Influence Of Elastic Foundation Research Articles

Influences of elastic foundation on bending analysis of multidirectional porous functionally graded plate under industrial used loading: a meshfree approach

Influences of elastic foundation on bending analysis of multidirectional porous functionally graded plate under industrial used loading: a meshfree approach

Dynamic Response of Rapidly Heated Rectangular Plates Made of Porous Functionally Graded Material

In this paper, the nonlinear thermally induced vibration in rectangular plates made of porous functionally graded materials (FGMs) due to thermal shock is studied based on a new numerical approach. The shear deformation influences are taken into consideration via Mindlin’s plate theory. The properties of the materials are also assumed to be temperature- and position-dependent. Moreover, the influence of elastic foundation is captured by the Winkler–Pasternak model. For deriving the governing equations, Hamilton’s principle, transient 1D Fourier-type heat conduction equation and von Kármán hypothesis are utilized. The relations of paper are written in a new matricized format for computational aims. The generalized differential quadarature (GDQ) method and Newmark’s direct integration scheme are used for solving the heat equation. Furthermore, solving motion equations is done based on the variational differential quadrature (VDQ) formulation. The effects of important parameters including material porosity and elastic foundation on the thermal shock response of porous FG plates are investigated in the numerical results.

Influences of elastic foundations on the nonlinear free vibration of composite shells containing carbon nanotubes within shear deformation theory

In this work, the solution of nonlinear free vibration problem of composite shells structures containing carbon nanotubes (CNTs) resting on elastic soils within shear deformation theory (ST) is presented. After modeling the mechanical properties of nanocomposite shell structures containing CNTs and elastic soils, the basic relations, and governing equations of double curved shell structures within the ST are established considering the geometric nonlinearity. The frequencies of nonlinear and linear free vibrations and their ratios for inhomogeneous nanocomposite structures on the soils within the ST are obtained using perturbation method for the first time. After checking the methodology of the research, the effects of soils, nonlinearity, shear strains and patterns of CNT on the frequency-amplitude dependence of nanocomposite shell structures for various geometric parameters are carried out.

Influences of elastic foundations and thermal environments on the thermoelastic buckling of nanocomposite truncated conical shells

Influences of elastic foundations and thermal environments on the thermoelastic buckling of nanocomposite truncated conical shells

Analysis of Nonlinear Vibrations of Slightly Curved Tripled-Walled Carbon Nanotubes Resting on Elastic Foundations in a Magneto-Thermal Environment

In this work, nonlocal elasticity theory is applied to analyze nonlinear free vibrations of slightly curved multi-walled carbon nanotubes resting on nonlinear Winkler and Pasternak foundations in a thermal and magnetic environment. With the aid of Galerkin decomposition method, the systems of nonlinear partial differential equations are transformed into systems of nonlinear ordinary differential equations which are solved using homotopy perturbation method. The influences of elastic foundations, magnetic field, temperature rise, interlayer forces, small scale parameter and boundary conditions on the frequency ratio are investigated. It is observed form the results that the frequency ratio for all boundary conditions decreases as the number of walls increases. Also, it is established that the frequency ratio is highest for clamped-simple supported and lowest for clamped-clamped supported. Further investigations on the controlling parameters of the phenomena reveal that the frequency ratio decreases with increase in the value of spring constant (k1) temperature and magnetic field strength. It is hoped that this work will enhance the applications of carbon nanotubes in structural, electrical, mechanical and biological applications especially in a thermal and magnetic environment.

