由基模态构造任意支撑杆的多项式型轴向刚度

给出了当杆的横截面积均匀而材料线密度为已知多项式时，由基模态构造任意支撑方式下杆的多项式型的轴向刚度系致的方法，证明了所得轴向刚度的正值性．

CONSTRACTING THE AXIAL STIFFNESS OF ARBITRARY SUPPORTED ROD FROM FUNDAMENTAL MODE SHAPE

As the non-uniform rods possessing non-homogeneous material density and elastic modulus along their axis, are widely applied in engineering, it is necessary to study free vibration of non-uniform rods. In this paper we have investigated the constructing method of the axial stiffness in polynomial form for arbitrary supported rod with homogeneous cross-section from the fundamental mode and corresponding frequency when rods density distribution in polynomial form is given. And the obtained elastic modulus is proved positive. Above given fundamental mode is proportional to the static displacement of the uniform rod under the constant loading. The supported forms include clamped-free and spring support in Particular, clamped-spring support, clamped-clamped and clamped-free rods are discussed. The results show that the paper 1] may be regarded a special example of this paper.