Distributed Mass System Research Articles

Rubble Stone Masonry Buildings with Cement Mortar: Base Shear Seismic Demand Comparison for Selected Countries Worldwide

Full base shear seismic demand analyses with calculated examples for heavy stone masonry buildings are not present in the literature. To address this shortcoming, analyses and calculations are performed on nominally reinforced rubble stone masonry house and school designs, as typically built in Nepal. The seismic codes are literally applied for countries where the technique is still allowed (Nepal, India, China, Tajikistan, Iran, Croatia), or should be reintroduced based on current practices (Pakistan, Afghanistan, Turkey). First, this paper compares the base shear formulas and the inertia forces distributions of these codes, as well as material densities, seismic weights, seismic zoning, natural periods of vibration, response spectra, importance factors and seismic load combinations. Large differences between approaches and coefficients are observed. Then, by following Equivalent Lateral Force-principles for Ultimate Limit State verifications (10%PE50y), the base shear and story shears are calculated for a design peak ground acceleration of 0.20 g, as well as the effects of critical load combinations on the forces and moments acting on the lateral-resisting elements. It is concluded that Pakistan has the most tolerant code, Nepal represents an average value, whereas India and China are most conservative toward the case study buildings. Overall, it is observed that heavy-masonry-light-floor systems with negligible diaphragm action behave different under seismic motion than most other building typologies. Given the observations in this paper, the applicability of conventional ELF, S-ELF and S-Modal methods for heavy masonry buildings is questionable. The codes however do not introduce modified approaches that address these differences. Possible implications of the exclusion of plinth masonry and large portions of seismic weight need further assessment and validation, for which different (possibly more sophisticated) concepts must be considered, such as the equivalent frame method or distributed mass system. Since Nepal allows stone masonry in areas with higher seismic hazard levels >0.40 g (opposed to India <0.12 and China <0.15 g), their code is taken as the reference and starting point for follow-up research, which aims to verify the seismic demand by performing seismic capacity checks of the masonry piers and spandrels. The paper ends with an appeal for global collaboration under the research project SMARTnet.

Effect of Free Vibration Frequency on Modeling of Bridge Pier

Pile groups are a widely used foundation system to support structures placed over soft soil or when the shallow foundation is not appropriate due to excessive settlement especially for bridges, flyovers, or metro piers. Estimation of appropriate free vibration frequency for a bridge pier in design procedure gives appropriate and more optimized design. The frequencies obtained by considering soil pile interaction are more realistic than considering bridge pier as single degree of freedom (SDOF) system fixed at top of a pile cap. In the present study, the frequency is calculated by modeling the pier as SDOF system as well as by considering the soil-pile interaction effect. It is observed that to evaluate free vibration frequency, pile-soil interaction effect including distributed mass system for pier should be accounted.

An application of the transfer matrix approach for a dynamic analysis of complex spatial pipelines

An effective method for the calculations of stress and residual strength of complex spatial pipelines at static and dynamic loading with taking into account the vibration of internal liquid and Puasson coupling is presented. It based on the well-known transfer matrix approach. The method utilizes the exact mechanical equations for the stress-strained state of straight beam with distributed mass, which connect unknown parameters of forces and displacements at the end of beam calculation element with the parameters at the beginning of the element. At a general level, the solution scheme and calculation models are the same for static and dynamic calculations, the only difference – are the equations. Two different methods are used to find natural vibration frequencies of the distributed mass system: straightforward (“brute force”) and quick, based on Williams-Wittrick frequencies counter. Within such counter a special procedure is developed for taking into account fluid vibration with consideration of volumetric balance condition at T-nozzles. The excellent accuracy of the method is demonstrated by the modeling of thin-walled, water filled pipe behavior after the rod impact. Two seismic analysis procedures are implemented on the base of developed method: standard response spectrum procedure and normal-mode summation procedure (“exact” dynamical), which uses accelerograms. These methods and procedures have been already implemented in calculation software for pipeline strength assessment with the possibility of building of arbitrary complexity models by the user-friendly, visual way. Their effectiveness is demonstrated by the seismic calculation for primary circuit pipings of Zaporizhia NPP.

