studia Geophysica et Geodaetica》2014,58(4):489-504
We present a boundary element method to compute numerical approximations to the non-linear Molodensky problem, which reconstructs the surface of the Earth from the gravitational potential and the gravity vector. Our solution procedure solves a sequence of exterior oblique Robin problems and is based on a Nash-Hörmander iteration. We apply smoothing with the heat equation to overcome a loss of derivatives in the surface update. Numerical results show the error between the approximation and the exact solution in a model problem. 相似文献
3.
The structure analysed herein is a tower and pier system of a long-span suspension bridge. The tower shaft is modelled to allow classical normal modes decomposition in order to reduce higher modes. The pier is assumed to be rigid body free to translation as well as to rocking motion, being reacted by the surrounding soil compliance that is derived from a continuum mechanics approach. Linear and non-linear soil and structural dynamic interaction is dealt with by random vibration theory with use of the linearization technique and complex modal analysis. Primary interest is placed on the investigation of the dynamic characteristics of the total interaction system and the rms response with change of the soil condition and input excitation level. Also discussed is the approximate response analysis, using classical normal modes for the interaction system, for purposes of practical design. 相似文献
4.
The evaluation of the dynamic response of non-classically damped linear structures requires the solution of an eigenproblem with complex eigenvalues and modal shapes. Since in practice only a small number of complex modes are needed, the complex eigenvalue problem is solved in the modal subspace in which the generalized damping matrix is not uncoupled by classical real modes. It follows that the evaluation of the structural response requires in both cases the determination of complex modes by numerical techniques, which are not as robust as techniques currently used for the solution of the real eigenvalue problem, and the use of complex algebra. In the present paper an unconditionally stable step-by-step procedure is presented for the response of non-classically damped structures in the modal subspace without using complex quantities. The method is based on the evaluation of the fundamental operator in approximated form of the numerical procedure. In addition, the method can be easily modified to incorporate the modal superposition pseudo-static correction terms. 相似文献
5.
The non-linear steady state vibration of shallow arch beams is studied by a finite element method based on the principle of virtual work. Both the free and forced periodic vibrations are considered. The axial and flexural deformations are coupled by the induced axial force along the beam element. The spatial discretization is achieved by the usual finite element method and the steady state nodal displacements are expanded into a Fourier series. The harmonic balance method gives a set of non-linear algebraic equations in terms of the vibrating frequency and the Fourier coefficients of nodal displacements. The non-linear algebraic equations are solved by the Newtonian algorithm iteratively. The combined algorithm is called the incremental harmonic balance method. The importance of the conditions of completeness and balanceability is presented. Since the non-linearity is essentially softening, different orders of internal resonances between two modes can occur repeatedly. Isolated response curves are possible and are connected to the bifurcation of a particular excited mode. 相似文献
6.
Based on an incremental Hamilton's principle a versatile and systematic computer method for analysing non-linear structural vibrations is developed in this paper. The essence of the proposed method can be regarded as an incremental harmonic balance method associated with a finite strip procedure in the time-space domain. Only linearized equations in terms of frequency increment, amplitude increments, etc. have to be formulated and solved in each incremental step. This method is applicable to highly non-linear problems and may be generalized to related non-linear periodic structural motions such as dynamic stability, flutter and some motions of a rotating body, etc. To show the effectiveness and versatility of this method, a typical time-space finite strip for beam problems is worked out and examples for a wide variety of vibration problems including free and forced vibrations, super- and sub-harmonic resonances, and complicated phenomena such as internal resonance are computed. Comparisons with previous results are also made. 相似文献
7.
Summary This paper presents a theory of the transient Bernoulli-Euler beam problem on an elastic foundation which takes into account the effects of axial load and linear damping. An analytical solution of the steady state and the transient components has been obtained due to physically realistic load distributions. With a view to extend its practical applicability, the characteristic features of the solution are explored. Several limiting situations are investigated as special cases. It is shown that the steady state vibration can be achieved as the limit of the solution of the transient problem. 相似文献
8.
