Papers by Keyword: Free Vibration

Abstract: This article presents an analytical approach to explore the free vibration behaviour of new functionally graded carbon nanotube-reinforced composite beams (FG-CNTRC) based on a two-variable higher-order shear deformation theory and nonlocal strain gradient theory. The beams resting on the Pasternak elastic foundation, including a shear layer and Winkler spring, are considered. The kinematic relations of the shaft are proposed according to novel trigonometric functions. The vibrated nanobeam’s motion equations are obtained via the classical Hamilton’s principle and solved using Navier’s steps. A comparative evaluation of results against predictions from literature demonstrates the accuracy of the proposed analytical model. Moreover, a detailed parametric analysis checks for the sensitivity of the vibration response of FG nanobeams to nonlocal length scale, strain gradient microstructure scale, material distribution, constant spring factors, and geometry. The current work presents the free vibration problem of supported (FG-CNTRC) beams reinforced by different patterns of carbon nanotube (CNT) distributions in the polymeric matrix.

Abstract: This study presents the analytical solutions of free vibration analysis of simply supported nanoplate FG porous using nonlocal high order shear deformation plate theory. This theory contains four unknowns without the use of shear correction factors unlike the others. The objective of this article is to develop a model to use the function f (z) on vibration and the natural frequencies of functionally graded nanoplates nonlocal to study the effect of the various parameters. The validity of the theory is shown by comparing the present results with obtained with those reported in the literature. The effects of various parameters are all discussed.

Abstract: In this paper, a numerical procedure is proposed for analyzing the effects of length scale parameter, external electric field, angular speed and nonlocal parameter on the free vibration of a functionally graded piezoelectric cylindrical nanoshell. Nonlocal strain gradient theory (NSGT) is employed to study Eringen’s size-dependent effect and the length scale parameter. This new proposed method can be considered as a combination of Eringen’s nonlocal model and classical strain gradient theory. The obtained results show that this model can be used reliably for small-scale systems. The effects of boundary conditions, applied voltage, nonlocal parameter, rotational speed and length scale parameter on natural frequencies are presented. Compared to other elasticity theories, NSGT achieves the highest natural frequency and critical rotational speed and also a wider stability region. Doubling and tripling the length scale increases the natural frequency by approximately 1.8 and 2.6 times, respectively; while doubling and tripling the nonlocal parameter value reduces the natural frequency by approximately 1.2 and 1.4 times, respectively. Therefore, the natural frequency is more sensitive to the length scale parameter than the nonlocal parameter. Finally, it was shown that the critical angular speed goes up by increasing the length scale parameter, applied voltage, or nonlocal parameter.

Abstract: The dynamic free and forced axial vibrations subjected to moving exponential and harmonic axial forces of a single-walled carbon nanotube (SWCNT) embedded in an elastic medium, are studied in this paper. Two different boundary conditions of SWCNT, including clamped-clamped and clamped-free, are taken into account. Eringen’s nonlocal elasticity theory is used to show the nonlocality for the model. The constitutive equations and their boundary conditions are derived by Hamilton’s principle. Employing the general solution, the derived equations are analytically solved to obtain two items. Firstly, the axial natural frequencies, secondly, the time-domain axial displacements at the middle of the carbon nanotube (CNT), and then the maximum axial displacements. The responses are validated with previous works, and the results demonstrates good agreement to them to verify the influence of the nonlocal parameter on the nondimensional natural frequencies for three various mode numbers. In the time-domain section, the effects of the nonlocal parameter, length, nondimensional stiffness of the elastic medium, and velocity of the moving load on the axial displacement are investigated. Also, the influences of the excitation frequency to natural frequency for the harmonic moving load, as well as the time constant for the exponential moving load on the axial displacement, are illustrated. Finally, the effect of the nonlocal parameter on the maximum axial deflection versus velocity parameter is schematically indicated.

Abstract: This article presents the free vibration analysis of simply supported plate FG porous using a high order shear deformation theory. In is work the material properties of the porous plate FG vary across the thickness. The proposed theory contains four unknowns unlike the other theories which contain five unknowns. This theory has a parabolic shear deformation distribution across the thickness. So it is useless to use the shear correction factors. The Hamilton's principle will be used herein to determine the equations of motion. Since, the plate are simply supported the Navier procedure will be retained. To show the precision of this model, several comparisons have been made between the present results and those of existing theories in the literature for non-porous plates. Effects of the exponent graded and porosity factors are investigated.

Abstract: An 8-noded quadratic isoparametric plate bending finite element that incorporates first-order transverse shear deformation and rotary inertia is used to predict the free vibration response of sandwich plate structures. A programme has been developed using MATLAB. The finite element results presented here show good agreement with the available semi-analytical solutions and finite element results. Parametric studies have been conducted by incorporating variation in support conditions, fibre angles of the skins and overall thickness and detail interpretations are provided.

Abstract: Functionally graded materials (FGMs) have mechanical properties that vary continuously from one phase to another within a confined volume. In general, these materials exhibit certain amount of scatter in their properties due to different factors. The dispersion in the response values of a structure is due to the scatter in the values of material properties and applied external load. For design purposes, it is essential to know the potential variations in the structural response due to the system material or external randomness. In the present work, free vibration and static analysis on FGM structures with material randomness are considered.

Abstract: In thermal environment, vibration behavior of Functionally Graded Materials (FGMs) plates is investigated, and the materials are developed with mixing ceramic and metal. Present study is based on the first-order shear deformation theory of plate. Then, mixture methods such as Power law (P-) and Sigmoid (S-) models are chosen. According to a volume fraction, the material properties are assumed to vary continuously through the thickness direction and to be temperature dependent properties. Further, thermal effects are considered as uniform temperature rise and one dimensional heat transfer. For the structure analysis, FEM is used to obtain the natural frequencies based on the virtual work principle.

Abstract: The paper deals with experimental estimation of the frequencies of free vibrations for composite plates with damage. Two different glass-epoxy composite plates with damage were tested and their mechanical behavior was compared with their non-damaged counterparts. Dynamical properties of the tested structures were examined with the Laser Scanning Vibrometer. Finite Element Analysis (FEA) was performed simultaneously for free vibration frequencies and mode shapes. The numerical results agreed well with the experiment.

Abstract: Nowadays, research on dynamic behavior of structural components is becoming one of the important parts in the design process for any mechanical system. In order to determine the dynamic behavior of a vibrating structure, measurements of the dynamic properties of structure are essential. Free vibration analysis is one of the approaches that apply the finite element method in determining the structure modes of vibration. Each mode is defined by its natural frequency and mode shape. In this paper, the free vibration analysis of grass trimmer was performed using commercial finite element software, such as Ansys®. The importance of determining these vibration characteristics are crucial as grass trimmer is a common machine that exposed to the dynamic and static forces coming from the engine and rotating blade. A long term exposure of grass trimmer's operator may or potentially suffering a risk of hand arm vibration syndrome. The preliminary results of free vibration analysis demonstrated that the grass trimmer experienced a global first bending mode for 1st natural frequency, a global second bending mode for 2nd natural frequency, a local first torsion mode for third natural frequency, and a combination of global and local bending mode for 4th natural frequency. Later, the analyses were further carried out on the modification of the grass trimmer.