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Showing 2 results for Incremental Harmonic Balance Method
Ehsan Torkan, Mostafa Pirmoradian, Mohamad Hashemian,
Volume 17, Issue 9 (11-2017)
Abstract
In this paper, instability due to occurrence of parametric resonance in transverse vibration of a rectangular plate on an elastic foundation under passage of continuous series of moving masses is examined as a model of bridge-moving loads interaction. The extended Hamilton’s principle is employed to derive the partial differential equation of motion. Subsequently, the governing partial differential equation is transformed into a set of ordinary differential equations by the Galerkin procedure. Considering local, Coriolis and centripetal acceleration components of the moving masses in the analysis leads to appearance of time-varying mass, damping and stiffness matrices in the coefficients of the governing equation. The passage of continuous series of moving masses along the rectilinear path results in a parametrically excited system with periodic coefficients. Applying incremental harmonic balance method as a semi-analytical method to the governing equations, stability of the system is investigated for a wide range of masses and velocities of the passing loads and different boundary conditions of the plate. Moreover, effect of the foundation stiffness on stability of the plate is examined. Results indicate that using clamped supports for the edges of entrance and departure of masses over the plate’s surface leads to formation of an instability tongue in the parameters plane which does not appear for the case of using simply supports. Also, it is observed that critical velocities of the moving masses will be increased by escalation the foundation stiffness. Numerical simulations confirm the accuracy of the semi-analytical results.
E. Torkan, M. Pirmoradian, M. Hashemian,
Volume 19, Issue 9 (9-2019)
Abstract
In this paper, the dynamic stability of a moderately thick rectangular plate carrying an orbiting mass and lying on a visco-elastic foundation is studied. Considering all inertial terms of the moving mass and using plate first-order shear deformation theory, the governing equations on the dynamic behavior of the system are derived. The Galerkin’s method on the basis of trigonometric shape functions is applied to change the coupled governing partial differential equations to a system of ordinary differential equations. Due to the alternative motion of the mass along the circular path over the plate’s surface, the governing equations are the equations with the periodic constant. Applying the semi-analytical incremental harmonic balance method, the influences of the relative thickness of the plate, radius of the motion path, and stiffness and damping of the visco-elastic foundation on the instability conditions of the system are investigated. A good agreement can be observed by comparing the predicted results of the incremental harmonic balance method with the numerical solution results. Based on the findings, increasing the radius of the motion path broadens the instability regions. Moreover, increasing the stiffness and damping of the foundation cause the system more stable.
