zbMATH — the first resource for mathematics

On the discretization of weakly nonlinear spatially continuous systems. (English) Zbl 0855.73042
Kliemann, Wolfgang (ed.) et al., Nonlinear dynamics and stochastic mechanics. Dedicated to Prof. S. T. Ariaratnam on the occasion of his sixtieth birthday. Boca Raton, FL: CRC Press. CRC Mathematical Modelling Series. 175-200 (1995).
Summary: Methods for the study of weakly nonlinear continuous (distributed-parameter) systems are discussed. Approximate solution procedures based on discretization via the Galerkin method are contrasted with direct application of the method of multiple scales to the governing partial-differential equations and boundary conditions. By means of several examples, it is shown that discretization of nonlinear continuous systems can lead to erroneous results if the discretization is not performed by using a complete set of basis functions that satisfy the boundary conditions.
For the entire collection see [Zbl 0847.00042].

74H45 Vibrations in dynamical problems in solid mechanics
74S99 Numerical and other methods in solid mechanics