Lateral Inertia Forces Research Articles

Damping control of polodes, inertia and natural frequencies: Theory and application to automotive suspensions

This paper shows how tunable dampers can help control the instant centre of rotation of a 2D rigid body and its polode in planar motion, which in turn implies that the inertia tensor can also be controlled. For mechanisms equipped with some elasticity the results show that damping can also control their natural frequencies. The foundation of a general theory to control the polode is presented, exploring the chance of an optimal control formulation of the problem via a variational control principle, approached by the LQR (Linear Quadratic Regulator) method, after a suitable linearization. Application to automotive suspension linkages is presented that demonstrates the control of the instant roll centre and axis and consequently its instant roll vibration frequency to optimize the response, when excited by lateral inertia forces.

Seismic Behaviour of Strengthened Unreinforced Masonry Walls using Kevlar-FRP

Unreinforced masonry walls (URM) in old buildings are vulnerable to collapse upon receiving high lateral inertia force due to earthquakes. However, a high strength fiber material such as Kevlar fiber has been identified as able to improve the URM-Wall performance, especially in shear strength enhancement. In this research, the seismic performance of an URM-Wall was analysed using SAP2000 by modeling the wall with three dimensional solid elements. Solids and springs as link connectors were assigned to represent the masonry behavior. The aim of this research is to compare between results obtained from the computer analyses and the previously conducted laboratory experiments. The effectiveness of Kevlar material installed in the diagonal directions of both wall surfaces was investigated. It was found that the failure mechanism shown by the SAP2000 model is similar to the laboratory test results.

Structural Behavior of Hollow Reinforced Concrete Beams: A Review

This paper reviews some experimental and numerical results about the hollow reinforced concrete beams (HRCB). Any subtraction in concrete quantity within the structural members without a considerable lack in load carrying capacity represents a common research trend nowadays due to the decrease in sections dimensions, reinforcing steel and lateral inertia forces in severe earthquakes as well as the sustainability gain for the resulting inhibiting of CO2 emission. In addition, the possibility of passing the electrical and mechanical facilities comprises another good feature of such type of structural members. During the traditional beam design process, the tension concrete is considered as strain transfer agent and do not have any role for structural resistance. As a result, longitudinal holes can be made within this area to produce the hollow reinforced concrete beams (HRCB). In this paper some remarkable research works are summarized with the most important conclusions within this field.

1:5 축소 10층 내력벽식 R.C. 공동주택의 지진모의실험

본 논문에서는 1:5 축소 10층 내력벽식 철근콘크리트(RC) 내력벽식 공동주택의 지진모의실험의 결과를 제시한다. 실험의 결과는 다음과 같다. (1) 본 실험 모델에서 재현주기 50년 지진에 대해서는 선형 탄성응답을 보이며, 우리나라의 설계지진에 대해서는 비선형 거동을 확인할 수 있다. (2) 재현주기 2400년의 최대지진에 대해 실험체의 강성 및 강도 저하가 현저하게 나타났다. (3) 횡 관성력에 대한 주 저항은 주로 엘리베이터 홀과 계단실 벽체로부터 유래되었다. (4) 실험체의 손상 및 파괴 모드는 벽과 슬래브의 휨 거동에 의해 지배되었다. 가진의 크기가 증가 할수록 현저한 강성의 저하와 고유주기의 증가가 발생하였다. This paper presents the results of shaking table tests on a 1:5 scale 10-story R.C. wall-type residential building model. The following conclusions are drawn based on the test results. (1) The model responded linear elastically under the excitations simulating an earthquake with a return period of 50 years, and showed a nonlinear response under the excitations simulating the design earthquake of Korea. (2) The model showed a significant strength drop under the maximum considered earthquake, with a return period of 2400 years. (3) The major portion of the resistance to lateral inertia forces came from the walls used for the elevator and stair case. (4) Finally, the damage and failure modes appear to be due to the flexural behavior of walls and slabs. A significant deterioration of stiffness and an elongation of the fundamental periods were observed under increased earthquake excitations.

Modal interaction in chaotic vibrations of a shallow double-curved shell-panel

Experimental results and analytical results are presented on chaotic vibrations of a shallow double-curved shell-panel subjected to gravity and periodic excitation. Modal interactions in the chaotic responses are discussed. The shell-panel with square boundary is simply supported for deflection. In-plane displacement at the boundary is elastically constrained. In the experiment, time histories of the chaotic responses at the spatial multiple positions of the shell-panel are measured for the inspection of modal interaction. In the analysis, the shallow shell-panel is assumed to have constant curvatures along to orthogonal directions and geometric initial imperfection. The Donnell–Mushtari–Vlasov type equation is used as governing equation with lateral inertia force. Assuming deflection with multiple modes of vibration, the governing equation is reduced to a set of nonlinear ordinary differential equations by the Bubnov–Galerkin procedure. Chaotic responses are integrated numerically. The chaotic responses, which are obtained by the experiment and the analysis, are inspected with the Fourier spectra, the Poincaré projections, the maximum Lyapunov exponents and the Lyapunov dimension. Contribution of modes of vibration to the chaotic responses is analyzed by the principal component analysis, i.e., Karhunen–Loève transformation.

