On Internal Resonances for a Weakly Nonlinear Beam Equation

Abstract The buckling and initial postbuckling behavior of face-sheet delaminations or face-sheet/core debonds is studied by a perturbation procedure. The procedure is based on the nonlinear beam equation with transverse shear included, and an asymptotic expansion of the load and deformation quantities. First the characteristic equation for the critical load is formulated and this is a nonlinear algebraic equation. Subsequently, the first order load is found from a system of linear equations and the initial postbuckling behavior can thus be studied. The procedure can be easily expanded to the higher order terms. The effect of transverse shear is illustrated with results on the critical strain and the initial postbuckling displacement.

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Remarks on the existence and decay of the nonlinear beam equation

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171294000578 ◽

1994 ◽

Vol 17 (2) ◽

pp. 409-412 ◽

Cited By ~ 1

Author(s):

Jaime E. Mũnoz Rivera

Keyword(s):

Weak Solution ◽

Beam Equation ◽

Nonlinear Beam

We will consider a class of nonlinear beam equation and we will prove the existence and decay weak solution

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Sharp criteria of blow-up solutions for the cubic nonlinear beam equation

Boundary Value Problems ◽

10.1186/s13661-019-1149-5 ◽

2019 ◽

Vol 2019 (1) ◽

Cited By ~ 1

Author(s):

Jun Qing ◽

Chuangyuan Zhang

Keyword(s):

Blow Up ◽

Beam Equation ◽

Nonlinear Beam

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Blow-up of solutions for a nonlinear beam equation with fractional feedback

Nonlinear Analysis ◽

10.1016/j.na.2010.10.012 ◽

2011 ◽

Vol 74 (4) ◽

pp. 1402-1409 ◽

Cited By ~ 14

Author(s):

Soraya Labidi ◽

Nasser-eddine Tatar

Keyword(s):

Blow Up ◽

Beam Equation ◽

Nonlinear Beam

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Parameter Identification of a Nonlinear Beam Energy Harvester

Volume 1: 24th Conference on Mechanical Vibration and Noise, Parts A and B ◽

10.1115/detc2012-70190 ◽

2012 ◽

Cited By ~ 2

Author(s):

Dennis J. Tweten ◽

Brian P. Mann

Keyword(s):

Parameter Identification ◽

Harmonic Balance ◽

Beam Energy ◽

Restoring Force ◽

Nonlinear Beam ◽

Weakly Nonlinear ◽

Closed Form Solutions ◽

Energy Harvesters ◽

Identification Method ◽

Balance Parameter

This paper describes the application of the harmonic balance parameter identification method to beam energy harvesters. The method is applied to weakly nonlinear and nonlinear, bistable fixed-free piezoelectric beams with tip masses. It is shown that only one measurement is required to identify parameters even though the systems are continuous. In addition, an experimental method of determining the number of restoring force coefficients required to accurately model the systems is presented. The harmonic balance parameter identification method is extended to account for multiple concurrent frequencies in order to identify parameters of weakly nonlinear systems. Finally, parameters are identified for two experimental energy harvesters. Good agreement is shown between the experimental data and the identified parameters using simulations and closed form solutions.

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Analytical Approximations to Buckling Deformation of the Sandwich Beams Including Transverse Shear

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.317-319.1783 ◽

2011 ◽

Vol 317-319 ◽

pp. 1783-1786

Author(s):

Yong Ping Yu ◽

Lin Zang ◽

You Hong Sun

Keyword(s):

Transverse Shear ◽

Harmonic Balance ◽

Approximate Solutions ◽

Beam Equation ◽

Sandwich Beams ◽

Nonlinear Beam ◽

Sandwich Construction ◽

Analytical Approximations ◽

Post Buckling ◽

Approximate Procedure

This paper presents analytical approximate solutions for the initial post-buckling deformation of the sandwich beams including transverse shear. The approximate procedure is based on the nonlinear beam equation (with transverse shear included), by combining the Newton’s method with the method of harmonic balance, we establish analytical approximations to deformation of the sandwich beams. Illustrative examples are presented for a few typical sandwich construction configurations, and it is shown that these approximate solutions are excellent agreement with the “reference” solutions.

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