Segmented taper equation was selected to model stem profile of Dahurian larch （Larix gmelinii Rupr.）. The data were based on stem analysis of 74 trees from Dailing Forest Bureau in Heilongjiang Province, Northeaster...Segmented taper equation was selected to model stem profile of Dahurian larch （Larix gmelinii Rupr.）. The data were based on stem analysis of 74 trees from Dailing Forest Bureau in Heilongjiang Province, Northeastern China. Two taper equations with crown ratio and stand basal area were derived from the Max and Burkhart’s （1976） taper equation. Three taper equations were evaluated： （1） the original equation, （2） the original equation with crown ratio, and （3） the original equation with basal area. SAS NLIN and SYSNLIN procedures were used to fit taper equations. Fit statistics and cross-validation were used to evaluate the accuracy and precision of these models. Parameter estimates showed that the original equation with inclusion of crown ratio and basal area variables provided significantly different parameter estimates with lower standard errors. Overall fit statistics indicated that the root mean square error （RMSE） for diameter outside and inside bark decreased respectively by 10% and 7% in the original model with crown ratio and by 12% and 7.2% in the original model with basal area. Cross-validation further confirmed that the original equation with inclusion of crown ratio and basal area variables provided more accurate predictions at the lower section （relative heights, 10%） and upper section （relative heights, 50%） for both outside and inside bark diameters.展开更多
The present analysis demonstrates the thermal effect on vibrations of a symmetric, non-homoge- neous trapezoidal plate with parabolically varying thickness in both directions. The variation in Young’s modulus and mas...The present analysis demonstrates the thermal effect on vibrations of a symmetric, non-homoge- neous trapezoidal plate with parabolically varying thickness in both directions. The variation in Young’s modulus and mass density is the main cause for the occurrence of non-homogeneity in plate’s material. In this consideration, density varies linearly in one direction. The governing differential equations have been derived by Rayleigh-Ritz method in order to attain fundamental frequencies. With C-S-C-S boundary condition, a two term deflection function has been considered. The effect of structural parameters such as taper constants, thermal gradient, aspect ratio and non-homogeneity constant has been investigated for first two modes of vibration. The obtained numerical results have been presented in tabular and graphical form.展开更多
The main aim of the present work is to study the linear temperature behaviour of a non-homogeneous trapezoidal plate whose thickness varies linearly in both directions. The temperature behaviour considered linear alon...The main aim of the present work is to study the linear temperature behaviour of a non-homogeneous trapezoidal plate whose thickness varies linearly in both directions. The temperature behaviour considered linear along the length of the plate. Non-homogeneity in plate arises due to variation in density along the length of the plate. The two-term deflection function with clamped-simply supported-clamped-simply supported boundary condition is taken into consideration. The effect of structural parameters such as taper constants, thermal gradient, non-homogeneity constant and aspect ratio has been studied. Rayleigh-Ritz method is used to solve the governing differential equations and to obtain the fundamental frequencies for the first two modes of vibration. Results are presented in graphical form.展开更多
基金This study was supported by the National Natural Science Foundation of China(30972363)Special Fund for For-estry-Scientific Research in the Public Interest(201004026)+2 种基金China Postdoctoral Science Foundation(200902362,20100471014)the Fun-damental Research Funds for the Central Universities(DL10CA06)SRF for ROCS,SEM.
文摘Segmented taper equation was selected to model stem profile of Dahurian larch （Larix gmelinii Rupr.）. The data were based on stem analysis of 74 trees from Dailing Forest Bureau in Heilongjiang Province, Northeastern China. Two taper equations with crown ratio and stand basal area were derived from the Max and Burkhart’s （1976） taper equation. Three taper equations were evaluated： （1） the original equation, （2） the original equation with crown ratio, and （3） the original equation with basal area. SAS NLIN and SYSNLIN procedures were used to fit taper equations. Fit statistics and cross-validation were used to evaluate the accuracy and precision of these models. Parameter estimates showed that the original equation with inclusion of crown ratio and basal area variables provided significantly different parameter estimates with lower standard errors. Overall fit statistics indicated that the root mean square error （RMSE） for diameter outside and inside bark decreased respectively by 10% and 7% in the original model with crown ratio and by 12% and 7.2% in the original model with basal area. Cross-validation further confirmed that the original equation with inclusion of crown ratio and basal area variables provided more accurate predictions at the lower section （relative heights, 10%） and upper section （relative heights, 50%） for both outside and inside bark diameters.
文摘The present analysis demonstrates the thermal effect on vibrations of a symmetric, non-homoge- neous trapezoidal plate with parabolically varying thickness in both directions. The variation in Young’s modulus and mass density is the main cause for the occurrence of non-homogeneity in plate’s material. In this consideration, density varies linearly in one direction. The governing differential equations have been derived by Rayleigh-Ritz method in order to attain fundamental frequencies. With C-S-C-S boundary condition, a two term deflection function has been considered. The effect of structural parameters such as taper constants, thermal gradient, aspect ratio and non-homogeneity constant has been investigated for first two modes of vibration. The obtained numerical results have been presented in tabular and graphical form.
文摘The main aim of the present work is to study the linear temperature behaviour of a non-homogeneous trapezoidal plate whose thickness varies linearly in both directions. The temperature behaviour considered linear along the length of the plate. Non-homogeneity in plate arises due to variation in density along the length of the plate. The two-term deflection function with clamped-simply supported-clamped-simply supported boundary condition is taken into consideration. The effect of structural parameters such as taper constants, thermal gradient, non-homogeneity constant and aspect ratio has been studied. Rayleigh-Ritz method is used to solve the governing differential equations and to obtain the fundamental frequencies for the first two modes of vibration. Results are presented in graphical form.
