Vibration analysis of an axially functionally graded material non-prismatic beam under axial thermal variation in humid environment

Abstract

The vibration analysis of an axially functionally graded material non-prismatic Timoshenko beam under axial thermal variation in humid environment is carried out using the harmonic differential quadrature method. In this modeling, the length and width of the beam remains constant whereas thickness of the beam is linearly varied along the axis of the beam. The material properties are temperature dependent and are assumed to be varied continuously along the axial direction according to power law distribution. Three types of temperature variations are considered in this study, that is, uniform temperature rise, linear temperature rise, and non-linear temperature rise. The temperature of the beam remains constant under uniform temperature rise condition and it is varied linearly and nonlinearly along the length of beam for rest of the conditions. The beam is subjected to uniform moisture concentration to impose humidity. Hamiltonian’s approach is used to derive the governing equations of motion. The resultant governing equations are then solved using the harmonic differential quadrature method to obtain the natural frequencies of the axially functionally graded material non-prismatic beam. The results obtained using the harmonic differential quadrature method are compared with results obtained for special cases. The effects of thermal variation, humidity, non-homogeneity parameter, and end conditions on natural frequencies of the non-prismatic beam are reported.

On the wave dispersion of a multi-scale hybrid nanocomposite microstructure via deep neural network technique

“…The formulations associated with the current problem are obtained via the energy method explained as follows (Singh and Sharma, 2021; Mohammadgholiha et al, 2019):where (Al-Furjan et al, 2020c, 2020g; Jalali et al, 2020; Habibi et al, 2020)…”

“…Therefore, artificial neural network (ANN) (Lingamdinne et al, 2023; Moradi et al, 2022) and PINN could be feasible procedures to obtain results in a short time span. The numerical solutions in structural mechanics have been used in nonlinear buckling (Al-Furjan et al, 2020a; Moayedi et al, 2020; Safarpour et al, 2020a, 2020b), wave propagation (Al-Furjan et al, 2021c; Ebrahimi et al, 2019b; Habibi et al, 2019b), and vibration (Sui et al, 2021; Dai et al, 2022) in different members including beams (Kharazan et al, 2021; Singh and Sharma, 2021; Ramírez-Neria et al, 2021; Shariati et al, 2020a, 2020b, 2020c), shells (Ansari et al, 2021; Habibi et al, 2019b, 2019c, 2021b), and plates (Shariyat and Khani Arani, 2022; Habibi et al, 2019a, 2021a; Huo et al, 2021). The nonlinear vibrations of shell structures with conical geometry made of composite materials and complicated cut-outs were investigated by Ansari et al (2021).…”

“…With presence of crack in the beam structure, a jump was seen in the vibrational responses. Singh and Sharma (2021) investigated nonlinear vibration under the effect of humidity and thermal loadings. Effects of different parameters are reported using numerical solution.…”

Crack identification of functionally graded beam using distributed piezoelectric sensor

“…Functionally Graded Material (FGM), the material with continuously varying properties, has got increasing application in many high-tech fields because of its advantages (Birman and Byrd, 2007; Gupta and Talha, 2015). Various problems in dynamics of FGM structures were studied in Chakraborty and Gopalakrishnan (2003), Li (2008), Sina et al (2009), Su and Banerjee (2015), and Singh and Sharma (2021). Numerous works have been devoted also to study vibrations of FGM beams with cracks (Yang and Chen, 2008; Wei et al, 2012; Aydin, 2013; Akbas, 2016; Khiem et al, 2017, 2020; Lien et al, 2019) and some procedures were proposed for crack identification in the structures.…”