Elastic Foundations In Thermal Environments Research Articles

Nonlinear vibration of hybrid laminated plates resting on elastic foundations in thermal environments

This paper deals with large amplitude vibration of hybrid laminated plates containing piezoelectric layers resting on an elastic foundation in thermal environments. The motion equation of the plate that includes plate-foundation interaction is based on a higher order shear deformation plate theory and solved by a two-step perturbation technique. The thermo-piezoelectric effects are also included and the material properties of both orthotropic layers and piezoelectric layers are assumed to be temperature-dependent. The numerical illustrations concern nonlinear vibration characteristics of unsymmetric cross-ply and antisymmetric angle-ply laminated plates with fully covered or embedded piezoelectric actuators under different sets of thermal and electrical loading conditions. The results show that the foundation stiffness and stacking sequence have a significant effect on the nonlinear vibration characteristics of the hybrid laminated plate. The results also reveal that the temperature rise reduces the natural frequency, but it only has a small effect on the nonlinear to linear frequency ratios of the hybrid laminated plate. The results confirm that the effect of the applied voltage on the natural frequency and the nonlinear to linear frequency ratios of the hybrid laminated plate is marginal except the plate is sufficiently thin.

Nonlinear vibration and bending of sandwich plates with nanotube-reinforced composite face sheets

This paper studied the large amplitude vibration and the nonlinear bending of a sandwich plate with carbon nanotube-reinforced composite (CNTRC) face sheets resting on an elastic foundation in thermal environments. The material properties of CNTRC face sheets are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The governing equation of the plate that includes plate-foundation interaction is solved by a two-step perturbation technique. The thermal effects are also included and the material properties of both CNTRC face sheets and homogeneous core layer are assumed to be temperature-dependent. A detailed parametric study is conducted to study the effects of nanotube volume fraction, core-to-face sheet thickness ratio, temperature change, foundation stiffness and in-plane boundary conditions on the nonlinear vibration characteristics and nonlinear bending behaviors of sandwich plates with functionally graded CNTRC face sheets. The results for the same plate with uniformly distributed CNTRC face sheets are also provided for comparison.

Nonlinear analysis of sandwich plates with FGM face sheets resting on elastic foundations

Nonlinear vibration, nonlinear bending and postbuckling analyses are presented for a sandwich plate with FGM face sheets resting on an elastic foundation in thermal environments. The material properties of FGM face sheets are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equation of the plate that includes plate-foundation interaction is solved by a two-step perturbation technique. The thermal effects are also included and the material properties of both FGM face sheets and homogeneous core layer are assumed to be temperature-dependent. The numerical results reveal that the foundation stiffness and temperature rise have a significant effect on the natural frequency, buckling load, postbuckling and nonlinear bending behaviors of sandwich plates. The results also reveal that the core-to-face sheet thickness ratio and the volume fraction distribution of FGM face sheets have a significant effect on the natural frequency, buckling load and postbuckling behavior of the sandwich plate, whereas this effect is less pronounced for the nonlinear bending, and is marginal for the nonlinear to linear frequency ratios of the same sandwich plate.

Nonlinear vibration of nanotube-reinforced composite plates in thermal environments

This paper deals with the large amplitude vibration of nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs) resting on an elastic foundation in thermal environments. The SWCNTs are assumed aligned, straight and a uniform layout. Two kinds of carbon nanotube-reinforced composite (CNTRC) plates, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements, are considered. The material properties of FG-CNTRC plates are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The motion equations are based on a higher-order shear deformation plate theory that includes plate-foundation interaction. The thermal effects are also included and the material properties of CNTRCs are assumed to be temperature-dependent. The equations of motion are solved by an improved perturbation technique to determine nonlinear frequencies of CNTRC plates. Numerical results reveal that the natural frequencies as well as the nonlinear to linear frequency ratios are increased by increasing the CNT volume fraction. The results also show that the natural frequencies are reduced but the nonlinear to linear frequency ratios are increased by increasing the temperature rise or by decreasing the foundation stiffness. The results confirm that a functionally graded reinforcement has a significant effect on the nonlinear vibration characteristics of CNTRC plates.

Nonlocal beam model for nonlinear analysis of carbon nanotubes on elastomeric substrates

Postbuckling, nonlinear bending and nonlinear vibration analyses are presented for single-wall carbon nanotubes (SWCNTs) resting on a two-parameter elastic foundation in thermal environments. The SWCNT is modeled as a nonlocal nanobeam which contains small scale effects. The elastomeric substrate with finite depth is modeled as a two-parameter elastic foundation. The thermal effects are included and the material properties of both SWCNTs and the substrate are assumed to be temperature-dependent. The governing equation that includes beam–foundation interaction is solved by a two-step perturbation technique. The numerical results reveal that the small scale parameter e0a reduces the postbuckling equilibrium paths, the static large deflections and natural frequencies of SWCNTs resting on an elastic foundation. The results also reveal that the effect of the small scale parameter is significant for compressive buckling, but less pronounced for static bending and marginal for free vibration of SWCNTs resting on an elastic foundation.

Nonlocal plate model for nonlinear analysis of thin films on elastic foundations in thermal environments

Postbuckling, nonlinear bending and nonlinear vibration analyses are presented for a simply supported stiff thin film resting on a two-parameter elastic foundation in thermal environments. The stiff thin film is modeled as a nonlocal orthotropic plate which contains small scale effects. The elastomeric substrate with finite depth is modeled as a two-parameter elastic foundation. The thermal effects are included and the material properties of the substrate are assumed to be temperature-dependent. The governing equation that includes plate-foundation interaction is solved by a two-step perturbation technique. The numerical results reveal that the small scale parameter e0a reduces the postbuckling equilibrium paths, the static large deflections and natural frequencies, but increases the nonlinear to linear frequency ratios of the thin film slightly. The results also reveal that the effect of the small scale parameter is significant for compressive buckling, but less pronounced for static bending and marginal for free vibration of the thin film resting on an elastic foundation.

Stochastic nonlinear free vibration of laminated composite plates resting on elastic foundation in thermal environments

This paper presents the nonlinear free vibration analysis of laminated composite plates resting on elastic foundation with random system properties in thermal environments. System parameters are modeled as basic random variables for accurate prediction of system behavior. A C0 nonlinear finite element based on HSDT in von Karman sense is used to descretize the laminate. A direct iterative method in conjunction with first-order perturbation technique is outlined and applied to solve the stochastic nonlinear generalized eigenvalue problem. The developed stochastic procedure is successfully used for thermally induced nonlinear free vibration problem with a reasonable accuracy. Numerical results for various combinations of boundary conditions, geometric parameters, amplitude ratios, foundation parameters and thermal loading have been compared with those available in literature and an independent MCS. Some new results are also presented which clearly demonstrate the importance of the randomness in the system parameters on the response of the structures.