Time-displacement History Research Articles

Influence of harmonic and pulse excitations on response of foundations

ABSTRACT This investigation reports analysis of foundations to study its time-displacement response with due consideration to hardening and softening behaviour under combined harmonic and pulse loadings. Based on time of application of pulse loading to foundation and the occurrence of maximum deflection, two cases of analysis are considered and solutions are obtained for underdamped system using semi-analytical approach. The influence of combined action of two different loading is studied. Detailed parametric study is carried out to understand the influence of parameters such as mass of machine-foundation system, ratio of plastic to elastic stiffnesses, damping, frequency ratio and, resistance of soil on time-displacement history of system. Maximum displacement of the system increases to the extent of 48% with 22% increase in initial pulse load magnitude. Damping, mass and stiffness of SDOF system affected the response significantly. Results showed interaction due to combined action of harmonic and pulse loading should not be neglected.

Study on Dynamic Response of Visco-elastic Plate Under Transverse Periodic Load

Abstract The dynamic behavior of simple supported rectangular thin plate subjected to transverse harmonic excitation is investigated in this paper. The compressive loads N1 and N2 is applied on edges of the plate. On assumption of small deformation, dynamic governing equation is derived. The constitutive relation of material obeys can be stood for an integral equation. By use of nonlinear Galerkin method, the partial differential governing equation is turned into integral-differential variation of the Duffing equation. The different kinds of behaviors are investigated making use of the classical tools of nonlinear dynamics, such as the phase portrait, the time-displacement history and Lyapunov exponent analysis. The results of analysis show that the values of N1 and N2 , character time of material have large influence on the dynamic response. When they satisfy some condition, chaotic motions may occur in the dynamic system.

Generation of internal and surface waves by seafloor movement in a two layer fluid system

Internal and surface waves generated by the deformations of the solid bed in a two layer fluid system of infinite lateral extent and uniform depth are investigated. An integral solution is developed for an arbitrary bed displacement on the basis of a linear approximation of the complete description of wave motion using a transform method (Laplace in time and Fourier in space) analogous to that used to study the generation of tsunamis by many researchers. The theoretical solutions are presented for three interesting specific deformations of the seafloor; the spatial variation of each seafloor displacement consists of a block section of the seafloor moving vertically either up or down while the time-displacement history of the block section is varied. The generation process and the profiles of the internal and surface waves for the case of the exponential bed movement are numerically illustrated, and the effects of the deformation parameters, densities and depths of the two layers on the solutions are discussed. As expected, the solutions derived from the present work include as special cases that obtained by Kervella et al. [Theor Comput Fluid Dyn 21:245-269, 2007] for tsunamis cased by an instantaneous seabed deformation and those presented by Hammack [J Fluid Mech 60:769-799, 1973] for the exponential and the half-sine bed displacements when the density of the upper fluid is taken as zero.

Solitary waves and chaos in nonlinear visco-elastic rod

The dynamics behavior of a nonlinear visco-elastic rod subjected to axially periodic load is investigated theoretically and numerically. The weak longitudinal periodic load is distributed uniformly along the rod. Firstly, equation of motion of the rod is derived. Utilizing perturbation technique, we acquire Kdv type equation describing strain wave in the rod. By use traveling wave method, the elliptic cosine wave solution and the solitary wave solution in the rod are provided. Then, Melnikov method is applied to analyze the dynamic behaviour of the rod qualitatively. The explicit conditions for the onset of chaotic dynamics are yielded. With the help of the Poincare map method, phase trajectory and time-displacement history diagrams, the theoretical results obtained are checked.

초대형 부유식 구조물의 상부구조체에 대한 동적응답해석

전세계적인 인구증가와 산업화로 인하여 육지면적의 부족, 육상자원의 고갈 등의 문제로 해양의 이용 및 개발의 관심이 늘어나고 있으며, 환경친화적인 해양공간을 확보하기 위하여 초대형 부유식 해상구조물에 대한 기술개발이 요구되고 있다. 본 논문에서는 초대형 부유식 구조물의 상부구조물에 대한 시간이력해석법에 대하여 소개하고 파랑하중에 의한 부체변형을 이용한 시간변위이력 산정 방법을 제안한다. 또한 주기 및 진폭의 변화에 따른 상부구조물의 동적 시간이력응답 결과를 분석하고 초대형 부유식 상부구조물 시설계안의 동적구조안전성을 평가한다. The importance of utilization of ocean space is increased due to high population and narrow land space. The development of a new technology for future use of ocean space, such as a design technology of Very Large Floating Structures(VLFS) is needed. This paper introduces the rime history analysis of superstructures on very large floating structures and proposes the estimation method of time displacement history considering wave loads. The dynamic responses of superstructure according to variation of period and amplitude are analysed using an example frame structure and the dynamic structural safety of VLFS pilot superstructure is evaluated.

