An analytical study on wave propagation in functionally graded nano-beams/tubes based on the integral formulation of nonlocal elasticity

• Published in: Waves in random and complex media Vol. 30; no. 3; pp. 562 - 580
• Main Authors: Norouzzadeh, A., Ansari, R., Rouhi, H.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.07.2020; Taylor & Francis Ltd
• Subjects: Beam theory (structures); Dispersion curve analysis; functionally graded material; Functionally gradient materials; Integral nonlocal constitutive equations; Integrals; Kernel functions; Mathematical models; nano-beam; nano-tube; Nonlocal elasticity; Parameters; Propagation; S waves; Timoshenko beams; Tubes; Wave propagation
• ISSN: 1745-5030; 1745-5049
• DOI: 10.1080/17455030.2018.1543979

In the context of integral formulation of Eringen's nonlocal elasticity theory, flexural, axial and shear wave propagations in nano-beams/tubes made of functionally graded materials (FGMs) are analytically studied. The nano-beams/tubes are modeled according to the Timoshenko beam theory whose governing equations are derived via Hamilton's principle. The nonlocal formulation is developed generally so that it can be adopted for arbitrary kernel functions. For the comparison aim, the differential counterpart of the formulation is also developed. Selected numerical results are presented to compare the predictions of the local model, differential nonlocal model and integral nonlocal model according to various types of the kernel function, made on the wave propagation characteristics of nano-beams/tubes. The small-scale influences on the dispersion curves of flexural, axial and shear waves are also studied for different nonlocal parameter-to-length and thickness-to-nonlocal parameter ratios. In addition, the wave frequencies are obtained for FGM nano-beams/tubes with different material gradient indexes.