Imperfection sensitivity of nonlinear primary resonance behavior in bi-directional functionally graded porous material beam

2021 ◽  
pp. 114142
Author(s):  
Xiaochao Chen ◽  
Lunting Chen ◽  
Yixin Lu
Keyword(s):  
Porous Material ◽  
Primary Resonance ◽  
Functionally Graded ◽  
Imperfection Sensitivity ◽  
Resonance Behavior

Imperfection sensitivity of the nonlinear axial buckling behavior of FGM nanoshells in thermal environments based on surface elasticity theory

2017 ◽  
Vol 06 (01) ◽  
pp. 1750003
Author(s):  
S. Sahmani ◽  
M. M. Aghdam
Keyword(s):  
Free Energy ◽  
Elasticity Theory ◽  
Surface Free Energy ◽  
Material Property ◽  
Shell Thickness ◽  
Surface Elasticity ◽  
Functionally Graded ◽  
Gradient Index ◽  
Imperfection Sensitivity ◽  
Geometric Imperfection

A size-dependent shell model which accounts for geometrical imperfection sensitivity of the axial postbuckling characteristics of a cylindrical nanoshell made of functionally graded material (FGM) is proposed within the framework of the surface elasticity theory. In accordance with a power law, the material properties of the FGM nanoshell are supposed to vary through the shell thickness. In order to eliminate the stretching-bending coupling terms, the change in the position of physical neutral plane corresponding to different volume fractions is taken into account. Based upon the virtual work’s principle, the non-classical governing differential equations are derived and then deduced to boundary layer-type ones. After that, a perturbation-based solution methodology is employed to predict the size dependency in the nonlinear instability of perfect and imperfect axially loaded FGM nanoshells with various values of shell thickness, material property gradient index and different uniform temperature changes. It was seen that for thicker FGM nanoshells in which the surface free energy effects diminish, the influence of the initial geometric imperfection on the critical buckling load is higher than its influence on the minimum load of the postbuckling domain. It is also found that through reduction of the surface free energy effects, the influence of material property gradient index on the critical end-shortening of FGM nanoshell decreases.

scholarly journals A Higher-Order Thermomechanical Vibration Analysis of Temperature-Dependent FGM Beams with Porosities

2016 ◽  
Vol 2016 ◽  
pp. 1-20 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Ali Jafari
Keyword(s):  
Differential Equations ◽  
Porous Material ◽  
Power Law ◽  
Material Properties ◽  
Solution Method ◽  
Equations Of Motion ◽  
Higher Order ◽  
Functionally Graded ◽  
Thickness Direction ◽  
Temperature Dependent

In the present paper, thermomechanical vibration characteristics of functionally graded (FG) Reddy beams made of porous material subjected to various thermal loadings are investigated by utilizing a Navier solution method for the first time. Four types of thermal loadings, namely, uniform, linear, nonlinear, and sinusoidal temperature rises, through the thickness direction are considered. Thermomechanical material properties of FG beam are assumed to be temperature-dependent and supposed to vary through thickness direction of the constituents according to power-law distribution (P-FGM) which is modified to approximate the porous material properties with even and uneven distributions of porosities phases. The governing differential equations of motion are derived based on higher order shear deformation beam theory. Hamilton’s principle is applied to obtain the governing differential equations of motion which are solved by employing an analytical technique called the Navier type solution method. Influences of several important parameters such as power-law exponents, porosity distributions, porosity volume fractions, thermal effects, and slenderness ratios on natural frequencies of the temperature-dependent FG beams with porosities are investigated and discussed in detail. It is concluded that these effects play significant role in the thermodynamic behavior of porous FG beams.

Imperfection sensitivity in the vibration behavior of functionally graded arches by considering microstructural defects

2018 ◽  
Vol 233 (8) ◽  
pp. 2763-2777 ◽  
Author(s):  
Mohammad Amir ◽  
Mohammad Talha
Keyword(s):  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Imperfection Sensitivity ◽  
Vibration Behavior ◽  
Microstructural Defects ◽  
Geometrical Imperfections ◽  
Parametric Studies ◽  
Benchmark Solutions

In this paper, imperfection sensitivity in the vibration behavior of functionally graded arches with microstructural defects (porosity) has been studied. The temperature-dependent material properties of functionally graded arches are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. The formulations are based on the Reddy’s higher order shear deformation theory using finite element method. Convergence and comparison studies have been performed to describe the efficacy of the present formulation. The obtained results have been compared with the limited available literature. The parametric studies have been performed to study the influence of the temperature rise, volume fraction index, and porosity index on the frequency response of the functionally graded arches. The effect of various modes of initial geometrical imperfections has also been examined. The obtained numerical results can be used as benchmark solutions for future researches in this field of study.

scholarly journals Nonlinear dynamics of a functionally graded piezoelectric micro-resonator in the vicinity of the primary resonance

2016 ◽  
Vol 23 (3) ◽  
pp. 400-413 ◽  
Author(s):  
Meysam T Chorsi ◽  
Saber Azizi ◽  
Firooz Bakhtiari-Nejad
Keyword(s):  
Nonlinear Dynamics ◽  
Shooting Method ◽  
Primary Resonance ◽  
Basins Of Attraction ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Electrostatically Actuated ◽  
Micro Resonator ◽  
Functionally Graded Piezoelectric ◽  
Damped Systems

This research is on the nonlinear dynamics of a two-sided electrostatically actuated capacitive micro-beam. The micro-resonator is composed of silicon and PZT as a piezoelectric material. PZT is functionally distributed along the height of the micro-beam according to the power law distribution. The micro-resonator is simultaneously subjected to DC piezoelectric and two-sided electrostatic actuations. The DC piezoelectric actuation leads to the generation of an axial force along the length of the micro-beam and this is used as a tuning tool to shift the primary resonance of the micro-resonator. The governing equation of the motion is derived by the minimization of the Hamiltonian and generalized to the viscously damped systems. The periodic solutions in the vicinity of the primary resonance are detected by means of the shooting method and their stability is investigated by determining the so-called Floquet exponents of the perturbed motions. The basins of attraction corresponding to three individual periodic orbits are determined. The results depict that the higher the amplitude of the periodic orbit, the smaller is the area of the attractor.

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