Accuracy of three-dimensional seismic ground response analysis in time domain using nonlinear numerical simulations

To provide appropriate uses of nonlinear ground response analysis for engineering practice, a three-dimensional soil column with a distributed mass system and a time domain numerical analysis were implemented on the OpenSees simulation platform. The standard mesh of a three-dimensional soil column was suggested to be satisfied with the specified maximum frequency. The layered soil column was divided into multiple sub-soils with a different viscous damping matrix according to the shear velocities as the soil properties were significantly different. It was necessary to use a combination of other one-dimensional or three-dimensional nonlinear seismic ground analysis programs to confirm the applicability of nonlinear seismic ground motion response analysis procedures in soft soil or for strong earthquakes. The accuracy of the three-dimensional soil column finite element method was verified by dynamic centrifuge model testing under different peak accelerations of the earthquake. As a result, nonlinear seismic ground motion response analysis procedures were improved in this study. The accuracy and efficiency of the three-dimensional seismic ground response analysis can be adapted to the requirements of engineering practice.

Theoretical Evaluation of Hybrid Simulation Applied to Continuous Plate Structures

AbstractHybrid simulation is a popular experimental technique whereby only part of a system is physically realized and the remainder is modeled in a computer with a set of actuators and sensors to connect the two subsystems. While the methodology is common, it lacks a theoretical structure that ensures users are getting valid simulation results of the entire system. Further, little attention has been paid to distributed mass systems and those that do not have a beam/column like topology. This work examines three basic issues: (1) an abstract geometric scheme is proposed by which one can reason about hybrid simulation systems and their underlying errors; (2) systems with distributed mass are explicitly considered; and (3) the model system utilized in this study has a distinctly nonbeam/column like system, namely, a Kirchhoff-Love plate with a continuous one-dimensional hybrid system interface. It is demonstrated that such systems are generally viable only below the first fundamental frequency of the system...

Research of Active Chatter Control for the Piezoelectric Intelligent Boring Bar with Distribution Quality

Seen as a cantilever beam with distributed mass system, the boring bar model and its state -space equation is built. On the basis of the dynamic model, a stability diagram of the boring system of the type of regenerative chatter is obtained. According to the stability diagram of the system, we get main analysis and comparison of the system stability near the fundamental frequency. In this paper, piezoelectric smart flutter suppression is carried out on a boring system with distributed mass, which improved the stability of the boring system

Dynamic Analysis under Uniformly Distributed Moving Masses of Rectangular Plate with General Boundary Conditions

The problem of the flexural vibrations of a rectangular plate having arbitrary supports at both ends is investigated. The solution technique which is suitable for all variants of classical boundary conditions involves using the generalized two-dimensional integral transform to reduce the fourth order partial differential equation governing the vibration of the plate to a second order ordinary differential equation which is then treated with the modified asymptotic method of Struble. The closed form solutions are obtained and numerical analyses in plotted curves are presented. It is also deduced that for the same natural frequency, the critical speed for the system traversed by uniformly distributed moving forces at constant speed is greater than that of the uniformly distributed moving mass problem for both clamped-clamped and simple-clamped end conditions. Hence resonance is reached earlier in the uniformly distributed moving mass system. Furthermore, for both structural parameters considered, the response amplitude of the moving distributed mass system is higher than that of the moving distributed force system. Thus, it is established that the moving distributed force solution is not an upper bound for an accurate solution of the moving distributed mass problem.

637 片持ち梁型動吸振器による円筒形状構造物の振動低減方法の検討

Advantages of a cantilever-type dynamic absorber are simple shape, ease of manufacture and low-cost. In many past studies, the cantilever-type dynamic absorber is composed of lumped mass and zero mass plate spring or rigid beam and elastic fixation. However, the later has extra rigid modes, and these modes may become a source of unnecessary vibration. In this paper, we considered how to design and apply the cantilever-type dynamic absorber that consists of rigid fixed distributed mass system in order to absorb vibration of a cylindrical structure. Especially, a stator of a rotating machine as an example of the cylindrical structure is excited by electromagnetic force. And its circular vibration modes often become a problem. We conducted fundamental impact testing by using simple circular ring and cantilever. The testing results showed that the cantilever-type dynamic absorber is available to reduce the vibration of a cylindrical structure.

