Effect of in-plane boundary conditions on forced vibration analysis of stiffened plates with a free edge

Abstract

This paper undertakes a large amplitude forced vibration analysis of stiffened plates with free edges under harmonic excitation through a numerical method. The methodology adopted is an indirect one in which the dynamic system is assumed to satisfy the force equilibrium condition at peak excitation amplitude. Free vibration analysis at the deflected configuration of the same system is also carried out separately to determine the backbone curves. The mathematical formulation is based on energy principles and the governing equations in both forced and free vibration cases are derived using Hamilton’s principle. The set of nonlinear governing equations is solved by employing an iterative direct substitution method with an appropriate relaxation technique. A multidimensional quasi-Newton method, known as Broyden’s method, is separately used when the system becomes computationally stiff. The results for a reduced system are validated with the published results of other researchers. For different combinations of boundary conditions including free edge results are furnished in the dimensionless amplitude-frequency plane. The effect of in-plane end conditions is studied by considering immovable and movable edges. Response in the vicinity of the second mode is also studied. Three dimensional operational deflection shape plots along with contour plots are also provided in a few cases.