Parametric resonance analysis of rectangular plates subjected to moving inertial loads via IHB method

• Published in: International journal of mechanical sciences Vol. 142-143; pp. 191 - 215
• Main Authors: Pirmoradian, Mostafa, Torkan, Ehsan, Karimpour, Hossein
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2018
• Subjects: Extended Hamilton's principle; Incremental harmonic balance method; Parametric resonance; Plate–moving mass interaction; Time-varying systems; Plate–moving mass interaction; Extended Hamilton's principle; Incremental harmonic balance method; Time-varying systems; Parametric resonance
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2018.04.047

•The parametric resonance phenomenon of rectangular plates induced by moving mass excitation is examined.•All inertial components of the moving masses are included in the analyses.•Different loading trajectories and various boundary conditions are taken into account in the analyses.•The emergence of instability tongues is detected in the parameter plane.•Conditions for the coexistence of periodic solutions are investigated.•The mechanism of instability is explored according to the work done by the successive entrances and exits of the external loading. This paper deals with the induced instability due to parametric resonance of rectangular plates traversed by inertial loads and lying on elastic foundations. The extended Hamilton's principle is employed to derive the partial differential equation associated with the transverse motion of the plate. Subsequently, this equation is transformed into a set of ordinary differential equations by the Galerkin method. Including vertical, centripetal and Coriolis acceleration terms related to the moving mass transition in the analysis leads to governing equations with time-varying mass, damping and stiffness coefficients. Particularly, the intermittent passage of masses along rectilinear paths, or the motion of an individual mass along an orbiting path, permits to subcategorize the problem as a parametrically excited system with periodic coefficients. By applying the incremental harmonic balance (IHB) method, the stability of the induced plate vibrations is investigated, revealing an emersion of instability tongues in the parameters plane. Semi-analytical results are provided for various boundary conditions of the plate which got verified through direct numerical simulations and other results reported in the literature. [Display omitted]