A semi-analytical approach for solving forced vibration problems based on a convolution-type variational principle

In this paper a semi-analytical approach for solving forced vibration problems is developed which is based on Gurtin's convolution-type variational principle, where a finite element discretization in the space domain and a series representation in the time domain are considered. This approach overcomes the shortcomings of existing methods, yet utilizes their advantages for solving forced vibration problems. A beam example indicates that this new approach is a very effective method in obtaining solutions for forced vibration problems. The paper also concentrates on utilizing time domain series for various boundary conditions, in order that solutions calculated by this approach render a very high degree of accuracy and efficiency.