Search

In this article, an elastic foundation is used to study the characteristics of flexural edge waves propagating on a piezoelectric structure. The nonlocal elasticity theory is introduced to investigate the microscale effect on edge wave propagation. The traditional Kirchhoff plate hypothesis is used to determine the kinematics of the piezoelectric plate. By considering the sinusoidal waveform, a closed-form dispersion relation can be obtained. In the context of a flexural edge wave on a piezoelectric plate, an analytical and graphical comparison between the two boundary conditions (i.e. short circuit and open circuit) is discussed. In the presence of nonlocal elasticity, the dispersion relation is implied as an implicit function of frequency and wave number. A significant difference occurred between the dispersion curves for piezoelectric plates with different foundations and nonlocal parameters. Due to the Pasternak elastic foundation, an increasing rate of the fundamental mode of frequency is observed at the traction-free edge of a thin, semi-infinite piezoelectric plate. In contrast, the nonlocal elasticity tends to decrease this fundamental frequency mode for a particular wave number value. The corresponding phase velocity decreases rapidly within a short range of wave numbers. [ABSTRACT FROM AUTHOR]

Today, due to the many applications of sandwich beams in industry, studying the forced vibrations of these structures is important. In these structures, amplifiers are used to improve mechanical properties. In this paper, metal-based graphene (copper) is used to improve the mechanical properties. This research uses a functionally graded (FG) graphene-reinforced copper-based composite (GRCC) sandwich beam and FG soft porous core, subjected to two moving loads and located on an elastic foundation. The equations are derived using Soldatos' higher-order shear deformation theory in axial and transverse directions. The exact problem under the magnetic field is solved using the Laplace method, which has not been done. The advantages of this method are the simplicity of solving and reducing to zero the error percentage that exists in numerical solutions. The results are compared with previous works. Finally, the effect of various parameters such as magnetic, porosity coefficient, elastic constant, thickness ratio, and velocity of moving load on the dynamic response of the sandwich beam is investigated. It should be noted that the results can be used to construct this type of structure. [ABSTRACT FROM AUTHOR]

A laminated composite plate designed is supposed to be used under different end supports. The elastic foundation is one of such conditions. The strength of the laminated composite plates can be enhanced by altering constituents or by the addition of filler materials. For localized strengthening of laminated composite plates, such as at particular layers, it is not cost-effective to strengthen the whole structure. So, the laminated composite plates are strengthened at a particular layer by adding the fillering materials, for example, graphene or flyash. The addition of these filler materials in a particular region sometimes causes agglomeration. Agglomeration of filler materials causes adverse effects such as stress concentration or strain aging. In theoretical formulation, Eringen's nonlocal principle is applied to account for the impact of agglomeration. In the current study, neat epoxy glass laminated composite plates as well as rectangle laminated composite plate variants with outer layer graphene, core layer graphene, functionally graded laminated composite plate, laminated composite plates exclusively rich in graphene, and laminated composite plates only rich in flyash are taken into consideration. Using a layer-wise model, the fifth-order shear deformation theory is applied. The laminated composite plates are assumed to rest on an elastic foundation. The consequence of elastic coefficient of foundation on procured parameters such as fundamental frequencies, stress parameters, center deflections, and buckling performance is determined. For this purpose, computerized programs are developed using MATLAB and validated first for isotropic material. Further, the work is extended to study these effects on the laminated composite plate variants. [ABSTRACT FROM AUTHOR]

Efficient and accurate simulation of the vibration characteristics of a composite pipeline system is the key to the study of the stability and vibration control of the pipeline system. A simulation method called transfer matrix method for multibody systems is used to predict the vibration of a composite pipeline resting on an elastic soil. The transfer matrix of the Euler–Bernoulli beams considering the internal fluid velocity and high-efficiency dynamics model of the pipeline system under the action of the elastic foundation are derived. The simulation results have good agreement with that of the literature and commercial software ANSYS Workbench which verified the accuracy of the numerical model. The simulation results show that with the increase of the velocity, the natural frequencies of each mode of the pipeline decrease continuously. When the first frequency is zero, the pipeline buckling occurs and the velocity reaches the critical velocity; the elastic coefficient and shear coefficient in the foundation coefficient are positively related to the stability of the pipeline system. The damping coefficient is negatively related to pipeline stability. [ABSTRACT FROM AUTHOR]

