Mahendra P. Singh

Dynamic condensation method for structural eigenvalue analysis

An improved dynamic condensation approach is presented for accurate calculation of structural eigenproperties. The approach is iterative. The kept and reduced degrees of freedom in the approach are related through a condensation matrix that is used to form a condensed eigenvalue problem. An initial condensation matrix can be defined in terms of the system submatrices. The eigenproperties calculated in an iterative step are utilized to update the condensation matrix. Matrix inversions or Gaussian eliminations are avoided in the updating process by employing the orthogonality of the eigenvectors. The process of updating the condensation matrix and the eigenvalue problem is repeated until a desired convergence in the eigenvalues is achieved; usually a few iterations are quite adequate. Iterations for both the lower as well as the higher modes can be performed as the condensation matrices for the two sets of modes are very simply related. Numerical examples are presented to show the applicability of the proposed approach. Several methods that have been used in practice to select the kept degrees of freedom for condensing are also evaluated numerically with respect to their effectiveness in providing accurate estimates of the eigenproperties with a minimum number of iterations.

Roads and Bridges

INTRODUCTION Bridges in the Kachchh region are generally stream or railway crossings. The affected area has significant road and rail networks. There are several major highway and railway bridges, and many small to medium bridges. As per Roads and Buildings (R&B) Department of the Government of Gujarat, 900 km of roadways and over 500 bridges were damaged in the January 26, 2001 earthquake. Bridges in the area are typically composed of short spans with span lengths of approximately 15 m. Bridges are simple spans with expansion joints at each pier and supported on elastomeric bearings with no continuity of the superstructure or any fixity at the intermediate diaphragms. Lshaped abutments are typical for all newer concrete and older masonry bridges. The substructure of most bridges is wall piers supported on shallow foundations with no consideration for ductility. Use of deep foundations is not prevalent, even though liquefaction and lateral spreading is to be expected in the region in a seismic event. Both existing bridges and those under construction suffered extensive damage during the earthquake (Jain et al., 2001). Precast concrete members are occasionally used in the construction of bridges. Precast/ prestressed concrete bridges performed better, relatively, than cast-in-place concrete or other types of bridges. The better performance of the precast/prestressed bridges can be attributed to the higher quality of construction in the fabrication of precast members. The State Highway system suffered damage primarily to road surfaces, while the National Highway systems main damage was to bridge structures. A summary of damages sustained by the roads and bridges along State Highway and National Highway in the affected area is presented in Tables 19-1 and 19-2.

Neural-network control of building structures by a force-matching training scheme

A method to generate an efficient control law for a neural-network controller is presented to reduce the dynamic response of buildings exposed to earthquake-induced ground excitations. The proposed training scheme for the neural-network controller does not rely on the emulation of the structure to be controlled. The approach used for this work is based on a force-matching procedure, and it directly utilizes the dynamic data characterizing the structure response to generate an efficient training signal. The proposed controller has a feedback structure, utilizing a limited set of response quantities. A shear building actuated at its top by a tuned-mass damper is utilized to demonstrate the effectiveness of the controller. For training purposes, an ensemble of synthetically generated ground-motion time histories, with appropriate site spectrum characteristics, have been used. The performance of the trained controller is then evaluated for two different historic ground-acceleration records that do not belong to the training set of time histories. The numerical simulations show the control effectiveness of the proposed scheme with modest control requirements.

Dynamic Condensation Approach for Nonclassically Damped Structures

An iterative dynamic condensation procedure for calculating the elgenproperties of damped dynamic systems is presented. The kept and reduced degrees of freedom of the systems are related through dynamic condensation matrices. The formulation to define the condensation matrices is developed. The procedure starts with a classical static condensation scheme but iteratively improves the results. The complex eigenproperties calculated in an iteration step are used to construct an updated condensation matrix for the following iteration step, which in turn is utilized to form a revised condensed system. A few iterations can provide accurate values of the eigenproperties. The iterative process can be expedited initially by a proper selection of the kept and reduced coordinates. Numerical results are presented to demonstrate the accuracy and convergence characteristics of the proposed condensation scheme.

Dynamic condensation with synthesis of substructure eigenproperties

Abstract For structures divided into substructures which are defined by their eigenproperties, a combination of the node synthesis and condensation techniques is presented to obtain a first few important eigenproperties of the combined system accurately. The accuracy of the calculated modal properties can be increased by iteratively solving an improved and condensed eigenvalue problem. If desired, the higher modal properties can also be obtained by solving a complementry eigenvalue problem associated with the higher modes. The availability of the substructure modes in this approach also provides a very convenient and efficient means of selecting the most appropriate kept degrees of freedom in the condensed eigenvalue problem to expediate the convergence to the correct eigenproperties. The methods for coupling of the substructure eigenproperties obtained with different boundary conditions at the interface are described. Several examples are presented to demonstrate the application of the approach.

