Study on Vibration and Buckling of Wedge Shaped Rod with Approximate Solutions of Second-Order Conjugate Equation
It was proved that any second-order linear equation with variable coefficients could be transformed into second-order conjugate linear equation.Approximate solutions of the second-order conjugate linear equation with large parameters were obtained by using the transformation of independent variable and dependent variable.And they are the modal function of the natural longitudinal vibration,torsional vibration,shear vibration and buck-ling of the wedge shaped rod.The characteristic equations for determining the frequencies of natural longitudinal vi-bration,torsional vibration,shear vibration and buckling load were derived by combining the modal function with the boundary conditions.The frequencies of natural longitudinal vibration,torsional vibration,shear vibration and buckling load could be obtained with solving the characteristic equation.Compared with Bessel function method in relevant literatures,the natural longitudinal vibration,torsional vibration,shear vibration frequency and buckling load obtained by approximate solutions of second-order conjugate linear equation,the method is simpler in the cal-culation process with high calculation accuracy,which is more suitable for engineering designers to master for appli-cation.
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维普
