Vibration of viscoelastic axially graded beams with simultaneous axial and spinning motions under an axial load

For the first time, the structural dynamics and vibrational stability of a viscoelastic axially functionally graded (AFG) beam with both spinning and axial motions subjected to an axial load are analyzed, with the aim to enhance the performance of bi-gyroscopic systems. A detailed parametric study is also performed to emphasize the influence of various key factors such as material distribution type, viscosity coefficient, and coupled rotation and axial translation on the dynamical characteristics of the system. The material properties of the system are assumed to vary linearly or exponentially in the longitudinal direction with viscoelastic effects. Adopting the Laplace transform and a Galerkin discretization scheme, the critical axial and spin velocities of the system are obtained. An analytical approach is applied to identify the instability thresholds. Stability maps are examined, and for the first time in this paper, it is demonstrated that the stability evolution of the system can be altered by fine-tuning of axial grading or viscosity of the material. The variation of density and elastic modulus gradient parameters are found to have opposite effects on the divergence and flutter boundaries of the system. Furthermore, the results indicate that the destabilizing effect of the axial compressive load can be significantly alleviated by the simultaneous determination of density and elastic modulus gradation in the axial direction of the system

Natural Frequencies of Pressurized Hot Fluid Conveying Pipes

In this study, the transverse natural frequencies of a pressurized hot fluid conveying pipe is investigated using complex mode function. Employing the dispersive relations and the non-trivial solution of the coefficient matrix obtained from the boundary equations, the eigenvalues and the linear natural frequencies are obtained numerically. The parametric study is conducted to highlight the effects of variation in operating pressure and pressure drop on the first two modes of the natural frequency of the system. The natural frequency was found to increase nonlinearly with the increase in the operating pressure and pressures drop but decreases with flow velocity. Keywords— Fluid-conveying pipe, natural frequency, pressure variation, transverse vibration

Forced vibration characteristics of embedded graphene oxide powder reinforced metal foam nanocomposite plate in thermal environment

Abstract Dynamic behavior of a new class of nanocomposites consisted of metal foam as matrix and graphene oxide powders as reinforcement is presented in this study in the framework of forced vibration. Graphene oxide powders are dispersed through the thickness of a plate made from metal foam material according to four various functionally graded patterns on the basis of the Halpin-Tsai micromechanical homogenization method. Also, three kinds of porosity distributions including two symmetric and one uniform patterns are considered for the metal foam matrix. As external effects, the plate is rested on the Winkler-Pasternak substrate and under uniform thermal and transverse dynamic loadings. By an incorporation of the refined higher order plate theory and Hamilton's principle, the governing equations of the dynamically loaded graphene oxide powder reinforced metal foam nanocomposite plate are derived and then solved with Galerkin exact solution method to achieve the resonance frequencies and dynamic deflections of the structure. Moreover, the influence of different boundary conditions is taken into account. The results indicate that the forced vibrational response of the graphene oxide powder strengthened metal foam nanocomposite plate is dramatically dependent on various parameters such as graphene oxide powders' weight fraction, different boundary conditions, various porosity distributions, foundation parameters and temperature change of uniform thermal loading

Periodic response of a nonlinear axially moving beam with a nonlinear energy sink and piezoelectric attachment

An efficient semi-numerical framework is used in this paper to analyze the dynamic model of an axially moving beam with a nonlinear attachment composed of a nonlinear energy sink and a piezoelectric device. The governing equations of motion of the system are derived by using the Hamilton’s principle with von Karman strain-displacement relation and Euler - Bernoulli beam theory. The nonlinear energy sink is modeled as a lumped - mass system composed of a point mass, a spring with nonlinear cubic stiffness and a linear viscous damping element. The piezoelectric device is placed in the ground configuration. Frequency response curves of the presented nonlinear system are determined by introducing the incremental harmonic balance and continuation method for different values of material parameters. Based on the Floquet theory, the stability of the periodic solution was determined. Moreover, the presented results are validated with the results obtained by a numerical method as well as the results from the literature. Numerical examples show a significant effect of the nonlinear attachment on frequency response diagrams and vibration amplitude reduction of the primary beam structure

Transducer applications, a compilation

The characteristics and applications of transducers are discussed. Subjects presented are: (1) thermal measurements, (2) liquid level and fluid flow measurements, (3) pressure transducers, (4) stress-strain measurements, (5) acceleration and velocity measurements, (6) displacement and angular rotation, and (7) transducer test and calibration methods