Output-feedback sliding-mode control with generalized sliding surface for civil structures under earthquake excitation

The paper presents a control scheme based on the sliding-mode-control approach. The analytical formulation focuses on the development of (1) a convenient, systematic and general scheme to achieve the so-called regular form of the equations of motion required to uncouple the control actions from the sliding motion description, (2) a systematic treatment of control redundancy where the number of sliding constraints imposed are less than the number of independent control actions, and (3) a method to improve sliding surface design by incorporating auxiliary dynamic systems. Both full-state-feedback and output-feedback cases are considered. In the output-feedback formulation, a generalized procedure is developed so that arbitrary combinations of unavailable system states (unmeasured displacements or velocities, for example) need not participate in the design of the sliding surface or the controller. A controller design utilizing only bounding information on the intensity of ground motion and the unmeasured states is proposed. The analytical formulation developed herein is applied to a 10-storey building structure to obtain the numerical results. The advantages of introducing auxiliary systems in the design of the sliding surface and the corresponding controller are noted. The results for both full-state-feedback and output-feedback cases are presented and compared to demonstrate applicability of the proposed control scheme.

Mode acceleration-based response spectrum approach for nonclassically damped structures

Abstract The paper describes the development of a mode accleration-based response spectrum approach for calculating the seismic design response of the nonclassically damped structures. The response is divided into a pseudo-static part and a dynamic part. The pseudo-static part is calculated by a simple static analysis of the structure for the inertial forces, induced by a unit ground acceleration, applied statically. The dynamic part, of course, pends upon the dynamic characteritics of the structure which are defined in terms of the complex-valued modal characteristics. The correlation between the pseudo-static and dynamic components is properly considered. The design ground input in this approach is defined in terms of the relative acceleration and relative velocity response spectra. The proposed approach has the desired attribute of the mode acceleration approach as the response can be accurately calculated even if only a first few modes are used in the analysis. The approach is computationally more efficient than the convenionally used mode displacement approach. The applicability of the approach is verified by numerical simulation results.

A perturbation analysis of the eigenproperties of equipment-structure systems

Abstract In the calculations involving the dynamic response of equipment, it often is of interest to include the effect of the dynamic interaction between the equipment and its supporting structure. This can be done by calculating the eigenproperties of the combined equipment-structure systems, through either a mode synthesis approach or a perturbation approach. Herein, the details of a systematic perturbation expansion scheme are given for the calculation of the combined modal properties. Ready-to-use closed form expressions are provided for calculating the frequencies, mode shapes and participation factors, both for a detuned as well as a tuned equipment. These expressions can be used for equipment which are not heavier than 1/10 the mass of the supporting floor. However, if only the combined frequencies are desired the expressions can also be utilized for equipment as heavy as one-half the mass of the supporting floor without much error.

Seismic response of structural frameworks with flexible connections

A method is presented to incorporate the flexibility of connections in the seismic analysis of framed structures. The flexible connections are represented by rotational springs with linear moment rotation relationships. Although additional deformation coordinates representing the rotational deformations of the connections exist, the formulation developed here avoids this increase in the degrees of freedom. The changes in the element matrices introduced by the eccentricity and flexibility of mass and stiffness on the connections are explicitly defined in closed form. Numerical results showing the effects of flexibility and eccentricity on the dynamic characteristics as well as on the seismic response of a building frame are presented.

Optimal Feedback Flow Rates for Pedestrian Evacuation in a Network of Corridors

This paper presents a methodology for the computation of optimal feedback flow rates (flow velocities and flow discharges) for pedestrian evacuation from a network of corridors using network-wide pedestrian congestion data. The pedestrian flow is defined in a macroscopic sense, wherein ordinary differential equations (ODEs) for each corridor and node are obtained using the conservation of pedestrian mass. The effect of congestion on the flow velocities and discharges in the corridor and the corridor intersections is explicitly modeled. Collectively, these corridor and node equations define the state-space model of the pedestrian flow in the network. The state variables signify the congestion in a corridor or an intersection, whereas the control variables directly affect the flow velocities and the flow discharges. For this model, an optimization-based control algorithm is developed to ensure a maximum total instantaneous input discharge that is subject to tracking the optimal congestion state and boundedness of the control variables. A comparison of the simulation results in the controlled and uncontrolled scenarios shows superior performance in the controlled case due to convergence to the optimal congestion state and consistently high network input and exit discharges.