On the dynamic of graphene reinforced nanocomposite cylindrical shells subjected to a moving harmonic load

This paper describes the dynamic analysis of prestressed Bernoulli beams resting on a two-parameter elastic foundation under a moving harmonic load by the finite element method. Using the cubic Hermitian polynomials as interpolation functions for the deflection, the stiffness of the Bernoulli beam element augmented by that of the foundation support and prestress is formulated. The nodal load vector is derived using the polynomials with the abscissa measured from the left-hand node of the current loading element to the position of the moving load. Using the formulated element, the dynamic response of the beams is computed with the aid of the direct integration Newmark method. The effects of the foundation support, prestress as well as excitation frequency, velocity and acceleration on the dynamic characteristics of the beams are investigated in detail and highlighted.

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VIBRATION OF 2D-FGSW TIMOSHENKO BEAMS UNDER A MOVING HARMONIC LOAD

Vietnam Journal of Science and Technology ◽

10.15625/2525-2518/58/5/14936 ◽

2020 ◽

Vol 58 (6) ◽

pp. 760

Author(s):

Kien Dinh Nguyen

Keyword(s):

Moving Load ◽

Excitation Frequency ◽

Vibration Characteristics ◽

Functionally Graded ◽

Element Formulation ◽

Harmonic Load ◽

Timoshenko Beams ◽

Power Functions ◽

Material Inhomogeneity ◽

Moving Harmonic Load

Vibration of two-directional functionally graded sandwich (2D-FGSW) Timoshenko beams under a moving harmonic load is investigated. The beams consist of three layers, a homogeneous core and two functionally graded skin layers with the material properties continuously varying in both the thickness and length directions by power functions. A finite element formulation is derived and employed to compute the vibration characteristics of the beams. The obtained numerical result reveals that the material inhomogeneity and the layer thickness ratio play an important role on the natural frequencies and dynamic response of the beams. A parametric study is carried out to highlight the effects of the power-law indexes, the moving load speed and excitation frequency on the vibration characteristics of the beams. The influence of the beam aspect ratio on the vibration of the beams is also examined and discussed.

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Vibration analysis of embedded curved carbon nanotube subjected to a moving harmonic load based on nonlocal theory

SCIENTIA SINICA Physica, Mechanica & Astronomica ◽

10.1360/132012-727 ◽

2013 ◽

Vol 43 (4) ◽

pp. 486-493 ◽

Cited By ~ 2

Author(s):

ZiChen DENG ◽

XiaoJian XU ◽

Bo WANG ◽

Yan WANG

Keyword(s):

Carbon Nanotube ◽

Vibration Analysis ◽

Nonlocal Theory ◽

Harmonic Load ◽

Moving Harmonic Load

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Nonlinear Forced Response of Infinitely Long Circular Cylindrical Shells

Journal of Applied Mechanics ◽

10.1115/1.3173071 ◽

1987 ◽

Vol 54 (3) ◽

pp. 571-577 ◽

Cited By ~ 29

Author(s):

A. H. Nayfeh ◽

R. A. Raouf

Keyword(s):

Multiple Scales ◽

Cylindrical Shells ◽

Period Doubling ◽

Threshold Value ◽

Resonant Mode ◽

Forced Response ◽

Harmonic Load ◽

Flexural Mode ◽

Long Time ◽

Circular Cylindrical Shells

A combination of the Galerkin procedure and the method of multiple scales is used to analyze the nonlinear forced response of infinitely long circular cylindrical shells (or circular rings) in the presence of internal (autoparametric) resonances. If ωf and af denote the frequency and amplitude of a flexural mode and ωb and ab denote the frequency and amplitude of the breathing mode, the steady-state response is found to exhibit a saturation phenomenon when ωb = 2ωf if the shell is excited by a harmonic load having a frequency Ω near ωb. As the amplitude f of the excitation increases from zero, ab increases linearly with f until a threshold value fc of f is reached. Beyond fc, ab remains constant and the extra energy spills over into the flexural resonant mode whose amplitude grows nonlinearly. Results of numerical investigations, guided by the perturbation analysis, show that the long-time response exhibits a Hopf bifurcation, yielding amplitude and phase-modulated motions. The amplitudes and phases experience a cascade of period-doubling bifurcations ending up with chaos. The bifurcation values are finely tuned.

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