• Structural Engineering and Mechanics
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• v.3 no.3
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• pp.229-244
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• 1995

The parametric instability behaviour of a plate subjected to localized in-plane compressive or tensile periodic edge loading is studied, considering the effects of damping into the system. Different edge loading cases have been considered. Damping has been introduced in the form of proportional damping. Dynamic instability behaviour under compressive or tensile periodic edge loading shows that the instability regions are influenced by the load band width and its location on the edge. The effects of damping on the instability regions show that there is a critical value of dynamic load factor beyond which the plate becomes dynamically unstable. The critical dynamic load factor increases as damping increases. Damping generally reduces the widths of the instability regions.

• Structural Engineering and Mechanics
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• v.19 no.5
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• pp.503-517
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• 2005

The parametric dynamic stability of an asymmetric sandwich beam with viscoelastic core on viscoelastic supports at the ends and subjected to an axial pulsating load is investigated. A set of Hill's equations are obtained from the non-dimensional equations of motion by the application of the general Galerkin method. The zones of parametric instability are obtained using Saito-Otomi conditions. The effects of shear parameter, support characteristics, various geometric parameters and excitation force on the zones of instability are investigated.

• International Journal of Aerospace System Engineering
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• v.2 no.2
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• pp.34-39
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• 2015

Experimental studies were conducted on the liquid sloshing characteristics in a spherical tank covered with a flexible membrane. A spherical acrylic tank with 145.2 mm in radius was used as a test tank, and it was half-filled with water. Silicon membranes with 0.2 mm thickness were used as a test membrane with plane or hemispherical types. The test tank was harmonically excited in a vertical direction by an electro-dynamic exciter. In this case, a parametric instability vibration comes up when the excitation frequency is twice the natural frequency. Parametric instability regions of natural modes were measured for three cases, i.e. liquid surface is free, covered with plane membrane and hemi-spherical membrane.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.3
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• pp.526-533
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• 1990

The dynamic stability of a single cam drive mechanism is investigated by an analytical approach. The nonlinear differential equation describing the motion of a single cam drive mechanism is linearized with respect to the imput power angle, and results a linear parametric differential equation. The instability region is examined by applying the harmonic balance method to linearized parametric equation having periodicity. Through the dynamic stability analysis of a single cam drive mechanism, it is observed that the parametric resonances exist and the instability regions tend to become wide as increasing the drive speed and follower mass.

• Journal of Advanced Marine Engineering and Technology
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• v.16 no.5
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• pp.67-76
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• 1992

This paper describes the vibration characteristic of second-order nonlinear systems subjected to parametric excitation. Emphasis is put on the examination of the hydrodynamic nonlinear damping effect on limiting the response amplitudes of parametric vibration. Since the parametric vibration is described by the Mathieu equation, the Mathieu stability chart is examined in this paper. In addition, the steady-state solutions of the nonlinear Mathieu equation in the first instability region are obtained by using a perturbation technique and are compared with those by a numerical integration method. It is shown that the response amplitudes of parametric vibration are limited even in unstable conditions by hydrodynamic nonlinear damping force. The largest reponse amplitude of parametric vibration occurs in the first instability region of Mathieu stability chart. The parametric excitation induces the response of a dynamic system to be subharmonic, superharmonic or chaotic according to their dynamic conditions.

• Smart Structures and Systems
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• v.8 no.5
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• pp.487-499
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• 2011

The parametric resonance problems of axisymmetric sandwich annular plate with an electrorheological (ER) fluid core and constraining layer are investigated. The annular plate is covered an electrorheological fluid core layer and a constraining layer to improve the stability of the system. The discrete layer annular finite element and the harmonic balance method are adopted to calculate the boundary of instability regions for the sandwich annular plate system. Besides, the rheological property of an electrorheological material, such as viscosity, plasticity, and elasticity can be changed when applying an electric field. When the electric field is applied on the sandwich structure, the damping of the sandwich system is more effective. Thus, variations of the instability regions for the sandwich annular plate with different applying electric fields, thickness of ER layer, and some designed parameters are presented and discussed in this study. The ER fluid core is found to have a significant effect on the location of the boundaries of the instability regions.

• Steel and Composite Structures
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• v.31 no.3
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• pp.277-290
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• 2019

This paper investigates the parametric instability (PI) of multilayered composite conical shells (MLCCSs) under axial load periodically varying the time, using the first order shear deformation theory (FOSDT). The basic equations for the MLCCSs are derived and then the Galerkin method is used to obtain the ordinary differential equation of the motion. The equation of motion converted to the Mathieu-Hill type differential equation, in which the DI is examined employing the Bolotin's method. The expressions for left and right limits of dimensionless parametric instability regions (PIRs) of MLCCSs based on the FOSDT are obtained. Finally, the influence of various parameters; lay-up, shear deformations (SDs), aspect ratio, as well as loading factors on the borders of the PIRs are examined.

• Journal of KSNVE
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• v.11 no.1
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• pp.118-124
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• 2001

The effect of a concentrated mass on the regions of dynamic instability of an axially oscillating cantilever beam is investigated in this paper. The equations of motion are derived using Kane's method and the assumed mode method. It is found that the bending stiffness is harmonically varied by axial inertia forces due to oscillating motion. Under the certain conditions between oscillating frequency and the natural frequencies, dynamic instability may occur and the magnitude of the bending vibration increase without bound. By using the multiple time scales method, the regions of dynamic instability are obtained. The regions of dynamic instability are found to be depend on the magnitude of a concentrated mass or its location.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.1 s.173
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• pp.232-239
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• 2000

The paper describes the parametric instability of free-free beams subjected to a controlled pulsating follower force. The beam has a tip rigid body not a mass point, and the direction of pulsating follower force is controlled by the direction control sensor. Equations of motion are derived by Hamilton's principle and the instability regions are obtained by finite element formulation. The effects of magnitude, rotary inertia, the distance between free end of the beam and the center of gravity of the rigid body on the instability types and regions are investigated by the change of the constant and periodic part of the follower force.

• International Journal of Aeronautical and Space Sciences
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• v.13 no.3
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• pp.332-348
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• 2012

The present study deals with the parametric resonance behaviour of laminated composite curved shell panels in a hygrothermal environment using Bolotin's approach. A simple laminated model is developed using first order shear deformation theory (FSDT) for the vibration and dynamic stability analysis of laminated composite shells subjected to hygrothermal conditions. A computer program based on the finite element method (FEM) in a MATLAB environment is developed to perform all necessary computations. Quantitative results are presented to show the effects of curvature, ply-orientations, degree of orthotropy and geometry of laminates on the parametric instability of composite curved shell panels for different temperature and moisture concentrations. The excitation frequencies of laminated composite panels decrease with the increase of temperature and moisture due to reduction of stiffness for all laminates.