Hygrothermal analysis of heterogeneous piezoelectric elastic cylinders

The analytical solutions of hygrothermal effects in heterogeneous piezoelectric solid and hollow cylinders are obtained. The interaction of electric displacement, electric potentials, and elastic deformations is discussed. The present cylinder is subjected to a mechanical load at its lateral surfaces as well as an electric potential. The displacement, stresses and electric potentials in the heterogeneous piezoelectric cylinders are determined. The material properties coefficients of the present cylinder are assumed to be changed in the radial direction. The hygrothermoelastic responses of piezoelectric heterogeneous hollow and solid circular cylinders are presented. Numerical application examples for both cylinders are displayed. The significant of influence of material inhomogeneity, initial temperature, final moisture, and the pressure load and electric potential ratios are investigated. Suitable discussions and conclusions are presented

Nonlocal thermoelastic vibrations for variable thermal conductivity nanobeams due to harmonically varying heat

This article constructs a new model of nonlocal thermoelasticity beam theory with phase-lags considering the thermal conductivity to be variable. A nanobeam subjected to a harmonically varying heat is considered. The nonlocal theories of coupled thermoelasticity and generalized thermoelasticity with one relaxation time can be extracted as limited and special cases of the present model. The effects of the variable thermal conductivity parameter, the nonlocal parameter, the phase-lags and the angular frequency of thermal vibration on the lateral vibration, the temperature, the displacement, and the bending moment of the nanobeam are investigated

Free vibration analysis of doubly convex/concave functionally graded sandwich beams

This paper presents the highly accurate analytical investigation of the natural frequencies for doubly convex/concave sandwich beams with simply-supported or clamped-supported boundary conditions. The present sandwich beam is made of a functionally graded material composed of metal and ceramic. The properties are graded in the thickness direction of the two faces according to a volume fraction power-law distribution. The bottom surface of the bottom face and the top surface of the top face are both metal-rich material. The core is made of a fully ceramic material. The thickness of the sandwich beam varies along its length according to a quadratic-law distribution. Two types of configuration with doubly convex and doubly concave thickness variations are presented. The governing equation and boundary conditions are derived using the dynamic version of the principle of minimum of the total energy. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effect of configurations of the constituent materials on the frequencies. Natural vibration frequencies of sandwich beams versus many parameters are graphically presented and remarking conclusions are made

Torsional Dynamic Response of a Carbon Nanotube Embedded in Visco-Pasternak’s Medium

The torsional dynamics of carbon nanotubes embedded in viscoelastic medium are presented by using the nonlocal elasticity theory. The medium is considered as a foundation model which characterized by the linear Winkler’s modulus, Pasternak’s (shear) foundation modulus and the damping coefficient. The governing torsional equation is obtained and solved for nanotubes subjected to various boundary conditions and stated under different loads. The effects of some parameters like nonlocal parameter, nanotube length, Winkler’s modulus, and damping coefficient on the angular displacement of the nanotube are investigated in detail. The angular displacements are very sensitive to all parameters, especially the inclusion of the viscous damping foundation. Present results can be useful in design of future nano composites, nano electromechanical systems like nano position sensors and linear servomotors. Sample angular displacements are tabulated and plotted for sensing the effect of all used parameters and to investigate the visco-Pasternak’s parameters for future comparisons

Two-Dimensional Coupled Solution for Thermoelastic Beams via Generalized Dual-Phase-Lags Model

The generalized thermoelastic problem of a thick-walled simply-supported beam subjected to different applied heat source and mechanical loads at its surfaces is studied. The thermoelastic coupling differential equations of motion of the beam are established. The generalized thermoelasticity based on the dual-phase-lags (DPLs) theory is considered to treat this problem. An exact 2-D coupled solution is presented to deduce analytical expressions for the temperature, displacements and stresses. The time-harmonic motion behavior as well as the thermal and mechanical conditions at the bounded faces of the beam is used for this purpose. The effect of the DPLs on the field quantities against the axial and normal directions of the beam under thermomechanical loads is discussed. Final investigations to various thermoelastic models are made

Axiomatic/asymptotic evaluation of multilayered plate theories by using single and multi-points error criteria

AbstractThis paper deals with refined theories for multilayered composites plates. Layer-Wise (LW) and Equivalent Single Layer (ESL) theories are evaluated by means of axiomatic–asymptotic approach. Theories with forth order displacement fields in the thickness layer/plate direction z are implemented by referring to the Unified Formulation by Carrera. The effectiveness of each term of the made expansion is evaluated by comparing the related theories with a reference solution. As a result a reduced model is obtained which preserve the accuracy of the full-model (model that include the whole terms of the z-expansion) but it removes the not-significant terms in the same expansion (those terms that do no improve the results according to a given error criteria). Various single-point and multi-point error criteria have been analyzed and compared in order to establish such an effectiveness: error localized in an assigned point along z, error localized at each interface, error located at the z-value corresponding to the maximum value of the considered variables, etc. Applications are given in case of closed form solutions of orthotropic cross-ply, rectangular, simply supported plates loaded by bisinusoidal distribution of transverse pressure. Symmetrically and unsymmetrical laminated cases are considered along with sandwich plates. It is found the reduced model is strongly influenced by the used localized error and that in same case the reduced model which is obtained by of single point criteria can be very much improved by the use of multi-point criteria

Fractional Thermoelasticity Model of a 2D Problem of Mode-I Crack in a Fibre-Reinforced Thermal Environment

A model of fractional-order of thermoelasticity is applied to study a 2D problem of mode-I crack in a fibre-reinforced thermal environment. The crack is under prescribed distributions of heat and pressure. The normal mode analysis is applied to deduce exact formulae for displacements, stresses, and temperature. Variations of field quantities with the axial direction are illustrated graphically. The results regarding the presence and absence of fiber reinforcement and fractional parameters are compared. Some particular cases are also investigated via the generalized thermoelastic theory. The presented results can be applied to design different fibre-reinforced isotropic thermoelastic elements subjected to the thermal load in order to meet special technical requirements

Thermoelastic Vibration of Temperature-Dependent Nanobeams Due to Rectified Sine Wave Heating—A State Space Approach

In this study, the second type of Green and Naghdi's thermoelasticity theory is applied to present the vibration of a nanobeam subjected to rectified sine wave heating based upon the nonlocal thermoelasticity theory. Both Young's modulus and thermal conductivity are considered to be linear functions of the temperature. The Laplace transform domain is adopted to solve the governing partial differential equations using the state space approach. Numerical computations are carried out using the inverse of Laplace transforms. The effects of nonlocal parameter and angular frequency on the thermal vibration quantities are discussed. The results of all quantities are illustrated graphically and investigated

Even and Uneven Porosities on Rotating Functionally Graded ‎Variable-thickness Annular Disks with Magneto-electro-thermo-‎mechanical Loadings

This paper investigates the porosity effect on rotating functionally graded piezoelectric (FGP) variable-thickness annular disk. Even and uneven porosity distributions for the disk are approximated. The porous annular disk is subjected to the influence of electromagnetic, thermal, and mechanical loadings. Material coefficients are graded and described as a power law in the radial direction of the annular rotating disk. The resulting differential equation with boundary conditions is solved using the semi-analytical technique. Two cases are studied for the porous annular disk, circular disk, and mounted disk. The effectiveness of the porosity factor and grading index on the temperature, stresses, and displacement are reported. Comparisons between non-porous and porous annular disks for even and uneven porosity are executed and discussed. The obtained results are presented to conclude the important role of porosity on the rotating variable-thickness annular disk for the purpose of engineering mechanical design