scholarly journals A Numerical Approach to Static Deflection Analysis of an Infinite Beam on a Nonlinear Elastic Foundation: One-Way Spring Model

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Jinsoo Park ◽  
Hyeree Bai ◽  
T. S. Jang
Keyword(s):  
Elastic Foundation ◽  
Numerical Procedure ◽  
Numerical Approach ◽  
Function Technique ◽  
Spring Model ◽  
Static Deflection ◽  
Infinite Beam ◽  
Nonlinear Elastic Foundation ◽  
Deflection Analysis ◽  
Nonlinear Elastic

A numerical procedure proposed by Jang et al. (2011) is applied for the numerical analyzing of static deflection of an infinite beam on a nonlinear elastic foundation. And one-way spring model is used for the modeling of fully nonlinear elastic foundation. The nonlinear procedure involves Green’s function technique and an iterative method using the pseudo spring coefficient. The workability of the numerical procedure is demonstrated through showing the validity of the solution and the convergence test with some external loads.

Postbuckling of Curved Carbon Nanotubes Using Energy Equivalent Model

2019 ◽  
Vol 57 ◽  
pp. 136-157 ◽  
Author(s):  
Mohamed A. Eltaher ◽  
Nazira Mohamed ◽  
Salwa Mohamed ◽  
Lila F. Seddek
Keyword(s):  
Carbon Nanotubes ◽  
Elastic Foundation ◽  
Lateral Displacement ◽  
Mechanical Strain ◽  
Numerical Procedure ◽  
Numerical Results ◽  
Equivalent Model ◽  
Energy Equivalent ◽  
Nonlinear Elastic Foundation ◽  
Nonlinear Elastic

This paper presents a novel numerical procedure to predict nonlinear buckling and postbuckling stability of imperfect clamped–clamped single walled carbon nanotube (SWCNT) surrounded by nonlinear elastic foundation. Nanoscale effect of CNTs is included by using energy-equivalent model (EEM) which transferring the chemical energy between carbon atoms to mechanical strain energy. Young’s modulus and Poisson’s ratio for zigzag (n, 0), and armchair (n, n) carbon nanotubes (CNTs) are presented as functions of orientation and force constants by using energy-equivalent model (EEM). Nonlinear Euler-Bernoulli assumptions are proposed considering mid-plane stretching to exhibit a large deformation and a small strain. To simulate the interaction of CNTs with the surrounding elastic medium, nonlinear elastic foundation with cubic nonlinearity and shearing layer are employed. The governing nonlinear integro-partial-differential equations are derived in terms of only the lateral displacement. The modified differential quadrature method (DQM) is exploited to obtain numerical results of the nonlinear governing equations. The static problem is solved for critical buckling loads and the postbuckling deformation as a function of applied axial load, curved amplitude, CNT length, and orientations. Numerical results show that the effects of chirality angle and curved amplitude on static response of armchair and zigzag CNTs are significant. This model is helpful especially in mechanical design of NEMS manufactured from CNTs.

Effects of Tuned Mass Damper on Fixed-Fixed 3D Nonlinear String Resting on Nonlinear Elastic Foundation

2017 ◽  
Vol 17 (04) ◽  
pp. 1750047 ◽  
Author(s):  
Yi-Ren Wang ◽  
Li-Ping Wu
Keyword(s):  
Elastic Foundation ◽  
Internal Resonance ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Maximum Amplitude ◽  
Tuned Mass Damper ◽  
Mode Shapes ◽  
Nonlinear Elastic Foundation ◽  
Mass Damper ◽  
Nonlinear Elastic

This paper studies the vibration of a nonlinear 3D-string fixed at both ends and supported by a nonlinear elastic foundation. Newton’s second law is adopted to derive the equations of motion for the string resting on an elastic foundation. Then, the method of multiple scales (MOMS) is employed for the analysis of the nonlinear system. It was found that 1:3 internal resonance exists in the first and fourth modes of the string when the wave speed in the transverse direction is [Formula: see text] and the elasticity coefficient of the foundation is [Formula: see text]. Fixed point plots are used to obtain the frequency responses of the various modes and to identify internal resonance through observation of the amplitudes and mode shapes. To prevent internal resonance and reduce vibration, a tuned mass damper (TMD) is applied to the string. The effects of various TMD masses, locations, damper coefficients ([Formula: see text]), and spring constants ([Formula: see text]) on overall damping were analyzed. The 3D plots of the maximum amplitude (3D POMAs) and 3D maximum amplitude contour plots (3D MACPs) are generated for the various modes to illustrate the amplitudes of the string, while identifying the optimal TMD parameters for vibration reduction. The results were verified numerically. It was concluded that better damping effects can be achieved using a TMD mass ratio [Formula: see text]–0.5 located near the middle of the string. Furthermore, for damper coefficient [Formula: see text], the use of spring constant [Formula: see text]–13 can improve the overall damping.

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