Large Amplitude Free Vibration of Shallow Spherical Shell on a Pasternak Foundation

1993 ◽  
Vol 115 (1) ◽  
pp. 70-74 ◽  
Author(s):  
D. N. Paliwal ◽  
V. Bhalla
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Large Amplitude ◽  
Free Vibrations ◽  
Numerical Results ◽  
Shallow Spherical Shell ◽  
Pasternak Foundation ◽  
New Approach ◽  
Foundation Parameters ◽  
Clamped Edges

Large amplitude free vibrations of a clamped shallow spherical shell on a Pasternak foundation are studied using a new approach by Banerjee, Datta, and Sinharay. Numerical results are obtained for movable as well as immovable clamped edges. The effects of geometric, material, and foundation parameters on relation between nondimensional frequency and amplitude have been investigated and plotted.

Vibrations of a Shallow Spherical Shell on a Kerr Foundation

1994 ◽  
Vol 116 (1) ◽  
pp. 47-52 ◽  
Author(s):  
D. N. Paliwal ◽  
R. Srivastava
Keyword(s):  
Spherical Shell ◽  
Elastic Foundation ◽  
Elastic Properties ◽  
Parametric Study ◽  
Large Amplitude ◽  
Free Vibrations ◽  
Shallow Spherical Shell ◽  
Foundation Model ◽  
Foundation Parameters ◽  
Clamped Edges

Large amplitude free vibrations of a clamped shallow spherical shell on a Kerr-type elastic foundation model are investigated. A detailed parametric study is conducted involving geometric and elastic properties of the shell as well as representative foundation parameters. Influence of these variables on the relation between the nondimensional frequency and amplitude are discussed. Shells with immovably clamped edges are more vulnerable to the changes in the above-referred parameters than those with movable clamped edges.

The Free Vibrations of a Spinning Centrally Clamped Shallow Spherical Shell

1971 ◽  
Vol 38 (3) ◽  
pp. 601-607 ◽  
Author(s):  
R. J. Beckemeyer ◽  
W. Eversman
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Flexural Rigidity ◽  
Polar Axis ◽  
Free Vibrations ◽  
Shallow Spherical Shell ◽  
Radius Of Curvature ◽  
Difficult Case ◽  
Equilibrium Equations ◽  
Continuous Transition

The results of a numerical analysis of the free-vibration characteristics of a thin shallow spherical shell spinning about its polar axis are presented. The shell is fully clamped by a central hub. The static equilibrium equations are formulated allowing for finite rotations. The free-vibration equations are derived by considering small perturbations about the spinning equilibrium configuration. Both flexural rigidity and membrane restoring forces due to spin are considered. Known techniques for the solution of stationary shell problems are extended to the more difficult case of the spinning shell. Plots of transverse frequency as a function of shell geometry are presented for the first two modes for shells with one and two nodal diameters for various values of inertia loading. Continuous transition from shell to flat disk results with increasing shell radius of curvature is shown.

A New Approach to Large Deflection Analyses of Spherical and Cylindrical Shells

1985 ◽  
Vol 52 (4) ◽  
pp. 872-876 ◽  
Author(s):  
G. C. Sinharay ◽  
B. Banerjee
Keyword(s):  
Spherical Shell ◽  
Large Deflection ◽  
Cylindrical Shells ◽  
Numerical Results ◽  
Shallow Spherical Shell ◽  
Large Deflections ◽  
New Approach ◽  
Edge Conditions

In this paper large deflections of thin elastic shallow spherical shell and cylindrical shells are investigated by a new approach. Numerical results for moveable as well as immoveable edge conditions are presented graphically and compared with other known results.

ANALYTICAL APPROXIMATE SOLUTIONS TO LARGE-AMPLITUDE FREE VIBRATIONS OF UNIFORM BEAMS ON PASTERNAK FOUNDATION

2014 ◽  
Vol 06 (06) ◽  
pp. 1450075 ◽  
Author(s):  
YONGPING YU ◽  
BAISHENG WU
Keyword(s):  
Large Amplitude ◽  
Approximate Solutions ◽  
Free Vibrations ◽  
Integration Scheme ◽  
Nonlinear Frequency ◽  
Pasternak Foundation ◽  
Analytical Approximations ◽  
Numerical Integration Scheme ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration

This paper is concerned with the large-amplitude vibration behavior of simply supported and clamped uniform beams, with axially immovable ends, on Pasternak foundation. The combination of Newton's method and harmonic balance one is used to deal with these vibrations. Explicit and brief analytical approximations to nonlinear frequency and periodic solution of the beams for various values of the two stiffness parameters of the Pasternak foundation, small as well as large amplitudes of oscillation are presented. The analytical approximate results show excellent agreement with those from numerical integration scheme. Due to brevity of expressions, the present analytical approximate solutions are convenient to investigate effects of various parameters on the large-amplitude vibration response of the beams.

Simple Formula to Study the Large Amplitude Free Vibrations of Beams and Plates

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
G. Venkateswara Rao ◽  
K. Meera Saheb ◽  
G. Ranga Janardhan
Keyword(s):  
Free Vibration ◽  
Large Amplitude ◽  
Simple Formula ◽  
Space Variable ◽  
Linear Time ◽  
Amplitude Ratio ◽  
Compressive Load ◽  
Maximum Amplitude ◽  
Free Vibrations ◽  
Structural Members

A simple formula to study the large amplitude free vibration behavior of structural members, such as beams and plates, is developed. The nonlinearity considered is of von Karman type, and after eliminating the space variable(s), the corresponding temporal equation is a homogeneous Duffing equation. The simple formula uses the tension(s) developed in the structural members due to large deflections along with the corresponding buckling load obtained when the structural members are subjected to the end axial or edge compressive load(s) and are equal in magnitude of the tension(s). The ratios of the nonlinear to the linear radian frequencies for beams and the nonlinear to linear time periods for plates are obtained as a function of the maximum amplitude ratio. The numerical results, for the first mode of free vibration obtained from the present simple formula compare very well to those available in the literature obtained by applying the standard analytical or numerical methods with relatively complex formulations.

Nonlinear Free Vibrations of a Timoshenko Beam Using Multiple Scales Method

Volume 2 ◽  
2004 ◽  
Author(s):  
Asghar Ramezani ◽  
Mehrdaad Ghorashi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Free Vibration ◽  
Timoshenko Beam ◽  
Large Amplitude ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Free Vibrations ◽  
Partial Differential ◽  
Cantilevered Beam

In this paper, the large amplitude free vibration of a cantilever Timoshenko beam is considered. To this end, first Hamilton’s principle is used in deriving the partial differential equation of the beam response under the mentioned conditions. Then, implementing the Galerkin’s method the partial differential equation is converted to an ordinary nonlinear differential equation. Finally, the method of multiple scales is used to determine a second order perturbation solution for the obtained ODE. The results show that nonlinearity acts in the direction of increasing the natural frequency of the thick-cantilevered beam.

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