Experiments and analysis on chaotic vibrations of a shallow cylindrical shell-panel

Detailed experimental results and analytical results are presented on chaotic vibrations of a shallow cylindrical shell-panel subjected to gravity and periodic excitation. The shallow shell-panel with square boundary is simply supported for deflection. In-plane displacement at the boundary is elastically constrained by in-plain springs. In the experiment, the cylindrical shallow shell-panel with thickness 0.24 mm, square form of length 140 mm and mean radius 5150 mm is used for the test specimen. All edges around the shell boundary are simply supported by adhesive flexible films. First, to find fundamental properties of the shell-panel, linear natural frequencies and characteristics of restoring force of the shell-panel are measured. These results are compared with the relevant analytical results. Then, geometrical parameters of the shell-panel are identified. Exciting the shell-panel with lateral periodic acceleration, nonlinear frequency responses of the shell-panel are obtained by sweeping the frequency of periodic acceleration. In typical ranges of the exciting frequency, predominant chaotic responses are generated. Time histories of the responses are recorded for inspection of the chaos. In the analysis, the Donnell equation with lateral inertia force is introduced. Assuming mode functions, the governing equation is reduced to a set of nonlinear ordinary differential equations by the Galerkin procedure. Periodic responses are calculated by the harmonic balance method. Chaotic responses are integrated numerically by the Runge–Kutta–Gill method. The chaotic responses, which are obtained by the experiment and the analysis, are inspected with the Fourier spectra, the Poincaré projections, the maximum Lyapunov exponents and the Lyapunov dimension. It is found that the dominant chaotic responses of the shell-panel are generated from the responses of the sub-harmonic resonance of 1 2 order and of the ultra-sub-harmonic resonance of 2 3 order. By the convergence of the maximum Lyapunov exponent to the embedding dimension, the number of predominant vibration modes which contribute to the chaos is found to be three or four. Fairly good agreements are obtained between the experimental results and the analytical results.

Chaotic Oscillations of a Suspended Curved Panel with Square Boundary

Experimental results and analytical results are presented on chaotic oscillations of a suspended curved panel with square boundary. In the experiment, the panel is simply supported along all edges. The configuration of the panel is deformed by the gravity force and in-plane elastic constraint. Nonlinear periodic responses of the panel are examined under periodic lateral acceleration. Chaotic responses are observed and measured for modal inspection at four points of the panel simultaneously. In the analysis, the configuration of the panel is assumed as a suspended curved form with double arcs parallel to each edge. The Donnell type equation with lateral inertia force is introduced. The governing equation is reduced to nonlinear differential equations of a multiple-degree-of-freedom system by the Galerkin procedure. The nonlinear periodic responses are calculated by the harmonic balance method. The chaotic responses are numerically integrated by the Runge-Kutta-Gill method. The chaotic responses are inspected with the Fourier spectra, the Poincaré projections, the maximum Lyapunov exponents and the principal components by the Karhunen-Loéve-transformation. Both results of the experiment and the analysis show that the chaotic responses are generated within the frequency range of the same ratio to the each lowest natural-frequency. Poincaré projections of the both results coincide fairly well in detail. The number of modes generated in the chaos is counted as three by the maximum Lyapunov exponent and the Lyapunov dimension. The principal component analysis shows the predominant contribution of the lowest mode of vibration.

Experimental investigation of steel fiber reinforced concrete box beams under bending

Reduction of dead weight of a reinforced-concrete (RC) structure without too much concession in its load carrying capacity has always been an attractive study subject because it engenders (1) a decrease in dimensions of the members, (2) a decrease in the reinforcement steel, and (3) a decrease in lateral inertia forces during severe earthquakes. In this study, nine RC beams of outer dimensions of 300 × 300 × 2000 mm, six of which are box beams, designed and produced using a C20 class steel fiber concrete, (SFRC) with the commonly used steel fiber type of Dramix-RC-80/0.60-BN at a dosage of 30 kg/m3, are tested under bending. The mechanical behaviours of all these nine beams under bending are recorded from the beginning of the test till the ultimate failure of the tensile reinforcement in a two-point beam-loading setup. The proportions of (1) loss in ultimate load versus reduction in dead weight and (2) (ultimate experimental load)/(ultimate theoretical load) of the SFRC box beams are determined for two different box thicknesses. Dimensionless behaviour relationships of all the SFRC beams are determined, and the experimentally obtained relationship between the ratio of (actual ultimate load)/(theoretical ultimate load) and the ratio of (wall thickness)/(beam height) for the SFRC box beams is expressed diagrammatically.

