• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.1
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• pp.56-63
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• 2004

Exact solutions are presented for the free vibration and buckling of rectangular plates haying two opposite edges ( x=0 and a) simply supported and the other two ( y=0 and b) clamped, with the simply supported edges subjected to a linearly varying normal stress $\sigma$$_{x}$=- $N_{0}$[1-a(y/b)]/h, where h is the plate thickness. By assuming the transverse displacement ( w) to vary as sin(m$\pi$x/a), the governing partial differential equation of motion is reduced to an ordinary differential equation in y with variable coefficients. for which an exact solution is obtained as a power series (the method of Frobenius). Applying the clamped boundary conditions at y=0 and byields the frequency determinant. Buckling loads arise as the frequencies approach zero. A careful study of the convergence of the power series is made. Buckling loads are determined for loading parameters a= 0, 0.5, 1, 1.5. 2, for which a=2 is a pure in-plane bending moment. Comparisons are made with published buckling loads for a= 0, 1, 2 obtained by the method of integration of the differential equation (a=0) or the method of energy (a=1, 2). Novel results are presented for the free vibration frequencies of rectangular plates with aspect ratios a/b =0.5, 1, 2 when a=2, with load intensities $N_{0}$ / $N_{cr}$ =0, 0.5, 0.8, 0.95, 1. where $N_{cr}$ is the critical buckling load of the plate. Contour plots of buckling and free vibration mode shapes ate also shown.shown.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.34 no.2
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• pp.515-527
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• 2014

This study conducted experiment for understanding engineering characteristics of domestic sands by examining standard sand and sand from Yokji Island and Nakdong River in terms of confining pressure, $K_0$, over consolidation and relative density factors through triaxial compression test. The test showed that deviator stress by strain positively changed as confining pressure and relative density grow while $K_0$ and over consolidation factors do not directly correlated with it. Angle of internal friction decreases as confining pressure increases which strengthens contact force between particles, and declines as relative density drops, whereas $K_0$ and over consolidation factors hardly affect the results. When it comes to volumetric strain, volume expansion decreases as confining pressure increase due to crushability and rearrangement of particles while $K_0$ and over consolidation shows same movement unconditionally, and relative density appears compressed as it grows at the beginning however it expands as axial strain increases. Modulus of elasticity ($E_{sec}$) by strain has tendency into convergence resulting in initial secant modulus of elasticity ($E_{ini}$) > secant modulus of elasticity($E_{sec}$) > tangent modulus of elasticity ($E_{tan}$). On the other hand, it grows as confining pressure and relative density increase while indicating similar modulus of elasticity ($E_{sec}$) regarding on $K_0$ and over consolidation. Slope of critical line (M) tended to decrease as confining pressure increases, follow same line according to $K_0$, confining pressure and relative density, and increase as relative density grows.