Support Excitation Research Articles

A boundary element solution to the vibration problem of plates

A boundary element method is presented for the dynamic analysis of thin elastic plates of arbitrary shape. In addition to the boundary supportes the plate may be also supported on point or line supports in the interior. Both free and forced vibrations are considered. The case of support excitation is also taken into account. The method utilizes the fundamental solution of the static problem to establish the integral representation for the deflection. The domain integrals involving the inertia forces are evaluated by employing an efficient Gauss integration technique over domains of arbitrary shape. This procedure yields a mass matrix and the equation of motion is derived with respect to the Gauss integration nodal points. Numerical results are presented to illustrate the method and demonstrate its efficiency.

Response of indeterminate two‐span beam to spatially varying seismic excitation

AbstractIn order to examine the effect of the spatial variation of ground motion on the response of an indeterminate structure, the stochastic responses of a two‐span beam to spatially varying support excitations are analysed. A space‐time earthquake ground motion model that accounts for both coherency decay and seismic wave propagation is used to specify the support motions, and the results are compared with those for various simplified excitations that are commonly used in practice. The response is computed through a linear random vibration approach with the structure being modelled by finite elements. The results of the study indicate that, even for moderate lengths, the effect of the spatial variation of ground motion can be significant. The assumption of fully coherent support motions (same excitations at all supports or delayed excitations allowing only for wave propagation) may be overconservative for some beams and unconservative for others.

A Test and Analysis of the Multiple Support Piping Systems

Abstract One of the current topics in the seismic design of piping systems is the overall reliability of them in earthquake events. Actual piping systems are generally supported by independent structures such as vessels and steel structures. So, it is very important to clarify the behavior of actual piping systems during the seismic events. For this purpose, the analytical method of multiple excitation problems is a preferable approach to not only evaluate the actual behavior of the piping systems, but also improve the reliability of piping systems. To clarify the dynamic characteristics of the piping systems and to assess the computational methods in the linear system subjected to multiple support excitations, an experimental study using a realistic large-scale piping model has been conducted. The equations for the multiple excitation problem have been validated and the adequacy of the multiple response spectra method has been confirmed by the comparison of the test results with the analytical one. This paper reports the results focusing on the analytical methods of the multiple support piping system. It is noted that the multiple response spectrum method is efficient for the multiple excitation problems.

A Load Combination Method for Aseismic Design of Multiple Supported Piping Systems

Abstract A new load combination scheme for seismic response calculation of piping systems subjected to multiple support excitations is presented. This scheme has an advantage, such that the cross-correlation among support excitations are properly taken into account by use of a stationary random vibration approach. The authors also present the idea of generating a “multi-excitation floor response spectrum.” First, using a simple analytical SDOF piping system to two support excitations and a simple Z-shaped piping model for shaking test, the combination law is supplied to various correlation cases of two support excitations and the maximum responses of piping in a fundamental mode is calculated. Second, nonlinear characteristics such as gap and friction appearing between piping itself and supports are specifically investigated. The response effect due to these nonlinearities is evaluated by the results through the shaking test with a piping-support structural model, and the amount of response reduction effect is represented by “a response reduction factor β.”

RMS Response of Cascaded MDOF Subsystem to Multiple Support Excitation

The RMS response of a general multiple degrees of freedom (MDOF) cascaded secondary system attached at several points to a primary system is obtained using time domain random vibration formulation. The primary system is excited by ground motion at multiple support points. This in turn excites the subsystem at the attachment points. To analyze a primary system, filter parameters are chosen to represent the spectral shapes of earthquakes. The output of the filter, i.e., the time histories of RMS ground excitation at support points and their cross‐correlation, is directly prescribed. Fictitious piecewise linear strength envelopes, which represent the corresponding input of the filter, are generated accordingly before engaging the filter to the system. The time history of the RMS modal coordinates of the supporting system and their cross‐correlation are evaluated and stored as input to its subsystems. To analyze a subsystem, filter parameters are chosen to represent the spectral shapes of the modal coordinates of the supporting system, with a predominant frequency equal to the corresponding natural frequency of the primary system. Piecewise linear strength envelopes are generated as the diagonal terms to match the RMS time histories of modal coordinates and the cross‐terms to match the time histories of cross‐correlation between corresponding modal coordinates. This formulation enables one to independently analyze and design various multiply supported cascaded subsystems attached to a primary system.

