Fundamental frequencies of bidirectional functionally graded sandwich beams partially supported by foundation using different beam theories

Abstract

Investigation on the influence of beam theory and partial foundation support on natural frequencies play an important role in design of structures. In this paper, fundamental frequencies of a bidirectional functionally graded sandwich (BFGSW) beam partially supported by an elastic foundation are evaluated using various beam theories. The core of the sandwich beam is homogeneous while its two face sheets are made from three distinct materials with material properties varying in both the length and thickness directions by power gradation laws. The finite element method is employed to derive equation of motion and to compute the frequencies of the beam. The effects of the material gradation, the foundation parameters and the span to height ratio on the frequencies are studied in detail and highlighted. The difference of the frequencies obtained by different beam theories is also examined and discussed. The numerical results of the paper are useful in designing BFGSW beams with desired fundamantal frequencies.