In this study, free vibration and buckling behaviors of a functionally graded nanoplate supported by the Winkler–Pasternak foundation using a nonlocal classical plate theory are investigated. Eringen's nonlocal differential model has been used for considering the small-scale effect. The properties of the functionally graded nanoplate are considered to vary transversely following the power law. The governing vibration and buckling equations of an elastically supported functionally graded nanoplate have been derived using the principle of virtual work, and the solution is obtained using the Rayleigh–Ritz method and characteristic polynomials. The advantage of this method is that it disposes of all the drawbacks regarding edge constraints. The objective of the article is to see the effect of edge constraints, aspect ratios, material property exponent, nonlocal parameter, and foundation parameters on the nondimensionalized frequency and the buckling load of an embedded functionally graded nanoplate in a thermal environment. The study highlights that the nonlocal effect is pronounced for higher modes and/or higher aspect ratios and need to be considered for the analysis of the nanoplate. Further, it is observed that the effect of the Pasternak foundation is prominent on nondimensionalized frequencies and buckling of the functionally graded nanoplate. [ABSTRACT FROM AUTHOR]

Hydraulic crawler excavators have been widely used for construction in industry, mining, and agriculture because of their special ability to work on weak soil support. However, the elastic properties of the ground increase the undesired vibrations of the entire operating machine. These oscillations significantly influence the working productivity, the level of fuel expenditure, and the comfort of the driver. There have been many works addressing this problem, although they mainly focus on mechanical dampers. Considering the system from robotic and control aspects, this study presents a new approach to deal with the abovementioned problem. A controller design, which uses a combination of feedback linearization and sliding mode control, is proposed based on a dynamic model. This control law reduces the vibrations of the system working on an elastic foundation, while also allowing for accurate tracking performance of the links. This control law is applied to a small-scale platform to investigate its feasibility for practical applications. [ABSTRACT FROM AUTHOR]

This paper develops a nonlocal strain gradient plate model for vibration analysis of double-layered graded nanoplates under linearly variable in-plane mechanical loads in hygro-thermal environments. For more accurate analysis of nanoplates, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. The double-layered nanoplate is modeled via a four-variable shear deformation plate theory needless of shear correction factors. Governing equations of a nonlocal strain gradient nanoplate on elastic substrate are derived via Hamilton’s principle. Galerkin’s method is implemented to solve the governing equations. Effects of different factors such as in-plane loading, load factor, nonlocal parameter, length scale parameter, moisture percentage rise, temperature rise, elastic foundation, and boundary conditions on vibration characteristics of a double-layered nanoplate have been examined. [ABSTRACT FROM AUTHOR]

In this article, stresses and free-vibration behaviors of annular circular piezoelectric nanocomposite plate reinforced by functionally graded single-walled boron nitride nanotubes (FG-SWBNNTs) embedded in an elastic foundation based on modified couple stress theory (MCST) are explored. The mechanical properties of FG-SWBNNT-reinforced nanocomposite plate are assumed to be graded in the direction of thickness and estimated through the micro-mechanical approach. The governing equations are obtained using the energy method. The natural frequencies and stresses of FG-SWBNNT-reinforced nanocomposite plate are computed using the differential quadrature method (DQM). An excellent agreement is observed between the obtained results and the results in the literature. Influences of the internal radius to the external radius, the thickness to the internal radius ratio, the material length scale parameter, the functionally graded parameter, temperature changes and elastic coefficients on the natural frequencies and stresses of the hollow circular nanocomposite plate are investigated. The results of this research show that the natural frequencies of the piezoelectric nanocomposite plate increase by increasing the material length scale parameter, the elastic foundation parameters, the ratio of the inner radius to the outer radius, the ratio of the thickness to the inner radius, and decreasing the power index and temperature change. The radial stress of the nanocomposite plate varies proportionally to its mode shape. The results can be employed to design smart structures in micro-electro-mechanical systems (MEMS). [ABSTRACT FROM AUTHOR]

Free vibration analysis of embedded functionally graded carbon nanotube-reinforced composite (FG-CNTRC) conical, cylindrical shells and annular plates is carried out using the variational differential quadrature (VDQ) method. Pasternak-type elastic foundation is taken into consideration. It is assumed that the functionally graded nanocomposite materials have the continuous material properties defined according to extended rule of mixture. Based on the first-order shear deformation theory, the energy functional of the structure is calculated. Applying the generalized differential quadrature method and periodic differential operators in axial and circumferential directions, respectively, the discretized form of the energy functional is derived. Based on Hamilton’s principle and using the VDQ method, the reduced forms of mass and stiffness matrices are obtained. The comparison and convergence studies of the present numerical method are first performed and then various numerical results are presented. It is found that the volume fractions and functionally grading of carbon nanotubes play important roles in the vibrational characteristics of FG-CNTRC cylindrical, conical shells and annular plates. [ABSTRACT FROM AUTHOR]