Influence of non-structural components on lateral stiffness of tall buildings

A building is a complex assemblage of both structural and non-structural components (NSC). Although many NSC, such as partition walls, external walls, parapet walls, stairwells, elevator shafts and so forth, are connected directly to the structural system, their behaviour and stiffening effects under lateral loading have normally been ignored by design engineers, despite significant advances in computer technology and the availability of modern computational resources. The performance of structures can be greatly improved by the increase in strength arising from the NSC; on the contrary, this increase in strength also accompanies an increase in the initial stiffness of the structure, which may consequently attract additional seismically induced lateral inertia forces. This paper is concerned with the estimation of the lateral stiffness contributed by the NSC to the total stiffness of three common forms of tall building structures constructed in Hong Kong. Both dynamic tests and numerical modelling of the buildings have been carried out for this purpose. Natural period estimates from dynamic tests and from analyses using calibrated finite element models were found to be in remarkable agreement. Significant stiffness contributions from NSC to the total lateral stiffness of tall buildings have been observed in the study. The extent of the contributions depends on the structural form and the type of components. Other contributions to the additional stiffness have also been analysed for comparison in the study. Copyright © 2005 John Wiley & Sons, Ltd.

Static and dynamic post-buckling behavior of truss structures

This paper proposes a vibration model in which the lateral inertia force is considered in order to analyze the dynamic post-buckling behavior of truss members. The post-buckling behavior of perfectly symmetrical truss-structures and symmetrical truss-structures with a small imperfection are analyzed. The structures analyzed are a plane parallel chord truss structure and a double-layer space truss structure. The load-deformation relationships obtained by static and dynamic analyses are compared. It is found that the dynamic load-displacement relationship oscillates around the static relationship after buckling. Some examples show that the buckling mode and the post-buckling load-displacement relationship differ remarkably between static and dynamic analysis.

Dynamic elastic-plastic buckling phenomena in a rod due to axial impact

Dynamic elastic-plastic buckling phenomena which might develop in a rod from an axial impact loading are studied in order to identify the conditions for quasi-static behaviour. A discrete model for dynamic elastic-plastic buckling, which retains the axial and the lateral inertia forces, is proposed, and the relationship between the model parameters and the characteristics of an actual structure is given. Examples of different external loadings and boundary conditions are considered in order to clarify the influence of elastic-plastic axial wave propagation on the buckling process. The critical time for the initiation of buckling is obtained and the post-buckling behaviour of the model is analysed. Particular attention is paid to the role of the striking mass on the characteristics of the buckling process and on the development of the buckling shape. The numerical study reveals that the inertia of the striking mass affects considerably the development of the buckling shape causing different patterns of axial strain distributions at the initiation of buckling. The comparisons which are made between the model predictions and some previously published experimental data show that the buckling process is governed by the impact velocity as well as by the external loading history provided by the experimental technique.

Reduction and distribution of lateral seismic inertia forces on base isolated multistorey structures

This paper presents some important results of a thorough investigation into the seismic behaviour of a wide range of Base Isolated multistorey structures. The benefits of implementing BI systems are highlighted. The reduction and distribution patterns of lateral inertia forces due to the inclusion of this isolation system are specifically discussed.

Effect of sliding on lateral seismic forces of a building structure

The effect on maximum lateral seismic inertia forces of sliding between the foundation of a heavy-stiff building structure and the soil is studied. The lateral inertia force acting on the structure is limited to a value FD, which is determined by multiplying a prescribed coefficient of friction times the total structural weight. Effects of rocking of the structure are not considered. The soil is modeled as a two-dimensional elastic half space. Results are evaluated by comparing the effect of increased sliding on the spectrum response of the lateral motion of the foundation mass.

The Propagation of Longitudinal Wave in a Visco-Elastic Circular Bar with Consideration of the Lateral Inertia

It is important to clarify how the propagation of a longitudinal wave in a visco-elastic bar is affected by the lateral inertia. This paper purports to clarify the coupling effect of the viscous force and the lateral inertia force on the propagation of the wave, especially in the vicinity of the wave front. It is assumed that the visco-elastic material is represented by a Voigt model. The equation of motion of the bar, in which the effect of the lateral inertia is taken into consideration, is obtained with Hamilton's principle. The solutions of the equation are presented for two cases. One is the case of one end of the bar being impacted at a constant velocity and the other is the case of the stress or strain at the impacted end being kept constant.

Lateral structure-foundation interaction of structures with base masses

abstract The interaction of lateral inertia forces of an N-mass structure with a base mass and lateral seismic motion of the foundation is formulated as an integral equation of the Volterra type. Flexibility of the foundation is based on the transient solution of a two-dimensional elastic half-space. Interaction effects are evaluated by comparing the response spectra of the free-field motion to that of the foundation motion. Results show that changes in the response spectra are significant for heavy, stiff structures such as a reactor-containment vessel.

Non-linear vibrations of a beam on a viscoelastic foundation

In this paper, the equation of motion for transverse vibrations of a slender beam on a continuous viscoelastic foundation is derived and analyzed. The study includes the non-linear parameters which arise when one considers the non-linearities inherent in the expression for the curvature of the beam, the system's external couplings, and the effect of change in longitudinal position of the beam elements on the bending moment caused by the lateral inertia forces of the system.