An approximate solution of the classical eigenvalue problem governing the vibrations of a structure on an elastic soil is derived through the application of a perturbation analysis. For stiff soils, the full solution is obtained as the sum of the solution for a rigid-soil and small perturbing terms related to the inverse of the soil shear modulus. The procedure leads to approximate analytical expressions for the system frequencies, modal damping ratios and participation factors for all system modes that generalize those presented by other authors for the fundamental mode. The resulting approximate expressions for the system modal properties are validated by comparison with the corresponding quantities obtained by numerical solution of the eigenvalue problem for a nine-story building. The accuracy of the proposed approach and of the classical normal mode approach is assessed through comparison with the exact frequency response of the test structure. 相似文献
9.
An approximate solution of the classical eigenvalue problem governing the vibrations of a relatively stiff structure on a soft elastic soil is derived through the application of a perturbation analysis. The full solution is obtained as the sum of the solution for an unconstrained elastic structure and small perturbing terms related to the ratio of the stiffness of the soil to that of the superstructure. The procedure leads to approximate analytical expressions for the system frequencies, modal damping ratios and participation factors for all system modes that generalize those presented earlier for the case of stiff soils. The resulting approximate expressions for the system modal properties are validated by comparison with the corresponding quantities obtained by numerical solution of the eigenvalue problem for a nine-story building. The accuracy of the proposed approach and of the classical normal mode approach is assessed through comparison with the exact frequency response of the test structure. 相似文献
10.
The primary objective of this paper is to develop output only modal identifi cation and structural damage detection.Identif ication of multi-degree of freedom(MDOF) linear time invariant(LTI) and linear time variant(LTV—due to damage) systems based on Time-frequency(TF) techniques—such as short-time Fourier transform(STFT),empirical mode decomposition(EMD),and wavelets—is proposed.STFT,EMD,and wavelet methods developed to date are reviewed in detail.In addition a Hilbert transform(HT) approach to determine ... 相似文献
11.
A new method is introduced for the identification of modal quantities of self-adjoint distributed-parameter systems. The method uses the temporal and spatial orthogonality properties of distributed-parameter systems to form a pseudo-Rayleigh quotient. The stationary values of the pseudo-Rayleigh quotient can be determined by the solution of an eigenvalue problem, where the eigenvalues and eigenfunctions provide the frequencies and natural modes of the distributed-parameter system. By way of formulation, the method is insensitive to zero mean measurement noise and is applicable to continuous as well as discrete systems. Numerical examples are presented in which the modal quantities of a simply-supported beam and a discrete model of a membrane are identified. The results are compared with another modal identification technique, namely, the Ibrahim time domain method. 相似文献
12.
A. Nir 《Journal of Hydrology》1973,19(1):33-41
Tracer concentration in mixed lakes was usually calculated under assumption of steady hydrologic state, i.e., constant input, output, and volume. Departures from steady state were treated by the use of average flow or weighting the concentration by inflow values. An exact analytical solution indicates the limits of validity of the above approximations. The exact solution can be adapted for multiple inputs and outputs, exchange with atmospheric moisture, evaporation with isotope fractionation and formation of epilimnion. The solution is simplified for certain types of connection between outflow and volume. 相似文献
13.
A step-by-step integration method is proposed to compute within the framework of the conventional mode superposition technique the response of bilinear hysteretic structures subjected to earthquake ground motions. The method is computationally efficient because only a few modes are needed to obtain an accurate estimate of such a response, and because it does not require the use of excessively small time steps to avoid problems of accuracy or stability. It is developed on the basis that the non-linear terms in the equations of motion for non-linear systems may be considered as additional external forces, and the fact that by doing so such equations of motion can be interpreted as the equations of motion of an equivalent linear system, excited by a modified ground motion. These linear equations are then subjected to a conventional modal decomposition and transformed, as with linear systems, into a set of independent differential equations, each representing the system's response in one of its modes of vibration. To increase the efficiency of the method and account properly for the participation of higher modes, these independent equations are solved using the Nigam-Jennings technique in conjunction with the so-called mode acceleration method. The accuracy and efficiency of the method is verified by means of a comparative study with solutions obtained with a conventional direct integration method. In this comparative study, including only a few modes, the proposed method accurately predicts the seismic response of three two-dimensional frame structures, but requiring only, on an average, about 47 per cent less computer time than when the direct integration method is used. 相似文献
14.
