Master Dynamic Stability Formula for Structural Members Subjected to Periodic Loads

Abstract

Nomenclature G = system geometric stiffness matrix K = system stiffness matrix M = system mass matrix N = axial or in-plane compressive periodic load N cr = buckling load N s = constant part of N N t = periodic part of N = N s =N cr = N t =N cr fg = as given in Eq. (7) f 1 g = eigenvector of the dynamic stability problem f 2 g = eigenvector of the free vibration problem f 3 g = eigenvector of the buckling problem = radian frequency of N t = as defined in Eq. (12) = =! ! = natural radian frequency

Study of dynamic stability of simply supported beams on Pasternak foundation considering the effect of first transition foundation parameter

“…It is shown intuitively in this study that the dynamic stability curves obtained with the use of suitable nondimensional parameters, are the same, for any specified boundary conditions of the beam if the stability and vibration mode shapes are similar. In [3], it is proposed that these nondimensional parameters can be derived rigorously, and the existence of master dynamic instability curves, valid for any structural member, boundary condition and with complicating effects, is demonstrated for most of the structural members. If the requirement of the exactness of the mode shapes, but not the similarity as mentioned in [2], to obtain the master dynamic stability curves is violated, the error involved in the analysis is dependent on the deviation of these mode shapes and can be assessed by calculating the corresponding L 2 norms [4].…”

Prediction of dynamic stability behavior of thin square plates subjected to constant compressive and periodic including constant compressive loads on perpendicular edges

“…Some recent studies in this topic for plates subjected to periodic loading can be seen in (Dey and Singha, 2006), (Ramachandran and Sarat Kumar, 2012). In a recent study (Rao et al, 2008), it is shown that these nondimensional parameters used in (Brown et al 1968), can be derived rigorously and demonstrated the existence of the unique dynamic stability curves for many commonly used structural members, provided the requirement on the mode shapes (Brown et al 1968) is satisfied. It may be emphasized here that, these mode shapes, though similar as mentioned earlier (Brown et al 1968), differ by small extent depending on the boundary conditions and the error involved in the instability boundaries is tolerable small, for the engineering purposes, as has already been demonstrated by (Rao et al, 2011), based on the consideration of the Euclidean norm.…”