A novel numerical approach based on the weak form quadrature element method is developed to study the effect of initial stress on the attenuation zones and attenuation coefficients of periodic Timoshenko beams resting on a two-parameter elastic foundation. For some special cases, comparisons with other related investigations are conducted to validate the proposed method, and good agreement is found. The results show that the compressive initial stress enhances the maximum attenuation in the second attenuation zone while it weakens the maximum attenuation in the first attenuation zone. In addition, based on the detailed modal analysis, simplified models are proposed to determine the bound frequencies of the lowest attenuation zone. Furthermore, frequency domain analysis and transient response analysis for a beam with finite unit cells are performed to verify the theoretical analysis of the infinite-unit cell beam. The present investigation is very helpful for the design and application of periodic strip foundations and pipelines for vibration isolation in buildings and infrastructures. [ABSTRACT FROM AUTHOR]

A thorough understanding of the dynamic behavior of one-dimensional structural members such as beams plays a crucial role in specialized disciplines including ocean, bridge and railway engineering. The vibratory response of an in-service beam-like component may deviate from that expected from the intact structure when defects are present. In this work, we present a semi-analytical approach to predict the forced response of a multi-cracked Timoshenko beam traversed by a moving harmonic load with constant speed. The beam is fully or partially supported by the viscoelastic foundation, where the normal stiffness and shear modulus of the subgrade are considered. The effects of transverse open cracks are modeled by massless rotational springs with a linear moment-rotation constitutive law to account for the local flexibility induced by the damage. Based on the transfer matrix method, the defective structure is treated as an assembly of sub-beams to derive the eigenvalue solution of the system. The time response is then obtained by utilizing identical generalized coordinates for lateral and rotational displacement components when applying the modal expansion technique. The use of general elastic end constraints allows us to recover all possible boundary conditions. Numerical examples are also provided to demonstrate the robustness and accuracy of the proposed method, and also to investigate the influence of important parameters on the dynamic behavior of the damaged structure. [ABSTRACT FROM AUTHOR]

Wave propagation in sandwich structures with periodic assemblies on elastic foundation under external moving load is studied. Two types of periodic assemblies are considered, namely, a periodic core, and a core with periodically embedded resonators. Wave numbers and traveling wave characteristics are analyzed by introducing a moving coordinate system. Depending on whether the bandgap (attenuation zone) exists, the perturbation due to the external moving load can/cannot propagate through the structure. The bandgap properties of both types of structures in the velocity field are also investigated. It is found that the location and range of the bandgap can be tailored by the physical properties of the core/resonator. [ABSTRACT FROM AUTHOR]

This paper deals with the dynamic behavior of a non-uniform column reinforced by single-walled carbon nanotubes resting on an elastic foundation and subjected to follower force. The method of solution is the differential quadrature method. The carbon nanotube reinforced composite (CNTRC) columns have smooth variation of carbon nanotube (CNT) fraction in the thickness direction and the material properties are estimated by the extended rule of mixture. Detailed parametric studies have been carried out to reveal the influences of the kind of distribution and volume fractions of CNT on natural frequencies and the critical load for the CNTRC column. [ABSTRACT FROM AUTHOR]

This paper presents an analytical investigation on the nonlinear dynamic analysis of functionally graded double curved thin shallow shells using a simple power-law distribution (P-FGM) with temperature-dependent properties on an elastic foundation and subjected to mechanical load and temperature. The formulations are based on the classical shell theory, taking into account geometrical nonlinearity, initial geometrical imperfection, temperature-dependent properties and unlike other publications, Poisson ratio is assumed to be varied smoothly along the thickness ν=ν(z). The nonlinear equations are solved by the Bubnov-Galerkin and Runge-Kutta methods. The obtained results show the effects of temperature, material and geometrical properties, imperfection and elastic foundation on the nonlinear vibration and nonlinear dynamical response of double curved FGM shallow shells. Some results were compared with those of other authors. [ABSTRACT FROM PUBLISHER]

This paper presents a first proposal to investigate the nonlinear dynamic response of imperfect symmetric thin sigmoid-functionally graded material (S-FGM) plate resting on an elastic foundation and subjected to mechanical loads. The formulations use classical plate theory taking into account geometrical nonlinearity, initial geometrical imperfection of the S-FGM plate and stress function. The volume fractions of metal and ceramic are applied by sigmoid-law distribution (S-FGM) with metal-ceramic-metal layers. The nonlinear equations are solved by the Runge-Kutta and Bubnov-Galerkin methods using stress function. The obtained results show the effects of material, imperfection and elastic foundations on the dynamical response of S-FGM plate. [ABSTRACT FROM PUBLISHER]

