Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory Gui-Lin She, Kun-Ming Yan, Yan-Long Zhang, Hai-Bo Liu and Yi-Ru Ren Eur. Phys. J. Plus, 133 9 (2018) 368 Published online: 17 September 2018 DOI: 10.1140/epjp/i2018-12196-5