Analysis of uniformly and linearly distributed mass dampers under harmonic and earthquake excitation

The effectiveness of multiple mass dampers has been investigated by Igusa and Xu [Dynamic characteristics of multiple tuned mass substructures with closely spaced frequencies. Earthq. Engng Struct. Dynam. 21 (1992) 1050–70], Yamaguchi and Harnpornchai [Fundamental characteristics of multiple tuned mass dampers for suppressing harmonically forced oscillations. Earthq. Engng Struct. Dynam. 22 (1993) 51–62], Abe and Fujino [Dynamic characterization of multiple tuned mass dampers and some design formulas. Earthq. Engng Struct. Dynam. 23 (1994) 813–35] and Kareem and Kline [Performance of multiple mass dampers under random loading. J. Struct. Engng 121 (1995) 348–61]. In this paper, we extend the results of these previous investigations to examine the performance of uniformly and linearly distributed multiple mass dampers, respectively. These systems were selected to ascertain whether the distribution of masses located close to the central mass damper would influence the performance of the entire system in reducing vibration. We evaluate performance numerically through assessing the effectiveness and robustness of each system, as well as considering the effects of redundancy, under harmonic excitation. In this regard, we evaluate the performance of the system when certain individual dampers do not function. We show that the uniformly distributed mass system is more effective in reducing the peak dynamic magnification factor. The linearly distributed system is more robust under mistuning. It is more robust to damping variation for low damping values but the effectiveness of the two systems converges as damping increases. The uniformly distributed system is slightly more reliable when an individual damper fails. The eleven mass system is optimum for both configurations for harmonic excitation. The 21-mass system is more effective in structural vibration decay in both cases for the El Centro earthquake simulation.

Natural vibration analysis of diagonal networks

This paper describes an exact method of analysis for natural vibration of diagonal networks by considering an equivalent cyclic periodic structure and adopting the double U-transformation technique. Both a lumped mass system and a distributed mass system are considered to investigate the diagonal networks. The exact solution for the frequency equations and the natural modes of the networks can be derived. As numerical examples, square diagonal cable networks with different meshes are worked out.

Linear Forced Vibration Analysis of Two- and Three-dimensional Tree Structures by the Transfer Influence Coefficient Method.

An algorithm for free vibration analysis of a tree structure formulated in the previous reports by applying the transfer influence coefficient method is extended in order to analyze forced vibration of a tree structure which is mainly found in pipeline systems. The tree structure has some crooked parts and subsystems but has no closed loop in the systems. It is modeled as a distributed mass system with consideration of structural damping, and the present algorithm is formulated for both two- and three-dimensional tree structures. It is theoretically confirmed that some merits of the transfer influence coefficient method for free vibration analysis, for example, excellence in both computation accuracy and speed are also realized for the forced vibration analysis. Moreover, the present algorithm enables us to easily analyze a vibrating system excited by forced displacement by changing the corresponding spring constants conveniently.

Free Vibration Analysis of a Tree Structure by the Transfer Influence Coefficient Method (1st Report, Formulation for a Two-dimensional Tree Structure).

The authors apply the transfer influence coefticient method to a two-dimensional tree structure, and formulate a general algorithm to analyse in-plane longitudinal and flexural coupled free vibration. The tree structure, which is mainly found in the F-shaped structure of machine tools, pipeline systems and so on, has some crooked parts and subsystems but has no closed loop in the system. It is modeled as a distributed mass system in the present algorithm. It is theoretically confirmed that some merits of the transfer influence coefficient method also hold for the two-dimensional tree structure; that is, boundary conditions are easily controlled by the spring constants, and false roots in the use of the bisection method as a solution to the frequency equation can readily be eliminated by using the values obtained in the computational process. The occurrence mechanism of false roots is discussed in detail.

Free vibration analysis of a multiple straight-line structure regarded as a distributed mass system by the transfer influence coefficient method.

This paper describes the general formulation for the in-plane flexural free vibration analysis of a multiple-layered straight-line structure by the transfer influence coefficient method. The structure is modeled as a distributed mass system with lumped masses and lumped inertia moments, and massless linear and rotational springs. The results of the simple numerical computational examples demonstrate the validity of the present method giving the numerical high accuracy and the numerical high speed, compared with the transfer matrix method on a personal computer. The main features of this method are the unification of the frequency equation for all boundary conditions, and the elimination method of the false roots when the bisection method is used for solving the frequency equation. The cancelling attributable to the adding and subtracting of hyperbolic and trigonometric functions is overcome by partitioning the uniformly distributed beams.

Free vibrations analysis of a tree structure by the transfer influence coeffcient method. (1st report. Formulation for a two-dimensional tree structure).

The authors apply the transfer influence coefficient method to a two-dimensional tree structure, and formulate a general algorithm to analyse in-plane longitudinal and flexural coupled free vibration. The tree structure, which is mainly found in the Γ-shaped structure of machine tools, pipeline systems and so on, has some crooked parts and subsystems but has no closed loop in the system. It is modeled as a distributed mass system in the present algorithm. It is theoretically confirmed that some merits of the transfer influence coefficient method are kept also for the two-dimensional tree structure; that is, boundary conditions are easily controlled by the spring constants, and false roots in the use of the bisection method as a solution to the frequency equation can readily be eliminated by using the values obtained in the computational process. The occurrence mechanism of false roots is discussed in detail.