The study on the chaotic motion of a nonlinear dynamic system

In this paper, the system of the forced vibration\(\ddot T - \lambda _1 T + \lambda _2 T^2 + \lambda _3 T^3 = \varepsilon \left( {g\cos \omega t - \varepsilon '\dot T} \right)\) is discussed, which contains square and cubic items. The critical condition that the system enters chaotic states is given by the Melnikov method. By Poincare map, phase portrait and time-displacement history diagram, whether the chaos occurs is determined.

Morphology and growth history of delgada fan: Implications for the Neogene evolution of Point Arena Basin and the Mendocino Triple Junction

Long‐range side scan (GLORIA) sonographs and seismic reflection data acquired during a survey of the western U.S. Exclusive Economic Zone in 1984, coupled with information from Deep Sea Drilling Project sites, provide new insights into the growth and evolution of the Delgada Fan. Construction of the fan commenced in the latest Miocene (∼6 Ma) following the filling of the Neogene Point Arena Basin. The fan presently covers more than 50×103 km2 of the Pacific plate and contains approximately 15×103 km3 of predominantly terrigenous detritus. The large size of the fan is incompatible with the small present‐day supply of sediment to the canyon system. The GLORIA data show the Delgada Fan to be a hybrid‐type fan, exhibiting characteristics of both elongate and radial fans. The morphology and volume of the fan, along with evidence for a decline in accumulation rates on the lower fan during the Quaternary period, suggest that the fan experienced an early growth phase (latest Miocene and Pliocene) characterized by relatively rapid progradation of elongate fan lobes followed by a period (Quaternary) of slower growth that has featured a shift of depocenters to sites closer to the canyons and a transition to distributary channels bordered by less prominent levees and overbank deposits. We examine the growth of Delgada Fan in relation to the Neogene evolution of the North American‐Pacific plate boundary using a series of paleogeographic reconstructions based on recently published time displacement histories of the Mendocino triple junction (MTJ), the San Andreas fault (SAF), and the Pacific plate, upon which the fan rests. The time displacement curves for the SAF and the MTJ suggest that the MTJ and Mendocino Fracture Zone overtook and passed Point Arena Basin at about 10 Ma when the basin lay immediately southwest of the present San Francisco Bay area. We suggest that the MTJ joined the SAF at approximately that time and location, thus making the SAF the master fault in the transform system. This interpretation is compatible with evidence from seismic reflection profiles over the fan, which demonstrate that the fan and the canyon system and therefore Point Arena Basin have moved as a unit since the inception of fan growth (∼6–7 Ma). Point Arena Basin lay southwest of the San Francisco area at 10–12 Ma, and the passage of the MTJ caused the disruption of the forearc shelf and slope and the development of local uplifted and subsiding blocks. In particular, uplift of the “bay block” immediately east of the SAF may have provided the source area for the late Miocene sediments that filled Point Arena Basin and set the stage for the growth of Delgada Canyon and Fan system. The growth rate of the fan has decreased, and the style of deposition has changed as the system was tectonically transported to its present location adjacent to the small youthful drainages of the King Range.

LONG WAVES GENERATED BY COMPLEX BOTTOM MOTIONS

Studies of tsunami generation often employ simple models of the sea floor dislocations to permit tractable analytical solutions. Although these solutions provide basic insight into the generation process, they are incapable of producing explicit results for prototype events where both the spatial and temporal distributions of the sea floor dislocation may be quite complicated. Herein we exploit the apparent linearity of the generation process and demonstrate both the use and validity of the superposition principle to construct solutions for complex bed motions. Analytical and experimental results are presented for a monopolar dislocation (block upthrust or downthrow) with a complex time-displacement history. The time history used in the computations is obtained from an integrated accelerogram recorded at Pacoima Dam, near Los Angeles, during the earthquake of February 9, 1971. A complex spatial deformation is not used in order to enable experimental verification of the analytical results. This is unfortunate since it appears that the details of the time-displacement history are not important for prototype phenomena where the motion may be considered instantaneous. However, it is important to note that the analysis treats both space and time variations in an identical manner; hence, confirmation of this approach for complex time variations strongly suggests analogous behavior for complex spatial variations. Finally, we examine and compare several alternative time-displacement histories for the mean motion. It is shown that the results for each mean motion can be unified by introducing a velocity as a descriptive parameter which is based on the kinetic energy input of the moving bottom to the overlying fluid.

