In this paper, a simple and efficient method is presented to determine the natural frequencies of non-uniform Bernoulli-Euler beams resting on non-uniform elastic foundation with general elastic end restraints. The frequency equation of the system is derived and concisely expressed in terms of four normalized fundamental solutions of the governing characteristic differential equation. These four fundamental solutions can be obtained through a newly developed algorithm which has been demonstrated to be efficient, convenient and accurate. Several limiting cases of the general system are examined. The influence of elastic end restraints, non-uniformity of bending rigidity and elastic foundation on the natural frequencies is examined.
All Science Journal Classification (ASJC) codes
- Civil and Structural Engineering
- Modelling and Simulation
- Materials Science(all)
- Mechanical Engineering
- Computer Science Applications