Exact solution for frequency response of sandwich microbeams with functionally graded cores. (October 2019)

• Record Type: Journal Article
• Authors: Taati, Ehsan; Fallah, Famida
• Is Part Of: Journal of vibration and control. Volume 25:Number 19/20(2019)
• Page Start: 2641
• Page End: 2655
• Publication Date: 2019-10
• Subjects: Frequency response -- sandwich microbeams -- functionally graded core -- modified strain gradient theory -- exact solution; Vibration -- Periodicals; Damping (Mechanics) -- Periodicals; 620.3
• DOI: 10.1177/1077546319864645
• Languages: English
• ISSNs: 1077-5463

Abstract

Based on the Euler–Bernoulli beam model and the modified strain gradient theory, the size-dependent forced vibration of sandwich microbeams with a functionally graded (FG) core is presented. The equation of motion and the corresponding classical and nonclassical boundary conditions are derived using the Hamilton's principle. An exact solution of the governing equation is developed for sandwich beams with various boundary conditions and subjected to an arbitrarily distributed harmonic transverse load. Finally, parametric studies are presented to investigate the effects of geometric ratios, length scale parameters, power index, boundary conditions, layup, and thickness of the FG layer on the frequency response of clamped and simply supported microbeams. Numerical results show that in the case of clamped microbeams, the essential and natural size-dependent boundary conditions have a significant effect on the resonance frequency and transverse deflection of microbeams. Also, it is seen that an optimal layup (without change in total volume of each material) can significantly improve the frequency characteristics of sandwich microbeams.