Effects of Longitudinal Inertia Upon the Parametric Response of Elastic Columns

Abstract

Analytical and experimental investigations have been performed in a study of longitudinal inertia effects upon the parametric response of a column under an axial load P(t) = P0 + P1 cos γt. The analysis has led to stability criteria, imposed on the load and longitudinal inertia parameters, which have shown good agreement with experimental results. A certain degree of scatter between experimental runs has been observed, though agreement within (italics) each run has been very good. The scatter, attributed to small misalignments and departure from axiality of loading, stems from the realignment procedure necessary between each experimental run. To facilitate prediction of parametric response, the analytical stability criteria have been plotted in the form of two bounding surfaces of an instability region in a three-dimensional parameter space. Use of this region permits description of the conditions and responses associated with parametric instability, and allows evaluation of the effects of disturbances.

Parametric Instability of a Beam Under Electromagnetic Excitation

“…Iwatsubo et al [10] studied experimentally the simple and combination resonances of clamped}clamped and clamped simply supported columns under a periodic axial load. Evensen and Evan-Iwanowski [12] experimentally observed the principal simple resonance of an elastic simply supported column under a periodically axial end loading with the e!ects of longitudinal inertia. Handoo and Sundararajan [15] experimentally investigated the simple resonance of a cantilevered column with an end mass subjected to speci"ed axial motion at its "xed end.…”

“…Iwatsubo et al [9}11] examined numerically the parametric resonances of a beam with various boundary conditions under the excitation of a periodic axial or tangential loading at one end. Evensen and Evan-Iwanowski [12] investigated analytically the principal resonance of a simply supported column subjected to a periodic axial loading at one end; they discussed the e!ects of longitudinal inertia upon the parametric response of the column. Sato et al [13] studied the variation of the instability regions induced by the weight and position of a concentrated mass on a simply supported beam.…”

Failure of Elasto-Plastic Columns With Initial Crookedness in Parametric Resonance

“…em is the normalized strain when the normalized stress is taken equal to 2 in the second expression in Eq. (2). Fig.…”

“…(1) and Eq. (2). The curve by Yokoo and Nakamura is calculated by taking the normalized plastic strain amplitude ep=2 and the proposed curve is for e1=1.…”

Nonlinear dynamic response of beam and its application in nanomechanical resonator

“…The second one is to assume the uncoupling of the flexural displacement with axial one. In certain scenarios, the axial inertia effects are the dominant nonlinearity [28] and the coupling effects of flexural and axial displacements are very significant to the system dynamic response [43,44]. The uncoupling of flexural and axial displacement can only be valid when these two conditions are satisfied (1): shear and rotary inertia effects are negligible and (2): u = O(w 2 ) (u is axial displacement and w is flexural one) [27].…”