APPROXIMATE SPECTRAL MULTIPLE SUPPORT SEISMIC ANALYSIS: TRAVELLING WAVE APPROACH.

Keywords ISRAEL INSTITUTE OF TECHNOLOGY HAIFA., MCMASTER UNIVERSITY HAMILTON, ONTARIO. BRIDGES, STRUCTURES, EARTHQUAKES, GROUND, MOTION, SUPPORTS, SEISMIC, ANALYSIS, TRAVELLING, WAVES, TECHNIQUES, FORCES... Show All

Stochastic stability of a gyropendulum under random vertical support excitation

The mean square stability of a gyropendulum under random vertical support excitation is considered. The intensity and the correlation time of the stochastic excitations are assumed to be small in order to obtain approximate analytical results. The stochastic averaging procedure of Stratonovich and Khasminskii is used to establish the drift and diffusion coefficients in the corresponding Itô equation. Explicit results are obtained for stochastic stability boundaries.

The SMART I Accelerograph Array (1980-1987): A Review

SMART 1 is the first large digital array of strong-motion seismographs specially designed for engineering and seismological studies of the generation and near-field properties of earthquakes. Since the array began operation in September 1980, it has recorded over 3000 accelerogram traces from 48 earthquakes ranging in local magnitude ( ML) from 3.6 to 7.0. Peak ground accelerations have been recorded up to 0.33g and 0.34g on the horizontal and vertical components, respectively. Epicentral distances have ranged from 3 km 200 km from the array center, and focal depths have ranged from shallow to 100 km. The recorded earthquakes had both reverse and strike-slip focal mechanisms associated with the subduction zone and transform faults. These high quality, digital, ground motions provide a varied resource for earthquake engineering research. Earthquake engineering studies of the SMART 1 ground motion data have led to advances in knowledge in several cases: for example, on frequency-dependent incoherency of free-surface ground motions over short distances, on response of linear systems to multiple support excitations, on attenuation of peak ground-motion parameters and response spectra, on site torsion and phasing effects, and on the identification of wave types. Accelerograms from individual strong-motion seismographs do not, in general, provide such information. This review describes the SMART 1 array and the recorded earthquakes with special engineering applications. Also, it tabulates the unfiltered peak array accelerations, displays some of the recorded ground motion time histories, and summarizes the main engineering research that has made use of SMART 1 data.

Simplified seismic analysis of piping or equipment mounted on two points of a multistory structure

A simplified procedure is presented to calculate the maximum earthquake response of light mechanical or electrical equipment supported at two arbitrary points of a building structure. The procedure is derived on the basis of the application of the response spectrum method to a combined structure-equipment system, but, in an effort to avoid the complications of such an approach, it is formulated in terms of the dynamic characteristics of the two independent components. It fully takes into account the interaction between the two subsystems, and avoids the generation of floor response spectra and the need to consider two different support excitations. The formulation is attained by using Hurty's component mode synthesis technique and Rayleigh's principle. Linear systems with classical modes of vibration and small structure to equipment mass ratios are considered. The simplicity of the method is demonstrated by a numerical example, and its accuracy verified by a comparative study. In this comparative study, the suggested procedure estimates correct solutions with an average error of about 2%.

A study on a load combination method considering the correlation among dynamic loads. (3rd Report, Response analysis for multi-supported piping system, Part 1)

A dynamic load combination method proposed in previous papers for seismic analysis of a liquid storage tank has been developed for response calculations of piping systems subjected to multiple support excitations. This method has an advantage in which cross·correlation among support excitations are properly taken into account. The correlation factor can be semi-automatically evaluated by using a stationary random vibration approach. Investigation is mainly devoted to a maximum acceleration response calculation of a simple piping model to two-input excitation. Results for the system corresponded fairly well with the exact numerical results through analytical simulation. On the other hand, the SRSS procedure and the absolute value summation which neglect cross-correlation among excitations can lead to large errors. Finally, the authors have also proposed the idea of generating a multi-excitation floor response spectrum using the results.