Free vibration analysis of a multiple layered structure by the transfer infiuence coefficient method. (4th report. Computational results of a structure with two layers regarded as distributed mass system).

The authors apply the general formulation for the in-plane flexural free vibration analysis obtained in the previous report to a structure with two layers regarded as a distributed mass system. They state the effective method of numerical computations suitable for the remarkably stiff intermediate elastic supports between layers in detail. The results of the simple numerical computational examples demonstrate the frequency equation for all boundary conditions when the bisection method is used as a solution, and the flexibility for programming of the transfer influence coefficient method, compared with the transfer matrix method on a personal computer. The cancelling attributable to the sum and difference of the trigonometric and exponential functions is overcome by partition of the uniformly distributed beams.

Free vibration analysis of a multiple layered structure by the transfer influence coefficient method. (3rd report. Formulation for the distributed mass system).

This paper describes the general formulation for the in-plane flexural free vibration analysis of a multiple layered structure by the transfer influence coefficient method. The structure is modeled as a distributed mass system with lumped masses and lumped inertia moments, and massless linear and rotational springs. The present method does not require a change of fundamental algorithm but necessitates only substituting appropriately large values into the corresponding spring constants when intermediate elastic supports are many and very stiff. Boundary conditions are also easily controlled by the spring constants. Some devices are taken for high calculation accuracy and calculation speed. The occurrence mechanism and the simplified elimination of false roots involved in the frequency equation are discussed in the use of the bisection method.

Nonlinear free vibrations of multispan beams on elastic supports

This paper presents a numerical solution for geometrically nonlinear free vibrations of multispan beams on elastic supports. The horizontally and rotary inertia forces have been neglected and the beams are considered as distributed mass systems. The variational approach, dynamic finite element method and the iterative procedure are used for determining the frequencies and nonlinear mode of vibrations. Several examples show the usefulness of the method and moreover the influence of supports flexibility on the frequency-amplitude relation is examined.

Free vibration analysis of a multiple straight line structure regarded as a discrete system by the transfer influence coefficient method.

This paper describes the general formulation for the in-plane flexural free vibration analysis of a multiple-layered straight-line structure by the transfer influence coefficient method. The structure is modeled as a distributed mass system with lumped masses and lumped inertia moments, and massless linear and rotational springs. The results of the simple numerical computational examples demonstrate the validity of the present method giving the numerical high accuracy and the numerical high speed, compared with the transfer matrix method on a personal computer. The main features of this method are the unification of the frequency equation for all boundary conditions, and the elimination method of the false roots when the bisection method is used for solving the frequency equation. The cancelling attributable to the adding and subtracting of hyperbolic and trigonometric functions is overcome by partitioning the uniformly distributed beams.

Submicron spacing dynamics for flying head slider mechanisms using building block approach

This paper describes submicron spacing dynamics for total flying head slider mechanisms, considering suspension gimbal spring and actuator arm mechanisms as well as the air bearing slider, via building block approach (BBA). BBA, based on the modal synthesis method and finite element method, is applied to a system, which consists of a fluid film lubrication system and structure mechanisms system. It became clear that a suspension gimbal spring and an actuator arm, as a 3-dimensional distributed mass system, affects slider dynamics and that resonance or nonresonance, caused by those mechanisms, exists in slider frequency response in addition to air film resonance. Furthermore, a comparison between Winchester and Whitney mechanisms is discussed from the slider dynamics points of view. Allowable media accelerations are derived for both suspension mechanisms. A comparison between theoretical and experimental results is carried out. Results show good agreement and the BBA computer simulation is verified to be a valid and very highly efficient approach for integrated flying head mechanism dynamic analysis.

Consistent mass matrices for three dimensional beam element due to distributed and lumped non-structural mass systems acting on its span

This paper presents consistent mass matrices for the three dimensional beam element resulting from the distributed and the lumped non-structural mass systems acting on its span. First the consistent mass matrices are derived for the distributed mass systems by considering equivalent density functions for torsion, bending and axial directions. The consistent mass matrices for the lumped systems are obtained from those for the distributed systems by considering the limiting case in which the distributed mass length approaches zero. The general expressions for the mass matrix coefficients reduce to familiar forms for the special cases. Since no approximation is made over and above the general assumptions commonly used in deriving beam element properties, the derivation presented here is exact within the realm of beam bending theory.