Free vibration analysis of solar functionally graded plates with temperature-dependent material properties using second order shear deformation theory

Abstract

Second-order shear deformation theory (SSDT) is employed to analyze vibration of temperature-dependent solar functionally graded plates (SFGP's). Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Two different types of SFGP's such as ZrO 2 /Ti-6Al-4V and Si 3 N 4 /SUS304 are considered. Uniform, linear, nonlinear, heat-flux and sinusoidal thermal conditions are imposed at the upper and lower surface for simply supported SFGPs. The energy method is applied to derive equilibrium equations, and solution is based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent and temperature-independent SFGP's and validated with known results in the literature.Numerical results indicate the effect of material composition, plate geometry, and temperature fields on the vibration characteristics and mode shapes. The results obtained using the SSDT are very close to results from other shear deformation theories.

Free Vibration Analysis of Reinforced Composite Functionally Graded Plates with Steady State Thermal Conditions

“…Many researchers have concentrated their investigation on plate and beam structure (Jafari et al (2016); Arani et al (2011);Shishesaz et al (2016); Shahrjerdi et al (2011);Ansari et al (2016)). They analyzed free vibration of functionally graded fiber reinforced plates via three dimensional elasticity theory.…”

Free vibration analysis of FG nanoplates embedded in elastic medium based on second-order shear deformation plate theory and nonlocal elasticity

“…Khdeir and Reddy [42] analyzed free vibration of laminated composite plate and solved the problems by using the Levy solution. Shahrjerdi et al [43] studied the effect of temperature fields on the vibration characteristics of the solar functionally graded plates.…”

Natural vibration-induced parametric excitation in delaminated Kirchhoff plates

“…Similarly to the theory of laminated and composite beams [83][84][85][86][87][88][89][90] the literature is very rich in the different theories to model laminated composite plates and shells. Thin flat plates can be modeled by the classical or Kirchhoff plate theory, 91,92 while for relatively thick plates the first-order shear deformation theory (FSDT or Mindlin), [93][94][95][96][97][98][99][100] second-order shear deformation theory (SSDT), [101][102][103][104][105] general third-order theory (TSDT), [106][107][108] Reddy third-order theory, [109][110][111][112] other higher-order shear deformation theories (HSDT), [113][114][115] layerwise theories, [116][117][118][119][120][121] and the 3D elasticity solutions 122,123 are developed. These theories have been utilized to model curved shells [124][125][126] and delaminated and cracked laminates …”