Free vibration of SDOF systems with arbitrary time-varying coefficients
The author presents a new exact approach for analyzing free vibrations of single-degree-of-freedom (SDOF) system with one-step and multi-step nonperiodically varying mass and stiffness coefficients. The variation of mass with time is arbitrary, but the variation of stiffness is connected by a functional dependence with the mass variation. Using an appropriate functional transformations, the author reduces the governing differential equation to Bessel equation or to an ordinary differential equation with constant coefficients for six important particular cases. In order to simplify the free vibration analysis for multi-step time-varying coefficients, the author constructs fundamental solutions that satisfy some normalization conditions. The displacement response of SDOF systems is then determined by using these fundamental solutions and a recurrence formula. Numerical examples show that the proposed procedure is simple, efficient and exact.
ordinary differential equation with constant coefficients
scientific article; zbMATH DE number 1559218