THE GENERATION OF LONG WAVES IN THE LABORATORY

It became evident in the experimental aspects of a recent study of the propagation of nonlinear long waves past a step and up a slope that it was important to be able to generate waves which were initially well defined. The investigation dealt with the reflection and transmission of tsunamis past the continental shelf-break, and as such, two simple waves were used to represent certain characteristics of tsunamis: solitary waves and cnoidal waves. (Both of these permanent waves are solutions to the Korteweg-de Vries equation which to a certain order describe the propagation in two dimensions of nonlinear dispersive shallow water waves (see, e.g. Whitham, 1974).) The solitary wave actually can be generated in the laboratory in a simple manner if the wave tank is long enough and wave groups trailing the main wave are unimportant to the study. An example of the resulting waves obtained in the laboratory using a crude generation, procedure is demonstrated by the oscillograph record presented in Figure 1. Six traces are shown: the one at the bottom of the figure describes the time-displacement history of a vertical bulkhead wave generator which is moved by a hydraulic-servo system, the other five are the time variations of the water surface obtained using resistance wave gages spaced at the indicated number of depths downstream from the generator. (In the example presented, the depth of water was 10 cm and the wave plate was moved linearly with time a distance of 10.33 cm in 0.8 sec.) The wave generated and first shown 10 depths downstream appears to qonsist of a large wave followed by a series of oscillatory waves (termed the tail). As would be expected, as the waves propagate, due to the frequency content and the amplitude of the waves, the system separates into a leading wave followed some distance behind by the tail. The lead wave has the characteristic shape of a solitary wave. However, if the oscillatory tail is unacceptable for the type of experiments being conducted, and if it cannot be eliminated or the method of elimination is unacceptable, then a means of generation must be sought which eliminates the trailing waves initially.

A note on tsunamis: their generation and propagation in an ocean of uniform depth

The waves generated in a two-dimensional fluid domain of infinite lateral extent and uniform depth by a deformation of the bounding solid boundary are investigated both theoretically and experimentally. An integral solution is developed for an arbitrary bed displacement (in space and time) on the basis of a linear approximation of the complete (nonlinear) description of wave motion. Experimental and theoretical results are presented for two specific deformations of the bed; the spatial variation of each bed displacement consists of a block section of the bed moving vertically either up or down while the time-displacement history of the block section is varied. The presentation of results is divided into two sections based on two regions of the fluid domain: a generation region in which the bed deformation occurs and a downstream region where the bed position remains stationary for all time. The applicability of the linear approximation in the generation region is investigated both theoretically and experimentally; results are presented which enable certain gross features of the primary wave leaving this region to be determined when the magnitudes of parameters which characterize the bed displacement are known. The results indicate that the primary restriction on the applicability of the linear theory during the bed deformation is that the total amplitude of the bed displacement must remain small compared with the uniform water depth; even this restriction can be relaxed for one type of bed motion.Wave behaviour in the downstream region of the fluid domain is discussed with emphasis on the gradual growth of nonlinear effects relative to frequency dispersion duringpropagationand the subsequent breakdown of the linear theory. A method is presented for finding the wave behaviour in the far field of the downstream region, where the effects of nonlinearities and frequency dispersion have become about equal. This method is based on the use of a model equation in the far field (which includes both linear and nonlinear effects in an approximate manner) first used by Peregrine (1966) and morerecently advocated by Ben jamin, Bona & Mahony (1972) as a preferable model to the more commonly used equation of Korteweg & de Vries (1895). An input-output approach is illustrated for the numerical solution of this equation where the input is computed from the linear theory in its region of applicability. Computations are presented and compared with experiment for the case of a positive bed displacement where the net volume of the generated wave is finite and positive; the results demonstrate the evolution of a train of solitary waves (solitons) ordered by amplitude followed by a dispersive train of oscillatory waves. The case of a negative bed displacement in which the net wave volume is finite and negative (and the initial wave is negative almost everywhere) is also investigated; the results suggest that only a dispersive train of waves evolves (no solitons) for this case.

Blast-induced translational effects.

Abstract : A mathematical model was developed to predict the time displacement histories of objects translated by the blast winds from conventional or nuclear explosions; these predictions were then compared to actual experiments. The objects studied varied in size from 139 mg spheres to man and were all assumed to be free to move over a smooth horizontal surface. The effects of ground friction could either be included or neglected, but when they were considered the ground friction eventually brought the objects to rest after the winds had passed. The values of ground friction used were determined experimentally and were found to be functions of the velocity and mass of the object being displaced. The translational model was general enough for either classical or nonclassical blast waves to be considered. Results for a chemical explosion were obtained by using both the computed blast waves of various authors and the experimentally determined blast waves. These predicted results were compared with each other as well as with experimental data obtained with steel spheres. The model was used to determine dynamic pressure impulses necessary to explain the measured sphere velocities at three ranges from ground zero. Another mathematical model was briefly described which was developed to compute the detailed two-dimentional trajectories of objects as they roll, slide, and bounce along the ground. The model closely predicted the measured distances between bounces and the total displacements of concrete blocks and large stones and thus helped to explain the mechanisms of tumbling by which an irregular object may become airborne during both the accelerative and the decelerative phases of displacement.