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Free longitudinal vibrations of bimodular beams: a comparative study

Denis Kharenko, Cristina Padovani, Andrea Pagni, Giuseppe Pasquinelli, Leonid Semin

Nonlinear dynamics  Building and Construction  Ocean Engineering  Civil and Structural Engineering  Numerical solutions  Exact solutions  Aerospace Engineering  Mechanical Engineering  Applied Mathematics  Bimodular material 

In this paper, we consider the problem of the free longitudinal vibrations of a beam made of a bimodular material, i.e. an elastic material whose in-tension Young's modulus is a fraction of that under compression. After recalling the exact solutions for an infinite beam and for a beam with fixed ends calculated via the characteristics method, we apply high-resolution methods based on the finite-element approach to solve the nonlinear equation of the motion. In particular, we compare the exact solutions with the numerical solutions calculated using the collocation and least-squares method developed in the present study, the space-time element method, as well as total variation diminishing (TVD) and Newmark methods.

Source: International journal of structural stability and dynamics. 11 (2011): 23–56. doi:10.1142/S0219455411003975

Publisher: World Scientific,, Singapore , Singapore


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BibTeX entry
	title = {Free longitudinal vibrations of bimodular beams: a comparative study},
	author = {Denis Kharenko and Cristina Padovani and Andrea Pagni and Giuseppe Pasquinelli and Leonid Semin},
	publisher = {World Scientific,, Singapore , Singapore},
	doi = {10.1142/s0219455411003975},
	journal = {International journal of structural stability and dynamics.},
	volume = {11},
	pages = {23–56},
	year = {2011}