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Dynamic Formulation of Stiffness Matrix for Free Vibration Analysis


Roundal Vijay Baburao , Ph. D. Scholar at Shri Jagdish Prasad Jhabarmal Tibrewala University, Chudela, Dist: Jhunjhunu, Rajasthan; Dr. Kashinath Haribhau Munde, Professor in Mechanical Engineering Department at ABMSPs Anantrao Pawar College of Engineering & Research, Parvati, Pune, Maharashtra, India


Dynamic Stiffness Matrix, FEM, Free Vibration, Penalty Method, Wittrick-Williams Algorithm


The Wittrick–Williams algorithm is used as the solution technique when applying the dynamic stiffness matrix to compute the natural frequencies and mode shapes. This paper aims at the study of free vibration analysis investigated with the help of dynamic stiffness method. Research Papers having algorithm for computing natural frequencies of Elastic Structures and Dynamic Stiffness formulation are reviewed for free vibration analysis. Different paper discusses algorithm for determining the natural undamped frequencies of vibration of any linearly elastic structure. Finite Element Method is an approximate method, results of which cannot be guaranteed but it generally converges to the exact solution with increasing number of elements. Dynamic stiffness method retains all features of FEM but it is more accurate solution compared to FEM. Both techniques have different techniques where FEM uses linear Eigen Value problems and DSM uses non-linear Eigen Value problems which are solved by Wittrick–Williams algorithm.

Other Details

Paper ID: IJSRDV8I90002
Published in: Volume : 8, Issue : 9
Publication Date: 01/12/2020
Page(s): 1-5

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