Extremely large-amplitude dynamics of cantilevers under coupled base excitation

Extremely large-amplitude nonlinear dynamics of a cantilever with a mass at the tip under coupled base excitations is examined for the first time. An exact model of the centreline rotation of the cantilever is developed capable of accurately predicting the cantilever dynamic response even at extremely large amplitudes; a nonlinear static finite element analysis is conducted to verify the accuracy of the proposed model at very large deflection amplitudes. The proposed model is based on the theory of Euler-Bernoulli and the internal damping model of Kelvin-Voigt; the centreline of the cantilever is assumed to remain inextensible. The proposed model for the cantilever centreline rotation is discretised via the Galerkin modal decomposition method while keeping all terms exact. Extensive numerical simulations are conducted to examine the primary and parametric resonance of the cantilever due to transverse and axial base excitations, respectively. It is shown that under the same axial and transverse amplitudes of excitation, the parametric resonance is much stronger than the primary resonance

Transient behavior of imperfect bi-directional functionally graded sandwich plates under moving loads

An investigation of dynamic behaviors of a sandwich plate containing an imperfect two dimensional functionally graded (2D-FG) core surrounded by two faces on a two-parameter elastic foundation and subjected to a moving load is carried out in this paper. The present sandwich solid is composed of a porous 2D-FG core covered by two homogenous layers. It is assumed that the middle layer has micro voids dispersed uniformly and unevenly through the layer thickness. The fundamental equations are governed within the framework of first-order-shear deformation theory by utilizing Hamilton’s principle, von-Karman geometrical nonlinearity and the principal of mixtures. Newmark direct integration procedure is implemented to transform the dynamic equations into a static form and then the kinetic dynamic relaxation numerical technique in conjunction with the finite difference discretization method are employed to solve the nonlinear partial differential governing equations. Finally, the effects of porosity fraction and scattering patterns, boundary constrains, the variation of materials’ grading indexes and elastic foundation constants on the transient performances of the plate are studied in detail

Impact On Laminated Composite Materials

Laminated composite materials are used extensively in aerospace and other applications. With their high specific modulus, high specific strength, and the capability of being tailored for a specific application, these materials offer definite advantages compared to more traditional materials. However, their behavior under impact is a concern, since impacts do occur during manufacture, normal operations, or maintenance. The situation is critical for impacts which induce significant internal damage, undetectable by visual inspection, that cause large drops in the strength and stability of the structure. Impact dynamics, including the motion of both the impactor and the target and the force developed at the interface, can be predicted accurately using a number of models. The state of stress in the vicinity of the impact is very complex and requires detailed analyses. Accurate criteria for predicting initial failure are generally not available, and analyses after initial failure are questionable. For these reasons, it can be said that a general method for estimating the type and size of impact damage is not available at this time. However, a large amount of experimental data has been published, and several important features of impact damage have been identified. In particular, interply delamination\u27s are known to occur at the interface between plies with different fiber orientation. Their shape is generally elongated in the direction of the fibers in the lower ply at that interface. The delaminated area is known to increase linearly with the kinetic energy of the impactor after a certain threshold value has been reached. The effect of impact damage on the properties of the laminate has obvious implications for design and inspection of actual structures. Experimental results concerning the residual strength of impact damaged specimens subjected to tension, compression, shear, bending, and both static and fatigue loading are available. Analyses concentrate primarily on predicting residual tensile and compressive strength. In order to fully understand the effect of foreign object impact damage, one should understand impact dynamics and be able to predict the location, type, and size of the damage induced and the residual properties of the laminate. This article is organized along these lines and presents a comprehensive review of the literature on impact of laminated composites, considering both experimental and analytical approaches. © 1991 American Society of Mechanical Engineers

Forced vibration characteristics of embedded graphene oxide powder reinforced metal foam nanocomposite plate in thermal environment

Dynamic behavior of a new class of nanocomposites consisted of metal foam as matrix and graphene oxide powders as reinforcement is presented in this study in the framework of forced vibration. Graphene oxide powders are dispersed through the thickness of a plate made from metal foam material according to four various functionally graded patterns on the basis of the Halpin-Tsai micromechanical homogenization method. Also, three kinds of porosity distributions including two symmetric and one uniform patterns are considered for the metal foam matrix. As external effects, the plate is rested on the Winkler-Pasternak substrate and under uniform thermal and transverse dynamic loadings. By an incorporation of the refined higher order plate theory and Hamilton's principle, the governing equations of the dynamically loaded graphene oxide powder reinforced metal foam nanocomposite plate are derived and then solved with Galerkin exact solution method to achieve the resonance frequencies and dynamic deflections of the structure. Moreover, the influence of different boundary conditions is taken into account. The results indicate that the forced vibrational response of the graphene oxide powder strengthened metal foam nanocomposite plate is dramatically dependent on various parameters such as graphene oxide powders' weight fraction, different boundary conditions, various porosity distributions, foundation parameters and temperature change of uniform thermal loading.This research is financially supported by the Ministry of Science and Technology of China (Grant No. 2019YFE0112400), National Science Foundation of China (Grant No. 52078310), the Taishan Scholar Priority Discipline Talent Group program funded by the Shan Dong Province, and the first-class discipline project funded by the Education Department of Shandong Province. The publication of this article was funded by Qatar National Library.Scopu