scholarly journals Discussion: “Large-Amplitude Free Vibrations of a Beam” (Wagner, Hans, 1965, ASME J. Appl. Mech., 32, pp. 887–892)

1966 ◽  
Vol 33 (3) ◽  
pp. 711-712
Author(s):  
I. Tadjbakhsh
Keyword(s):  
Large Amplitude ◽  
Free Vibrations

Re-investigation of large-amplitude free vibrations of beams using finite elements

1990 ◽  
Vol 143 (2) ◽  
pp. 351-355 ◽  
Author(s):  
G. Singh ◽  
G. Venkateswara Rao ◽  
N.G.R. Iyengar
Keyword(s):  
Finite Elements ◽  
Large Amplitude ◽  
Free Vibrations

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.

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.

On various formulations of large amplitude free vibrations of beams

1988 ◽  
Vol 29 (6) ◽  
pp. 959-966 ◽  
Author(s):  
B.S. Sarma ◽  
T.K. Varadan ◽  
G. Prathap
Keyword(s):  
Large Amplitude ◽  
Free Vibrations
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