Review of the Nonlinear Vibration Analysis of Simply Supported Beams

2012 ◽  
Vol 446-449 ◽  
pp. 626-629 ◽  
Author(s):  
Wen Bin Sun ◽  
Wei Zhong He
Keyword(s):  
Nonlinear Vibration ◽  
Large Amplitude ◽  
Vibration Analysis ◽  
Complete Understanding ◽  
Simply Supported ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration

The research of large amplitude vibration of simply supported beams can be dated back to 1950; many achievements and some evolution were accomplished by many researchers over hundred and fifty years. The development of nonlinear vibration formulations for beams has gone through distinct phases–earlier continuum solutions, development of appropriate forms, extra-variational simplifications, debate and discussions, variationally correct formulations and finally applications. A review of work in each of these phases is very necessary in order to have a complete understanding of the process of evolution of this field. This paper attempts to achieve precisely this objective.

Large Amplitude Vibration Analysis of Composite Beams under Thermal Stresses: Closed-Form Solutions

2012 ◽  
Vol 245 ◽  
pp. 144-149 ◽  
Author(s):  
Ali Reza Daneshmehr ◽  
Mostafa Mohammad Abadi ◽  
Meisam Soleimani
Keyword(s):  
Closed Form ◽  
Large Amplitude ◽  
Composite Beam ◽  
Vibration Analysis ◽  
Thermal Stresses ◽  
Method Comparison ◽  
Laminated Composite ◽  
Closed Form Solutions ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration

In This study , the large amplitude vibration analysis of laminated composite beam under thermal stress with axially fixed ends is investigated with symmetric and asymmetric layup orientations by using the Rayleigh–Ritz (R–R) method. An exhaustive set of beam boundary condition are studied, namely, hinged-hinged, clamped-clamped, hinged- clamped, hinged-guided and clamped-guided beam in order to prove the efficacy of the present formulation. The composite beam is studied in this paper based on Euler-Bernoulli assumption together with von-Karman’s strain-displacement relation. The simple and efficient closed-form solutions are obtained for the nonlinear harmonic radian frequency as function of central amplitude of the beam using the R–R method. Comparison between results of the present study and those available in literature shows the accuracy of presented closed-form solutions.

Nonlinear Vibration of Temperature-Dependent FG-CNTRC Laminated Beams with Negative Poisson’s Ratio

2020 ◽  
Vol 20 (04) ◽  
pp. 2050043 ◽  
Author(s):  
Jian Yang ◽  
Xu-Hao Huang ◽  
Hui-Shen Shen
Keyword(s):  
Nonlinear Vibration ◽  
Environmental Conditions ◽  
Large Amplitude ◽  
Vibration Characteristics ◽  
Poisson's Ratio ◽  
Temperature Dependent ◽  
Laminated Beams ◽  
Amplitude Vibration ◽  
Negative Poisson's Ratio ◽  
Large Amplitude Vibration

Laminated beams made of nanocomposite materials have been used in many industrial sectors. This paper reports a study on the vibration behavior of laminated beams when experiencing the large amplitude vibration. The beams are made of perfectly bonded carbon nanotube-reinforced composite (CNTRC) layers. The novel constructions of CNTRC laminated beams with out-of-plane maximum negative Poisson’s ratio (NPR) are proposed. The volume fraction of CNT may change across the beam thickness which results in a piece-wise pattern. The material properties of the CNTRC layers are temperature-dependent and can be estimated by the extended rule of mixture model. The beams are considered to rest on a two-parameter elastic foundation and under differential thermal environmental conditions. The higher order shear deformation beam theory is applied to derive the motion equations of the nonlinear vibration of FG-CNTRC laminated beams. These equations include the influencing factors such as the geometrical nonlinearity in the von Kármán sense, the thermal effects and the beam–foundation interaction. The nonlinear vibration solutions can be obtained by employing a two-step perturbation approach. The nonlinear vibration characteristics of FG-CNTRC laminated beams under different sets of loading conditions and thermal environmental conditions are discussed in detail through a series of parametric studies. Numerical results show that the NPR has a significant effect on the large amplitude vibration characteristics of CNTRC laminated beams.

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