Coupled Free Vibrations of Liquid in a Three-Dimensional Rectangular Container with an Elastic Cover

The coupled free vibration of liquid and its elastic cover, such as a plate or a membrane, in a three-dimensional rectangular tank is investigated through an analytical scheme based on velocity potential theory for the flow and the linear elastic theory for the cover. For the fluid domain, the velocity potential is expanded into double cosine series along the longitudinal and transverse direction respectively, with the corresponding eigenvalues determined from the impermeable conditions on the side walls. The vertical modes of the potential are obtained from the Laplace equation. The deflection of rectangular cover is expanded into the same double cosine series to match the potential, together with additional terms for satisfying the edge conditions. The polynomials are used for these additional terms which are then expanded into cosine series. For the expansions of the higher-order derivatives of the deflection, the derivatives of these polynomial terms are expanded into cosine series directly, rather than being obtained through differentiating the cosine series of the deflection, to avoid the non-convergent series. Through imposing the boundary conditions on the fluid-plate interface and edge conditions, an infinite matrix equation for the unknown coefficients can be established. The natural frequencies can be obtained when the determinant of the matrix is zero. In practical computation, the infinite matrix equation is truncated into finite size. Results are first provided for natural frequencies. This is followed by the corresponding natural mode shapes and principal strains distribution on the cover. The underlying physics of these results are then provided

The annual cycle, intraseasonal oscillations, and roadblock to seasonal predictability of the Asian summer monsoon

Factors responsible for limited predictability of the Asian summer monsoon (ASM) are investigated within a conceptual framework for predictability. Predictability of the seasonal mean depends on the interannual variability (IAV) of the monsoon annual cycle (MAC) and is determined by relative contribution of the predictable "external" component of IAV compared to the unpredictable "internal" IAV. Contributions of slow processes such as those involving air-sea interactions associated with the El Nino-Southern Oscillation (ENSO) or local warm ocean-atmosphere interactions in generating IAV of the MAC are reviewed. Empirical evidence that these air-sea interactions modulate the MAC is presented. Estimates of internal IAV have been made from observations as well as atmospheric model simulations. In contrast to a large part of the Tropics where the summer climate is predictable, with the internal variability being much smaller than the external one, the limited predictability of the Asian monsoon appears to be due to the fact that the contribution from the external IAV over the region is relatively weak and comparable to that from internal IAV. Cause for large internal IAV over the ASM region is investigated, and it is proposed that the internal IAV of the MAC is primarily due to interaction between the MAC and the summer intraseasonal oscillations (ISOs). Two mechanisms through which ISOs lead to internal IAV of the MAC are unraveled. The seasonal bias of the ISO anomalies can influence the seasonal mean if the spatial structure of the ISO has significant projection on that of the seasonal mean and if frequency of occurrence of positive and negative phases is unequal. Evidence supporting this is presented. In addition, it is demonstrated that the chaotic summer ISOs modulated by the annually varying forcing associated with the "slow annual cycle" can lead to IAV of the seasonal mean. Empirical evidence that IAV of ISO activity is related to IAV of the seasonal mean or MAC is also presented. Thus, the Asian monsoon would remain a difficult system to predict. To exploit the predictable signal, however, it is imperative that systematic bias of the models is improved and the space-time structure of the summer ISOs is simulated accurately

Consolidation Theory for a Stone Column Composite Foundation under Multistage Loading

The consolidation theories considering instant load cannot fully reveal the consolidation mechanism of a stone column composite foundation used in the expressway embankments due to the time effect of loading; that is, the expressway embankments are often constructed in several stages for a long time. Meanwhile, owing to the special property that the pile-soil stress ratio is larger than 1, the consolidation theory for sand drain well foundation cannot be used directly in the consolidation analysis of stone column composite foundation. Based on the principle that the vertical load applied on the composite foundation is shared by the stone column and the surrounding soil, the governing solutions for the stone column composite foundation under a multistage load are established. By virtue of the separation of variables, the corresponding solutions of degree of consolidation for loading stage and maintaining load stage are derived separately. According to the Carrillo theorem, the solution for the average total degree of consolidation of entire composite foundation is also obtained. Finally, the reasonableness of the present solution has been verified by comparing the consolidation curve calculated by the present solution with that measured by site test

Disaster Risks Research and Assessment to Promote Risk Reduction and Management

Natural hazard events lead to disasters when the events interact with exposed and vulnerable physical and social systems. Despite significant progress in scientific understanding of physical phenomena leading to natural hazards as well as of vulnerability and exposure, disaster losses due to natural events do not show a tendency to decrease. This tendency is associated with many factors including increase in populations and assets at risk as well as in frequency and/or magnitude of natural events, especially those related to hydro-meteorological and climatic hazards. But essentially disaster losses increase because some of the elements of the multidimensional dynamic disaster risk system are not accounted for risk assessments. A comprehensive integrated system analysis and periodic assessment of disaster risks at any scale, from local to global, based on knowledge and data/information accumulated so far, are essential scientific tools that can assist in recognition and reduction of disaster risks. This paper reviews and synthesizes the knowledge of natural hazards, vulnerabilities, and disaster risks and aims to highlight potential contributions of science to disaster risk reduction (DRR) in order to provide policy-makers with the knowledge necessary to assist disaster risk mitigation and disaster risk management (DRM)