Dynamic behavior of FGM viscoelastic plates resting on elastic foundations

The free vibration (FV) and dynamic stability (DS) analyzes are presented for functionally graded viscoelastic plates (FGVPs) under compressive load and resting on elastic foundations (EFs). Winkler elastic foundation models and Pasternak elastic foundation models are used as elastic foundations. The basic equations of FGVPs interacting with EFs are derived using the concepts of Boltzmann and Volterra. An analytical method for studying the DS and FV of FGVPs interacting with EFs is developed using the integro-differential equations. To solve the current problem, Galerkin and Laplace methods are used. A technique for the analysis of DS and FV of FGVPs on the EFs is developed. To confirm the proposed formulation, the results are compared with other available solutions. Finally, the influences of EFs, volume fractions and rheological constants on the critical times and frequencies depending on the geometrical characteristics and loading parameters are examined.

Investigations on the influences of elastic foundations on the aerothermoelastic flutter and thermal buckling properties of lattice sandwich panels in supersonic airflow

The lattice sandwich panels supported on elastic mediums are often applied in the construction of aerospace structures because of the low specific weight, excellent bending rigidity and outstanding vibration properties. This elastic medium can be any spring materials including damping tapes or heat shields which are attached to one side of the sandwich panel. Therefore, in this paper, aerothermoelastic flutter and thermal buckling characteristics of sandwich panels with the pyramidal lattice core resting on elastic foundations in supersonic airflow are studied. The influences of geometrical parameters and elastic foundation on the panel flutter and thermal buckling of the structures are analyzed in detail. In the structural modeling, the first-order shear deformation theory is applied, and the effective material properties of the lattice core are used. The aerodynamic pressure is evaluated by the supersonic piston theory. Hamilton's principle and the assumed modes method are applied to formulate the equation of motion. The highlight point of this investigation is that an effective thermal buckling suppression method utilizing the elastic foundation is proposed, based on which the thermal buckling of the structure can be completely eliminated with the natural frequencies remaining unchanged when the shearing layer parameter is equal to the thermal load. Through the numerical results, the influences of the elastic foundation, aspect ratio, core-to-facesheet thickness ratio, and inclination angle of the core truss on the aerothermoelastic behaviors of the lattice sandwich panel are analyzed, and the thermal buckling elimination effects are also examined.

Local radial basis function collocation method for bending analyses of quasicrystal plates

• Meshless formulations are developed for static and dynamic bending of QC plates. • The phonon-phason coupling effects are studied numerically. • The influence of elastic foundation and variable plate thickness is investigated. • The response of QC plates to impact loading is simulated. The local radial basis function collocation method (LRBFCM) is proposed for plate bending analysis in orthorhombic quasicrystals (QCs) under static and transient dynamic loads. Three common types of the plate bending problems are considered: (1) QC plates resting on Winkler foundation (2) QC plates with variable thickness and (3) QC plates under a transient dynamic load. According to the Reissner–Mindlin plate bending theory, there is allowed to simulate the behavior of the two excitations in QC plates, phonon and phason, by 2D strong formulations for the system of governing equations. The governing equations, which describe the phason displacements, are based on Agiasofitou and Lazar elastodynamic model. Numerical results demonstrate the effect of the elastic foundation, as well as plate thickness on the phonon and phason characteristics in this paper. For the transient dynamic analysis, the influence of the phason friction coefficients on the responses of QC plate to transient dynamic loads is also studied.

Design of Multiple-level Parallel Dynamic Vibration Absorber Based on the Flexible Beam

The amplitude magnification factor dimensionless expression is gained through modeling multi-level parallel dynamic vibration absorber mathematical model combined with the impedance of elastic foundation based on the assumption of elastic foundation. It is found that the influence of elastic foundation on the main system cannot be ignored and the necessity is proposed to optimize the multiple-level parallel system combining the advantage of decaying vibration. The influence of the distance u between the connection and the end on the main system is also analyzed: the less u, the smaller the influence of the beam elastic vibration on the main system. The first frequency will not occur coupling vibration with the main system when u  1m, and u=2m has the most influence. The numerical optimization method is used to design the parameters of 2-grade parallel and 4-grade parallel system. The result shows: the result of rigid connects system is not applicable to the elastic system. It will effectively reduce the influence of the beam elastic vibration on the primary system through optimizing the whole system. At last, the connection dynamic stiffness is researched, it shows that the first natural frequency of beam has no effect on the first three nature frequencies when 40 d K  k , the influence can be neglected when 70 d K  k .

