Keywords: finite element, dynamic stiffness, beams, plates and shells, Wittrick-Williams algorithm.

Since its inception in the late fifties, the finite element method (FEM) has been wellrecognised as a break-through in solid mechanics. With the rapid growth of computing power, the FEM has become a universal tool which has occupied its rightful place in structural analysis and design. Many commercial packages based on the method are now readily available that are widely used by the academia and industry. Against this background, there appears to be an elegant and powerful alternative to the FEM for free vibration analysis of structures which has far superior modelling capability. This is the dynamic stiffness method (DSM) which, unlike the FEM, relies on the frequency dependent exact shape function of the structural element derived from its differential equation in free vibration. For the exactness of the shape function, the results obtained from the DSM are often called exact. In the DSM, separate mass and stiffness matrices are not derived, but a single frequency dependent element stiffness matrix which contains both the mass and stiffness properties of the element is utilised. Unlike the FEM, the results obtained from the DSM are independent of the number of elements used in the analysis. Despite its elegance and uncompromising accuracy, the DSM is still relatively unknown when compared with the FEM, but it has, nevertheless, made many inroads and has been successfully applied to investigate the free vibration problems of beams, plates, shells and their assemblies. The DSM literature is not as broad or diverse as the FEM. However, the DSM has matured sufficiently and reached a noteworthy stage which warrants the publication of a paper to elucidate its theory, practice and promise. Thus the essential purpose of this paper is to review the state of the art of the DSM and its applications, highlight many of the major advances made during its sustained period of developments over the years and to provide a vision for the future and challenges ahead.

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