A study on a load combination method considering the correlation among dynamic loads. (4th report Response analysis for multi-supported piping system, experimental investigation)

This paper is an extended study of a practical combination method of dynamic loads proposed in the previous paper in which problems of the maximum response calculation of piping systems to multiple support excitations were discussed. In this paper, experimental and numerical investigations are carried out in order to confirm the validity and feasibility of the proposed method. Using a simple Z-beam shaped piping model for a shaking test, the maximum response of piping in the fundamental mode is measured and the combination law is applied to various correlation cases among two vibrational loads. From the experimental results, it has been made clear that the proposed method could be reasonable by comparison with other combination laws, like the square root of the sum of the square (SRSS) method.

Spatial variation of ground motion determined from accelerograms recorded on a highway bridge

AbstractA set of time-synchronized strong-motion accelerograms, obtained on the San Juan Bautista 156/101 Separation Bridge in California during the 6 August 1979 Coyote Lake earthquake (ML = 5.9), are used to study the spatial variation of ground motion at the bridge site, including traveling wave effects and the influence of multiple-support excitation. Analysis of the ground motion recorded at the base of two of the bridge supports (32.6 m apart) revealed the presence of a differential support excitation having a period of ≈ 3 sec, much longer than any structural periods of the bridge. This signal also appeared as a noticeable long-period component in the superstructure displacements. Analysis of the vertical and radial components of the 3-sec ground motion indicated that ground displacements were retrograde for the duration of strong shaking, with several cycles exhibiting elliptical particle motions. These findings suggest that long-period differential support motions were induced by phase delays in a Rayleigh wave traveling across the bridge site. Further support to this premise is given by the location of the bridge site near a maxima of the Rayleigh wave radiation pattern for the Coyote Lake earthquake (based on published focal mechanism data). Traveling wave effects were also detected for compressional body waves by a correlation analysis which indicated a time delay of ≈ 7 msec between P-wave arrivals at two of the bridge supports.

Response of Rotors Subjected to Random Support Excitations

Response of rotor systems subjected to random support excitations is studied. Support excitations may occur for rotating machines installed either on the ground due to earthquake motion, or on board moving systems such as ships. These excitations in general are random in nature and hence the response of the machine can be obtained following a statistical analysis. In this paper, the amplitude power spectral densities (PSD) due to random support excitations are obtained for rotor systems, using modal analysis methods. The excitations are assumed to be stationary and Gaussian with a white noise type of PSD. Excitations through different supports are assumed to be statistically independent so that their cross correlations are zero. Results for rotors with various parametric combinations are presented.

A Theoretical and Experimental Analysis of Support-excited Non-linear Vibrations of the Extensible Pendulum

Using the Lagrangian formulation, the equations of motion are set up for a damped extensible pendulum subjected to support excitation. The well established perturbation technique known as the Method of Multiple Scales is used to investigate steady states, with the outstanding feature that the original non-autonomous problem is reduced to an autonomous form, thus easing the analysis and the stability verification. The theory is thereafter correlated with an extensive experimental study.

Torsional Earthquake Response of Suspension Bridges

The earthquake‐induced torsional response of suspension bridges when subjected to multiple support excitations is analyzed in the frequency domain by means of random vibration theory. Appropriate rocking and torsional ground motion inputs are defined from finite Fourier transforms of recorded translational motions by using a simplified approach based upon wave propagation theory. An example is presented in which the torsional response of the Golden Gate Bridge to earthquake ground motions (the 1979 Imperial Valley earthquake) with characteristics significantly different at each support point is investigated. It is observed that the participation of higher modes in the total response is essential to assess the torsional seismic behavior of such structures. It is also observed that both the vibrational displacement and vibrational cable tension induced by torsional vibration are very small but the flexural stresses induced by the torsional vibration are relatively large as live loads.