A procedure which involves a non‐linear eigenvalue problem and is based on the substructure method is proposed for the free‐vibration analysis of a soil–structure system. In this procedure, the structure is modelled by the standard finite element method, while the unbounded soil is modelled by the scaled boundary finite element method. The fundamental frequency, and the corresponding radiation damping ratio as well as the modal shape are obtained by using inverse iteration. The free vibration of a dam–foundation system, a hemispherical cavity and a hemispherical deposit are analysed in detail. The numerical results are compared with available results and are also verified by the Fourier transform of the impulsive response calculated in the time domain by the three‐dimensional soil–structure–wave interaction analysis procedure proposed in our previous paper. The fundamental frequency obtained by the present procedure is very close to that obtained by Touhei and Ohmachi, but the damping ratio and the imaginary part of modal shape are significantly different due to the different definition of damping ratio. This study shows that although the classical mode‐superposition method is not applicable to a soil–structure system due to the frequency dependence of the radiation damping, it is still of interest in earthquake engineering to evaluate the fundamental frequency and the corresponding radiation damping ratio of the soil–structure system. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
15.
This paper uses an incremental mode-superposition procedure to compute the inelastic dynamic response of multi-degree-of-freedom systems. A damping matrix proportional to the instantaneous properties is used throughout the analysis. The non-linear response of several shear type plane and space frames with elastic-plastic and bilinear column properties subjected to ground excitation was computed by both the incremental mode-superposition and the direct integration of the coupled equations of motion. When all modes are considered, the responses computed by the incremental mode-superposition are identical to those from the direct integration. Fewer modes can also be used to compute the response with reasonable accuracy by performing the modal truncation for each time increment. The study shows that incorporating instantaneous damping in non-linear dynamic analysis is relatively simple and requires less computational time than the direct integration. 相似文献
16.
Asymptotic methods and numerical simulations are used to examine the evolution of an internal gravity wave packet comprising a continuous spectrum of horizontal wavenumbers and propagating upwards in a continuously stratified shear flow. In the multiple-scale framework for a horizontally localized wave packet generated by stratified flow over a localized mountain range with multiple peaks, there are in general two horizontal scales: the “fast” scale which is defined by the oscillations within the packet, i.e. the number of peaks, and the “slow scale” which is defined by the horizontal extent of the packet, i.e. the width of the mountain range. The focus here is on the specific case of an isolated mountain where the spectrum of horizontal wavenumbers is centred at zero and the multiple-scaling procedure is thus simplified by the absence of the fast spatial scale. The background flow is vertically sheared and critical-level interactions occur. The time frame within which non-linear critical-level effects become significant is determined by the magnitude of the non-linear terms in the governing equations. With the isolated mountain forcing this time frame is significantly longer than in the case of a multiple-peak mountain range forcing and it depends on the horizontal scale of the forcing, as well as on the amplitude. At leading-order, the non-linear asymptotic solution approaches a steady state in the outer region at late time, but the zero-wavenumber component of the solution continues to evolve with time in the vicinity of the critical level. 相似文献
17.
Zdeněk Martinec 《Studia Geophysica et Geodaetica》1990,34(4):313-326
Summary A new method for computing the potential coefficients of the Earth's external gravity field is presented. The gravimetric
boundary-value problem with a free boundary is reduced to the problem with a fixed known telluroid. The main idea of the derivation
consists in a continuation of the quantities from the physical surface to the telluroid by means of Taylor's series expansion
in such a way that the terms whose magnitudes are comparable with the accuracy of today's gravity measurements are retained.
