Approximate natural vibration analysis of rectangular plates with openings using assumed mode method

ABSTRACTNatural vibration analysis of plates with openings of different shape represents an important issue in naval architecture and ocean engineering applications. In this paper, a procedure for vibration analysis of plates with openings and arbitrary edge constraints is presented. It is based on the assumed mode method, where natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion. The presented solution represents an extension of a procedure for natural vibration analysis of rectangular plates without openings, which has been recently presented in the literature. The effect of an opening is taken into account in an intuitive way, i.e. by subtracting its energy from the total plate energy without opening. Illustrative numerical examples include dynamic analysis of rectangular plates with rectangular, elliptic, circular as well as oval openings with various plate thicknesses and different combinations of boundary conditions. The results are compared with those obtained by the finite element method (FEM) as well as those available in the relevant literature, and very good agreement is achieved

Vaccine effectiveness and the epidemiological characteristics of a COVID-19 outbreak in a tertiary hospital in Republic of Korea

Objectives Healthcare facilities are high-risk sites for infection. This study analyzed the epidemiological characteristics of a coronavirus disease 2019 (COVID-19) outbreak in a tertiary hospital after COVID-19 vaccination had been introduced in Republic of Korea. Vaccine effectiveness (VE) and shared anti-infection strategies are also assessed. Methods The risk levels for 4,074 contacts were evaluated. The epidemiological characteristics of confirmed cases were evaluated using the chi-square test. The “1 minus relative risk” method was used to determine VE in preventing infection, progression to severe disease, and death. In the largest affected area (the 8th floor), a separate relative risk analysis was conducted. A multivariate logistic regression analysis (with 95% confidence interval [CIs]) was used to identify transmission risk factors with a significance level <10% via the backward elimination method. Results In total, 181 cases of COVID-19 were confirmed, with an attack rate of 4.4%. Of those cases, 12.7% progressed to severe disease, and 8.3% died. In the cohort isolation area on the 8th floor, where 79.0% of the confirmed cases occurred, the adjusted odds ratio was 6.55 (95% CI, 2.99–14.33) and 2.19 (95% CI, 1.24–3.88) for caregivers and the unvaccinated group, respectively. VE analysis revealed that 85.8% of the cases that progressed to severe disease and 78.6% of the deaths could be prevented by administering a second vaccine. Conclusion Caregiver training for infection prevention and control is necessary to reduce infection risk. Vaccination is an important intervention to reduce the risk of progression to severe disease and death

Simplified Procedure For The Free Vibration Analysis Of Rectangular Plate Structures With Holes And Stiffeners

Thin and thick plates, plates with holes, stiffened panels and stiffened panels with holes are primary structural members in almost all fields of engineering: civil, mechanical, aerospace, naval, ocean etc. In this paper, a simple and efficient procedure for the free vibration analysis of such elements is presented. It is based on the assumed mode method and can handle different plate thickness, various shapes and sizes of holes, different framing sizes and types as well as different combinations of boundary conditions. Natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange’s equations. Mindlin theory is applied for a plate and Timoshenko beam theory for stiffeners. The applicability of the method in the design procedure is illustrated with several numerical examples obtained by the in-house developed code VAPS. Very good agreement with standard commercial finite element software is achieved

Numerical procedure for the vibration analysis of arbitrarily constrained stiffened panels with openings

A simple and efficient vibration analysis procedure for stiffened panels with openings and arbitrary boundary conditions based on the assumed mode method is presented. Natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion, where Mindlin theory is applied for plate and Timoshenko beam theory for stiffeners. The effect of stiffeners on vibration response is taken into account by adding their strain and kinetic energies to the corresponding plate energies whereas the strain and kinetic energies of openings are subtracted from the plate energies. Different stiffened panels with various opening shapes and dispositions for several combinations of boundary conditions are analyzed and the results show good agreement with those obtained by the finite element analysis. Hence, the proposed procedure is especially appropriate for use in the preliminary design stage of stiffened panels with openings

Numerical procedure for the vibration analysis of arbitrarily constrained stiffened panels with openings

ABSTRACTA simple and efficient vibration analysis procedure for stiffened panels with openings and arbitrary boundary conditions based on the assumed mode method is presented. Natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion, where Mindlin theory is applied for plate and Timoshenko beam theory for stiffeners. The effect of stiffeners on vibration response is taken into account by adding their strain and kinetic energies to the corresponding plate energies whereas the strain and kinetic energies of openings are subtracted from the plate energies. Different stiffened panels with various opening shapes and dispositions for several combinations of boundary conditions are analyzed and the results show good agreement with those obtained by the finite element analysis. Hence, the proposed procedure is especially appropriate for use in the preliminary design stage of stiffened panels with openings