The Dynamic Stability of Elastic Systems

Bolotin, V. V.

doi:10.1119/1.1972245

Cited by 321 publications

(119 citation statements)

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“…An approximate solution of the governing equations (2), in the case of standing flexural waves, is sought in the form:…”

Section: Methods Of Solutionmentioning

confidence: 99%

Dynamic Stability and Nonlinear Parametric Vibrations of Rectangular Plates

Ostiguy

2001

Dynamics With Friction: Modeling, Analysis and Experiment

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The present work reviews the author's recent developments on the dynamic stability and nonlinear parametric vibrations of rectangular plates acted upon by periodic in-plane forces. General rectangular plates are considered, the aspect ratio of me plate being regarded as an additional parameter of me system. The problem is solved for different sets of boundary conditions and uie effects of various system parameters are evaluated. Numerical results are compared to experimental data to form a qualitative and quantitative verification of the solution. Dynamics with Friction: Modeling, Analysis and Experiment Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/23/15. For personal use only. 192 G. L. Ostiguy Dynamics with Friction: Modeling, Analysis and Experiment Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/23/15. For personal use only. Dynamic Stability and Nonlinear Parametric Vibrations of Rectangular Plates

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“…An approximate solution of the governing equations (2), in the case of standing flexural waves, is sought in the form:…”

Section: Methods Of Solutionmentioning

confidence: 99%

Dynamic Stability and Nonlinear Parametric Vibrations of Rectangular Plates

Ostiguy

2001

Dynamics With Friction: Modeling, Analysis and Experiment

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“…Afterward, the axial excitation compressive load is assumed as a periodic function in order to write the governing equations in the form of Mathieu-Hill equations and then Bolotin's method for determining the instability regions. 57 …”

Section: Solution Proceduresmentioning

confidence: 99%

Axial Buckling and Dynamic Stability of Functionally Graded Microshells Based on the Modified Couple Stress Theory

Gholami

Ansari

Darvizeh

et al. 2015

Int. J. Str. Stab. Dyn.

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A nonclassical¯rst-order shear deformation shell model is developed to analyze the axial buckling and dynamic stability of microshells made of functionally graded materials (FGMs). For this purpose, the modi¯ed couple stress elasticity theory is implemented into the¯rst-order shear deformation shell theory. Unlike the classical shell theory, the newly developed shell model contains an internal material length scale parameter to capture e±ciently the size e®ect. By using the Hamilton's principle, the higher-order governing equations and boundary conditions are derived. Afterward, the Navier solution is utilized to predict the critical axial buckling loads of simply-supported functionally graded (FG) microshells. Moreover, the governing equations are written in the form of Mathieu-Hill equations and then Bolotin's method is employed to determine the instability regions. A parametric study is conducted to investigate the in°uences of static load factor, axial wave number, dimensionless length scale parameter, material property gradient index, length-to-radius and length-to-thickness aspect ratios on the axial buckling and dynamic stability responses of FGM microshells. It is revealed that size e®ect plays an important role in the value of critical axial buckling load and instability region of FGM microshells especially corresponding to those with lower aspect ratios.

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“…The deviations observed by Drozdov et al for aircraft tires may result from the neglect of non-linear inertial effects accentuated by the high velocities experienced. (For a further discussion of nonlinear inertia see Bolotin [10].) , Biderman and Bukhin [6] modified the early Russian theory to include the deformation energy of the sidewall of the tire, but they retained the inextensible cord assumption.…”

Section: Early Literaturementioning

confidence: 99%

Waves in Tires

Ames¹

1970

Textile Research Journal

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498increases 'linearly with increasing fabric thickness but then approaches an asymptotic maximum. The implication is, therefore, that, although the heat generated increases linearly with fabric thickness, heat dissipation also increases with increasing temperature, so that the net increase in needle temperature with thick-'ness is less than linear. ' Although the results are exploratory, they do present some insight into the nature of the needle heating problem.

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The Dynamic Stability of Elastic Systems

Cited by 321 publications

References 0 publications

Dynamic Stability and Nonlinear Parametric Vibrations of Rectangular Plates

Dynamic Stability and Nonlinear Parametric Vibrations of Rectangular Plates

Axial Buckling and Dynamic Stability of Functionally Graded Microshells Based on the Modified Couple Stress Theory

Waves in Tires

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