Role of atmospheric wave interaction in the generation Of easterly zonal current in the monsoon region

One of the significant semi-permanent features of the monsoon circulation of the tropical easterly jet (TEJ).
 
 The present paper is an attempt to study the contribution from interaction amongst various waves tropical regions towards the generation of the TEJ. The multiple scale technique has been used to energy exchange process amongst the significant flow patterns of the monsoon circulation. Specifically, we have considered eleven sets of wave triads under the condition of resonance and it is noted that three of these support excitation or generation of TEJ type structure.

Response of sliding structures to earthquake support motion

AbstractTo study the effectiveness of sliding supports in isolating structures from damaging earthquake ground motions, a mathematical model of a single degree of freedom structure supported on a sliding foundation and subjected to the N‐S component of the El Centro 1940 earthquake is considered. Spectra for absolute accelerations, relative displacements, relative‐to‐ground displacements, sliding displacements and residual sliding displacements are evaluated for three mass ratios, four coefficients of friction and a damping of 5 per cent critical. It is observed that, for structures with periods less than 1‐8 s, for the coefficients of friction considered, the suprema of relative‐to‐ground displacements, sliding displacements and residual sliding displacements are only of the order of 1–25 times the peak ground displacement. To study the response sensitivities, the spectra for absolute acceleration and sliding displacement of the 1949 Olympia earthquake (S86E component) are also presented. It is concluded that sliding supports can be quite effective in isolating structures from support excitations.

Determination of dynamic properties of elastomers over broad frequency range

Support excitation of a small spring-mass system, consisting of a massm and two thin wafers in shear, is used as a simple and reliable method to determine the dynamic properties (storage-modulus and complex-modulus loss factor) of elastomeric materials over a fairly broad frequency range. No special equipment or instrumentation is required since ordinary vibration equipment is used. Microminiature accelerometers are used to monitor the support and mass accelerations which eliminates the measurement of small forces and displacements. The frequency range of interest over which experimental data can be obtained fromone specimen can be varied by the thicknessh of the elastomeric waters and/or the size of the massm. The method discussed has been used to determine the dynamic properties of a wide variety of elastomers with frequencies as high as 6000 Hz. Typical results demonstrating repeatability of the method are shown for a carboxyl-terminated butadiene acrylonitrile (CTBN) specimen over the frequency range of 500–3000 Hz. The small test setup is easily adaptable for use in small temprature-controlled chambers for temperature/frequency studies of elastomers. The mathematical model developed for reduction of experimental data is based on the complex shear modulus for the damping model of the elastomer where the spring-mass system is subjected to support excitation.

Response of sliding structures to harmonic support motion

AbstractThe problem of response of a single degree of freedom structure supported on a sliding foundation and subjected to harmonic support motions is considered. The non‐linear governing equations of motion are derived. It turns out that these equations are linear in each sliding and non‐sliding phase and can be solved in closed forms in each phase. The equations for evaluation of the beginning and ending times of different phases are also formulated and solved numerically. The response for different coefficients of friction and various levels of excitation is evaluated and presented graphically. It is concluded that sliding supports can be quite effective in isolating structures from support excitations.

Stochastic analysis of structures and piping systems subjected to stationary multiple support excitations

AbstractA stochastic method has been developed for seismic analysis of structures and piping systems subjected to multiple support excitations. In either the time or the frequency domain, mean and extreme values of structural and piping system response can be found, including the effects of cross‐correlations of modal response and cross‐correlations of multiple support excitations. Stationary white noise and stationary filtered white noise ground excitations are used. A computer program has been developed to carry out the stochastic seismic analysis. Results for a realistic nuclear power plant structure and piping system with and without modal cross‐correlations and support excitation cross‐correlations are compared. From these results, it is concluded that neglecting cross‐correlations can lead to large errors. The stochastic method reported is shown to be more accurate than the response spectrum method and more economical than the time‐history method; therefore, it is recommended for seismic analysis of nuclear power plants.