Electro-magnetic effects on nonlocal dynamic behavior of embedded piezoelectric nanoscale beams

This article investigates vibration behavior of magneto-electro-elastic functionally graded nanobeams embedded in two-parameter elastic foundation using a third-order parabolic shear deformation beam theory. Material properties of magneto-electro-elastic functionally graded nanobeam are supposed to be variable throughout the thickness based on power-law model. Based on Eringen’s nonlocal elasticity theory which captures the small size effects and using Hamilton’s principle, the nonlocal governing equations of motions are derived and then solved analytically. Then, the influences of elastic foundation, magnetic potential, external electric voltage, nonlocal parameter, power-law index, and slenderness ratio on the frequencies of the embedded magneto-electro-elastic functionally graded nanobeams are studied.

Influences of elastic foundations and shear deformations on the buckling behavior of functionally graded material truncated conical shells under axial compression

ABSTRACTThis article presents an investigation on the buckling of functionally graded (FG) truncated conical shells under an axial load resting on elastic foundations within the shear deformation theory (SDT). The governing equations are solved using the Galerkin method, and the closed-form solution of the axial buckling load for FG conical shells on elastic foundations within the SDT is obtained. Various numerical examples are presented and discussed to verify the accuracy of the closed-form solution in predicting dimensionless buckling loads for FG conical shells on the Winkler–Pasternak elastic foundations within the SDT.

The effect of elastic foundations on the nonlinear buckling behavior of axially compressed heterogeneous orthotropic truncated conical shells

The buckling problem of a heterogeneous orthotropic truncated conical shell subjected to an axial load and surrounded by elastic media is analyzed based on the finite deformation theory. Using von-Karman nonlinearity, the governing equations of elastic buckling of heterogeneous orthotropic truncated conical shells surrounded by elastic media are derived. The governing equations are solved using superposition and Galerkin methods and obtained expressions for upper and lower critical axial loads. The influences of elastic foundations, heterogeneity, orthotropy and geometric characteristics on the upper and lower critical loads of conical shells with and without elastic foundations are studied in detail.

The combined influences of heterogeneity and elastic foundations on the nonlinear vibration of orthotropic truncated conical shells

The aim of the present paper is to study the nonlinear vibration of heterogeneous orthotropic truncated conical shells resting on the Winkler–Pasternak elastic foundations. The formulation is based on the Donnell shell theory, exponential-law distribution of orthotropic material properties and von Karman geometric nonlinearity. The basic equations are reduced to a time dependent geometrical nonlinear differential equation and solved using homotopy perturbation method (HPM). Finally, the influences of elastic foundations, heterogeneity, material orthotropy and shell characteristics on the nonlinear vibration of the truncated conical shell are studied.

Influences of elastic foundations and boundary conditions on the buckling of laminated shell structures subjected to combined loads

This article presents to study the stability of laminated orthotropic cylindrical and truncated conical shells resting on elastic foundations and subjected to combined loads with the clamped and simply supported boundary conditions. Here, axial tensile loads separately applied to the small and large bases of a laminated truncated conical shell, respectively. The basic relations, the modified Donnell type stability and compatibility equations have been obtained for laminated orthotropic truncated conical shells on the Pasternak type elastic foundation. Applying Galerkin method, the critical combined loads of laminated orthotropic conical shells on the Pasternak type elastic foundation with different boundary conditions are obtained. The appropriate formulas for single-layer and laminated cylindrical shells on the Pasternak type elastic foundation made of orthotropic and isotropic materials are found as special cases. Finally, influences of the boundary conditions, the elastic foundation, the number and ordering of the layers and variations of the shell characteristics on the critical combined loads are investigated. The results are compared with their counterparts in the literature.