Study of dynamic stability of simply supported beams on Pasternak foundation considering the effect of first transition foundation parameter

The quasi-Greens function method (QGFM) is applied to solve the bending problem of simply supported polygonal shallow spherical shells on Pasternak foundation. A quasi-Greens function is established by using the fundamental solution and the boundary equation of the problem. And the function satisfies the homogeneous boundary condition of the problem. Then the differential equation of the problem is reduced to two simultaneous Fredholm integral equations of the second kind by the Greens formula. The singularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. The comparison with the ANSYS finite element solution shows a good agreement, and it demonstrates the feasibility and efficiency of the proposed method.

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Uniformly loaded, simply supported, antisymmetrically laminated, rectangular plate on a winkler-pasternak foundation

International Journal of Solids and Structures ◽

10.1016/0020-7683(77)90038-5 ◽

1977 ◽

Vol 13 (5) ◽

pp. 437-444 ◽

Cited By ~ 10

Author(s):

G.J. Turvey

Keyword(s):

Rectangular Plate ◽

Pasternak Foundation ◽

Simply Supported

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Static and dynamic stability analysis of an asymmetric sandwich beam resting on a variable pasternak foundation subjected to thermal gradient

Meccanica ◽

10.1007/s11012-015-0229-6 ◽

2015 ◽

Vol 51 (3) ◽

pp. 725-739 ◽

Cited By ~ 16

Author(s):

M. Pradhan ◽

P. R. Dash ◽

P. K. Pradhan

Keyword(s):

Stability Analysis ◽

Dynamic Stability ◽

Thermal Gradient ◽

Sandwich Beam ◽

Pasternak Foundation ◽

Static And Dynamic Stability

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Analytical Treatment of In-Plane Parametrically Excited Undamped Vibrations of Simply Supported Parabolic Arches

Journal of Vibration and Acoustics ◽

10.1115/1.1521952 ◽

2003 ◽

Vol 125 (1) ◽

pp. 73-79 ◽

Cited By ~ 2

Author(s):

Dimitris S. Sophianopoulos ◽

George T. Michaltsos

Keyword(s):

Differential Equations ◽

Free Vibration ◽

Dynamic Stability ◽

Parametric Excitation ◽

Stability Problem ◽

Axial Loading ◽

Time Dependent ◽

Analytical Treatment ◽

Simply Supported ◽

Forced Motion

The present work offers a simple and efficient analytical treatment of the in-plane undamped vibrations of simply supported parabolic arches under parametric excitation. After thoroughly dealing with the free vibration characteristics of the structure dealt with, the differential equations of the forced motion caused by a time dependent axial loading of the form P=P0+Pt cos θt are reduced to a set of Mathieu-Hill type equations. These may be thereafter tackled and the dynamic stability problem comprehensively discussed. An illustrative example based on Bolotin’s approach produces results validating the proposed method.

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Three alternative versions of the theory for a Timoshenko–Ehrenfest beam on a Winkler–Pasternak foundation

Mathematics and Mechanics of Solids ◽

10.1177/1081286520947775 ◽

2020 ◽

pp. 108128652094777

Author(s):

Giulio Maria Tonzani ◽

Isaac Elishakoff

Keyword(s):

Free Vibration ◽

Boundary Conditions ◽

Detailed Comparison ◽

Vibration Frequencies ◽

Pasternak Foundation ◽

New Model ◽

Simply Supported ◽

Model Based

This paper analyzes the free vibration frequencies of a beam on a Winkler–Pasternak foundation via the original Timoshenko–Ehrenfest theory, a truncated version of the Timoshenko–Ehrenfest equation, and a new model based on slope inertia. We give a detailed comparison between the three models in the context of six different sets of boundary conditions. In particular, we analyze the most common combinations of boundary conditions deriving from three typical end constraints, namely the simply supported end, clamped end, and free end. An interesting intermingling phenomenon is presented for a simply-supported (S-S) beam together with proof of the ‘non-existence’ of zero frequencies for free-free (F-F) and simply supported-free (S-F) beams on a Winkler–Pasternak foundation.

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EXACT EIGEN-RELATIONS OF CLAMPED-CLAMPED AND SIMPLY SUPPORTED PIPES CONVEYING FLUIDS

International Journal of Applied Mechanics ◽

10.1142/s1758825112500354 ◽

2012 ◽

Vol 04 (03) ◽

pp. 1250035 ◽

Cited By ~ 4

Author(s):

PIN LU ◽

HONGYU SHENG

Keyword(s):

Boundary Conditions ◽

Dynamic Stability ◽

Dynamic Properties ◽

Pipe Conveying Fluid ◽

Simply Supported ◽

Pipeline Systems ◽

Benchmark Solutions ◽

Conveying Fluid ◽

Flow Velocities

The exact eigen-equations of pipe conveying fluid with clamped-clamped and simply supported boundary conditions are derived. The simplified forms of the general eigen-equations for some specific cases are determined, and the corresponding dynamic properties are calculated and discussed. These properties provide a better understanding on the relationships between the dynamic stability and the flow velocities of the fluid-conveying components and help to design stable pipeline systems. In addition, the dynamic properties obtained by the exact eigen-equations can also serve as benchmark solutions for verifying results obtained by other approximate approaches.

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Stability of Empty and Fluid-Filled Circular Cylindrical Shells Subjected to Dynamic Axial Loads

5th International Symposium on Fluid Structure International, Aeroeslasticity, and Flow Induced Vibration and Noise ◽

10.1115/imece2002-32212 ◽

2002 ◽

Cited By ~ 1

Author(s):

F. Pellicano ◽

M. Amabili ◽

M. P. Pai¨doussis

Keyword(s):

Dynamic Stability ◽

Cylindrical Shells ◽

Travelling Wave ◽

Finite Amplitude ◽

Axial Loads ◽

Simply Supported ◽

Mean Oscillation ◽

Shell Motion ◽

Circular Cylindrical Shells ◽

The Mean

In the present study the dynamic stability of simply supported, circular cylindrical shells subjected to dynamic axial loads is analyzed. Geometric nonlinearities due to finite-amplitude shell motion are considered by using the Donnell’s nonlinear shallow-shell theory. The effect of structural damping is taken into account. A discretization method based on a series expansion involving a large number of linear modes, including axisymmetric and asymmetric modes, and on the Galerkin procedure is developed. Both driven and companion modes are included allowing for travelling-wave response of the shell. Axisymmetric modes are included because they are essential in simulating the inward deflection of the mean oscillation with respect to the equilibrium position. The shell is simply supported and presents a finite length. Boundary conditions are considered in the model, which includes also the contribution of the external axial loads acting at the shell edges. The effect of a contained liquid is also considered. The linear dynamic stability and nonlinear response are analysed by using continuation techniques.

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