In this paper the free vibration and the stability of axially loaded Timoshenko beams on elastic foundation are analyzed through the dynamic stiffness matrix method. The study is carried out considering a two–parameter elastic soil which contains the characteristics of both the Winkler and the Pasternak foundations. The equation of motion and the exact dynamic stiffness matrix of a beam–column including the effect of shear deformation and rotatory inertia is derived. The eigenproblem of the beam–column is therefore solved through the application of the general Wittrick and Williams algorithm. The effects of soil characteristics as well as shear deformations and rotatory inertia on the natural frequencies of the beam-column are investigated. An extensive parametric study highlights the main parameters that characterize the dynamical behavior of the considered beam–column. [ABSTRACT FROM AUTHOR]

The present work deals with the problem of the dynamic behavior of infinite beams resting on a Winkler-type elastic foundation under moving loads. The beam is subjected to a moving point load traveling with constant speed. Determining the effective length of the beam for a non-moving (static) load, and using the so-called quasi-stationary state of the beam, a solution is proposed with the aid of modal analysis and useful conclusions are obtained. Moving loads have a significant influence on the dynamic behavior of elastic or inelastic solid elements of an entire structure or parts of the structure, while they may produce strong vibrations on such systems, especially when high speeds are reached. The expressions obtained in this work allow the use of the same formulae for any values of speed or damping parameters. The analytical results obtained by the relations presented herein are compared to the ones given by Frýba in the relative chapter of his classic work. Finally, the possible speeds of moving loads that can be reached in the case of such types of beams are estimated and the application field of the gathered relations is determined. [ABSTRACT FROM PUBLISHER]

This article introduces an exact analytical method for free vibration analysis of functionally graded (FG) thin annular sector plates resting on Winkler and Pasternak elastic foundations. The annular sector plate has simply supported radial edges and arbitrary boundary conditions along the circular edges. Based on the displacement field of Kirchhoff plate theory, the governing equations of motion are obtained considering the in-plane displacements and rotary inertia. Using a set of functions, the three coupled governing equations of motion are converted into two decoupled equations. By applying the boundary conditions at inner and outer radii, an eigenvalue problem for finding the natural frequencies is obtained. The nine distinct cases are considered involve all possible combinations of boundary conditions along the circular edges. Accurate non-dimensional frequency is presented for over a wide range of sector angles, some inner to outer radii (aspect ratio) and different powers of functionally graded material. Accurate natural frequencies of FG annular sector plates resting on elastic foundations are presented for the first time and can be used as reference values for numerical analyses. [ABSTRACT FROM PUBLISHER]

In this work, we study, through one-mode simplification, the influence of frequency curve veering on the primary resonance response of an elastic Euler-Bernoulli attached to a linear Winkler elastic foundation. The beam is a hinged-hinged with one torsional spring at one end, has an initial ¼ sine deflection shape due to a constant differential edge settlement and is subjected to a uniformly distributed vertical load which is harmonically varying with a time part and a large mean part. A combined numerical-analytical procedure which accounts for the nonlinear interdependence between the vertical deflection and induced axial force due to mid-plane stretching was used to determine the beam static deflection. The assumed single mode approach is used to obtain the reduced nonlinear temporal equation of motion about the static equilibrium deflection which contains quadratic and cubic nonlinear terms. The results of numerical simulation indicate that the co-efficients of the quadratic and cubic nonlinear terms in the temporal problem can, depending on the selected range of system parameters, vary widely and take positive and negative values, and thus change the number and stability of equilibrium positions as well as the system behavior which can be a hardening or softening type. The harmonic balance and, for comparison purposes, the method of multiple-scales are used to obtain approximate analytical solution for the primary resonance response and its stability. The obtained primary frequency response results are presented over a selected range of system parameters near and away from veering points which show a significant change in response behavior. The obtained approximate-analytical results were compared with those obtained numerically. [ABSTRACT FROM AUTHOR]

In this work we present an investigation into nonlinear frequency veering of an elastic Euler- Bernoulli beam resting on a Winkler elastic foundation subjected to a static lateral load and hinged-hinged, with a torsional spring at one end. The beam is assumed to have an initial quarter-sine shape rise owing to a constant differential edge settlement. The beam static deflection is obtained by using a combined numerical-analytical procedure that accounts for the induced nonlinear axial force to mid-plane stretching. The harmonic balance method is used to solve for the nonlinear natural frequency of the associated nonlinear temporal problem obtained using the assumed mode method. The results are presented in the form of characteristic curves which show variation of the nonlinear natural frequency of the three modes of a selected range of system parameters. These results indicate that, depending on the system parameters, the nonlinear natural frequency of various modes can exhibit complicated behaviors not found using linear analysis. [ABSTRACT FROM AUTHOR]