The main objective of the present investigation is to study the vibration of visco-elastic parallelogram plate whose thickness varies parabolically. It is assumed that the plate is clamped on all the four edges and th...The main objective of the present investigation is to study the vibration of visco-elastic parallelogram plate whose thickness varies parabolically. It is assumed that the plate is clamped on all the four edges and that the thickness varies parabolically in one direction i.e. along length of the plate. Rayleigh-Ritz technique has been used to determine the frequency equation. A two terms deflection function has been used as a solution. For visco-elastic, the basic elastic and viscous elements are combined. We have taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here the elastic element means the spring and the viscous element means the dashpot. The assumption of small deflection and linear visco-elastic properties of “Kelvin” type are taken. We have calculated time period and deflection at various points for different values of skew angles, aspect ratio and taper constant, for the first two modes of vibration. Results are supported by tables. Alloy “Duralumin” is considered for all the material constants used in numerical展开更多
In this paper, the effect of thermal gradient on the vibration of parallelogram plate with linearly varying thickness in both direction having clamped boundary conditions on all the four edges is analyzed. Thermal eff...In this paper, the effect of thermal gradient on the vibration of parallelogram plate with linearly varying thickness in both direction having clamped boundary conditions on all the four edges is analyzed. Thermal effect on vibration of such plate has been taken as one-dimensional distribution in linear form only. An approximate but quiet convenient frequency equation is derived using Rayleigh-Ritz technique with a two-term deflection function. The frequencies corresponding to the first two modes of vibration of a clamped parallelogram plate have been computed for different values of aspect ratio, thermal gradient, taper constants and skew angle. The results have been presented in tabular forms. The results obtained in this study are reduced to that of unheated parallelogram plates of uniform thickness and have generally been compared with the published one.展开更多
文摘The main objective of the present investigation is to study the vibration of visco-elastic parallelogram plate whose thickness varies parabolically. It is assumed that the plate is clamped on all the four edges and that the thickness varies parabolically in one direction i.e. along length of the plate. Rayleigh-Ritz technique has been used to determine the frequency equation. A two terms deflection function has been used as a solution. For visco-elastic, the basic elastic and viscous elements are combined. We have taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here the elastic element means the spring and the viscous element means the dashpot. The assumption of small deflection and linear visco-elastic properties of “Kelvin” type are taken. We have calculated time period and deflection at various points for different values of skew angles, aspect ratio and taper constant, for the first two modes of vibration. Results are supported by tables. Alloy “Duralumin” is considered for all the material constants used in numerical
文摘In this paper, the effect of thermal gradient on the vibration of parallelogram plate with linearly varying thickness in both direction having clamped boundary conditions on all the four edges is analyzed. Thermal effect on vibration of such plate has been taken as one-dimensional distribution in linear form only. An approximate but quiet convenient frequency equation is derived using Rayleigh-Ritz technique with a two-term deflection function. The frequencies corresponding to the first two modes of vibration of a clamped parallelogram plate have been computed for different values of aspect ratio, thermal gradient, taper constants and skew angle. The results have been presented in tabular forms. The results obtained in this study are reduced to that of unheated parallelogram plates of uniform thickness and have generally been compared with the published one.