Thus not only linear, but also non-linear terms are taken into account. Explicitly, the terms up to the order of the third
power of the Earth's flattening are retained. The non-linear boundary-value problem on the telluroid is solved by an iteration
procedure with successive approximations. In each iteration step the solution of the non-linear problem is estimated by the
solutions of two linear problems utilizing the fact that the non-linear boundary condition may be split into two parts; the
linear spherical approximation of the gravity anomaly whose magnitude is significantly greater than the others and the non-linear
ellipsoidal corrections. Finally, in order to solve the problem in terms of spherical harmonics, the transform method composed
of the fast Fourier transform and Gauss Legendre quadrature is theoretically outlined. Immediate data processing of gravity
data measured on the physical Earth's surface without any continuation of gravity measurements to a reference level surface
belongs to the main advantage of the presented method. This implies that no preliminary data handling is needed and that the
error data propagation is, consequently, maximally suppressed. 相似文献
18.
It is well known that the solution of the forced vibration of a N-DOF dynamical problem is very cumbersome when conditions which allow the equations to uncouple do not exist. In the literature several techniques were proposed to overcome the problem, but they were mainly focused on a particular problem in turn. So, we deemed it useful to search for a unifying procedure able to deal with different sources of non-linear behaviour introducing only minor changes in the operation flow. In this respect, attention is paid to the Alternating Frequency/Time domain method (AFT) which draws its robustness from the speed and switching capabilities of the Fast Fourier Transform; moreover, taking advantage of the pseudo-force concept, we can arrive at a solution method featuring greater generality and able to solve different non-linear dynamical problems by means of specialization of the same conceptual framework (G-AFT or Generalized AFT). In the first section of the paper the theoretical background is discussed in detail and the proposed algorithms are presented. In the second one, several examples of technical relevance are documented and solved, highlighting the efficiency, convergence and accuracy of the presented algorithm. For cases such as an 11-storey building or a block simulated power plant we introduce the soil-structure interaction effect by means of non-proportional damping; the responses computed either by direct frequency analysis or by iteration are compared with existing solutions or with time domain solutions determined through the Newmark β method. An original example prepared by the authors and fully referenced is finally worked out in order to show the capability of the method when Coulomb damping is taken into account; this effect covers a significant practical relevance in the base isolation field. 相似文献
19.
In this paper, an effective active predictive control algorithm is developed for the vibration control of non-linear hysteretic structural systems subjected to earthquake excitation. The non-linear characteristics of the structural behaviour and the effects of time delay in both the measurements and control action are included throughout the entire analysis (design and validation). This is very important since, in current design practice, structures are assumed to behave non-linearly, and time delays induced by sensors and actuator devices are not avoidable. The proposed algorithm focuses on the instantaneous optimal control approach for the development of a control methodology where the non-linearities are brought into the analysis through a non-linear state vector and a non-linear open-loop term. An autoregressive (AR) model is used to predict the earthquake excitation to be considered in the prediction of the structural response. A performance index that is quadratic in the control force and in the predicted non-linear states, with two additional energy related terms, and that is subjected to a non-linear constraint equation, is minimized at every time step. The effectiveness of the proposed closed-open loop non-linear instantaneous optimal prediction control (CONIOPC) strategy is presented by the results of numerical simulations. Since non-linearity and time-delay effects are incorporated in the mathematical model throughout the derivation of the control methodology, good performance and stability of the controlled structural system are guaranteed. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
20.
We present some error expressions for approximate modal solutions of viscously damped linear structural vibration equations; these approximations are calculated by a variety of modal techniques. Motivated by our numerical experience, we show the equivalence of some different modal solutions in the presence of classical damping and, in passing, we obtain a previously unremarked manifestation of this type of damping. We make some brief comments about obtaining error estimates and, finally, we show some numerical results for a standard test problem which illustrate properties of the modal solutions. 相似文献