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In existent methods of analysis of stability of bars with continuously varying cross section, only the stability of several kinds of bars with particular shapes can be analyzed. Euler discussed columns of shapes, including a truncated cone and pyramid. The stability of bars bounded by a surface of revolution of the second degree was discussed by Lagrange. In this paper a general differential equation of matrix with variable coefficient is derived for analysis of stability of various bars with continuously varying cross section. By means of this equation the stability of the various bars with continuously varying cross section and different constraints at ends can be analyzed.

Analysis of Stability of Bars with Continuously Varying Cross Section by Means of Differential Equation of Matrix