附加连续荷载梁的横向振动方程的特征值问题

Eigenvalue Problems for Crosswise Vibration Equation of the Beam with Continuous Load

本文研究了附加连续荷载梁的横向振动方程的特征值及特征函数的性质。在一定的假设之下,附加连续荷载梁的横向振动方程对应一个微分–积分方程。对于此方程,在较弱的条件下,通过求解泛函的变分问题,得到极小函数和特征值存在性,并证明了特征值的单调性及无界性。借助Hilbert空间的理论证明了特征函数的正交性与完备性。

Concerned in this paper are the eigenvalues and the corresponding eigenfunctions for the crosswise vibration equation of a bean with continuous load, which can be related to a differentialintegral equation. By the variation method, the existence of the minimization function and the eigenvalues are given under some weak conditions, the monotonicity and the unboundness of the eigenvalues are given as well. The orthogonality and completeness of the eigenfunctions are proved according to certain theories of Hilbert space.