This article presents closed-form solutions for the frequency analysis of rectangular functionally graded material (FGM) thin plates subjected to initially in-plane loads and with an elastic foundation. Based on class...This article presents closed-form solutions for the frequency analysis of rectangular functionally graded material (FGM) thin plates subjected to initially in-plane loads and with an elastic foundation. Based on classical thin plate theory, the governing differential equations are derived using Hamilton's principle. A neutral surface is used to eliminate stretching-bending coupling in FGM plates on the basis of the assumption of constant Poisson's ratio. The resulting governing equation of FGM thin plates has the same form as homogeneous thin plates. The separation-of-variables method is adopted to obtain solutions for the free vibration problems of rectangular FGM thin plates with separable boundary conditions, including, for example, clamped plates. The obtained normal modes and frequencies are in elegant closed forms, and present formulations and solutions are validated by comparing present results with those in the literature and finite element method results obtained by the authors. A parameter study reveals the effects of the power law index n and aspect ratio a/b on frequencies.展开更多
The present study aims to analyze free vibration of thin skew plates made of functionally graded material(FGM)by using the weak form quadrature element method.The material properties vary continuously through the thic...The present study aims to analyze free vibration of thin skew plates made of functionally graded material(FGM)by using the weak form quadrature element method.The material properties vary continuously through the thickness according to a power-law form.A novel FGM skew plate element is formulated according to the neutral surface based plate theory and with the help of the differential quadrature rule.For verifications,Numerical results are compared with available data in literature.Results reveal that the non-dimensional frequency parameters of the FGM skew plates are independent of the power-law exponent and always proportional to those of homogeneous isotropic ones when the coupling and rotary inertias are neglected.In addition,employing the physical neutral surface based plate theory is equivalent to using the middle plane based plate theory with the reduced flexural modulus matrix.展开更多
基金supported by the National Natural Science Foundation of China (Grants 11172028, 1372021)Research Fund for the Doctoral Program of Higher Education of China (Grant 20131102110039)the Innovation Foundation of Beihang University for PhD graduates
文摘This article presents closed-form solutions for the frequency analysis of rectangular functionally graded material (FGM) thin plates subjected to initially in-plane loads and with an elastic foundation. Based on classical thin plate theory, the governing differential equations are derived using Hamilton's principle. A neutral surface is used to eliminate stretching-bending coupling in FGM plates on the basis of the assumption of constant Poisson's ratio. The resulting governing equation of FGM thin plates has the same form as homogeneous thin plates. The separation-of-variables method is adopted to obtain solutions for the free vibration problems of rectangular FGM thin plates with separable boundary conditions, including, for example, clamped plates. The obtained normal modes and frequencies are in elegant closed forms, and present formulations and solutions are validated by comparing present results with those in the literature and finite element method results obtained by the authors. A parameter study reveals the effects of the power law index n and aspect ratio a/b on frequencies.
基金supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘The present study aims to analyze free vibration of thin skew plates made of functionally graded material(FGM)by using the weak form quadrature element method.The material properties vary continuously through the thickness according to a power-law form.A novel FGM skew plate element is formulated according to the neutral surface based plate theory and with the help of the differential quadrature rule.For verifications,Numerical results are compared with available data in literature.Results reveal that the non-dimensional frequency parameters of the FGM skew plates are independent of the power-law exponent and always proportional to those of homogeneous isotropic ones when the coupling and rotary inertias are neglected.In addition,employing the physical neutral surface based plate theory is equivalent to using the middle plane based plate theory with the reduced flexural modulus matrix.
文摘目的研究空气消毒剂中和剂鉴定试验方法。方法按照评价空气消毒效果的试验体系,用含中和剂的琼脂培养基平板置于六级安德森空气撞击式采样器内,采样后进行培养观察中和效果。结果含100 mg/L硫代硫酸钠的普通营养琼脂培养基对白色葡萄球菌的生长无影响。气雾室内按10 m l/m3用量气溶胶喷雾30 g/L浓度的过氧化氢溶液,喷雾后作用30 m in,用含100 mg/L硫代硫酸钠的普通营养琼脂平板置于采样器内采集空气200 L,培养后平板上白色葡萄球菌生长正常,说明残留消毒剂被有效中和。喷雾消毒剂后,空气采集量对中和效果有影响,本方法中采集量为≤200 L。结论按照评价空气消毒效果的试验体系,用六级筛孔空气撞击式采样器采样的中和剂鉴定方法能准确判断中和剂和中和产物对试验菌生长的影响,并能选择出有效的中和剂。
