TY - JOUR
T1 - Vibration analysis of piezoelectric sandwich nanobeam with flexoelectricity based on nonlocal strain gradient theory
AU - Zeng, Shan
AU - Wang, Kaifa
AU - Wang, Baolin
AU - Wu, Jinwu
PY - 2020
Y1 - 2020
N2 - A nonlocal strain gradient theory (NSGT) accounts for not only the nongradient nonlocal elastic stress but also the nonlocality of higher-order strain gradients, which makes it benefit from both hardening and softening effects in small-scale structures. In this study, based on the NSGT, an analytical model for the vibration behavior of a piezoelectric sandwich nanobeam is developed with consideration of flexoelectricity. The sandwich nanobeam consists of two piezoelectric sheets and a non-piezoelectric core. The governing equation of vibration of the sandwich beam is obtained by the Hamiltonian principle. The natural vibration frequency of the nanobeam is calculated for the simply supported (SS) boundary, the clamped-clamped (CC) boundary, the clamped-free (CF) boundary, and the clamped-simply supported (CS) boundary. Effects of geometric dimensions, length scale parameters, nonlocal parameters, piezoelectric constants, as well as the flexoelectric constants are discussed. Results demonstrate that both the flexoelectric and piezoelectric constants enhance the vibration frequency of the nanobeam. The nonlocal stress decreases the natural vibration frequency, while the strain gradient increases the natural vibration frequency. The natural vibration frequency based on the NSGT can be increased or decreased, depending on the value of the nonlocal parameter to length scale parameter ratio.
AB - A nonlocal strain gradient theory (NSGT) accounts for not only the nongradient nonlocal elastic stress but also the nonlocality of higher-order strain gradients, which makes it benefit from both hardening and softening effects in small-scale structures. In this study, based on the NSGT, an analytical model for the vibration behavior of a piezoelectric sandwich nanobeam is developed with consideration of flexoelectricity. The sandwich nanobeam consists of two piezoelectric sheets and a non-piezoelectric core. The governing equation of vibration of the sandwich beam is obtained by the Hamiltonian principle. The natural vibration frequency of the nanobeam is calculated for the simply supported (SS) boundary, the clamped-clamped (CC) boundary, the clamped-free (CF) boundary, and the clamped-simply supported (CS) boundary. Effects of geometric dimensions, length scale parameters, nonlocal parameters, piezoelectric constants, as well as the flexoelectric constants are discussed. Results demonstrate that both the flexoelectric and piezoelectric constants enhance the vibration frequency of the nanobeam. The nonlocal stress decreases the natural vibration frequency, while the strain gradient increases the natural vibration frequency. The natural vibration frequency based on the NSGT can be increased or decreased, depending on the value of the nonlocal parameter to length scale parameter ratio.
KW - nanostructured materials
KW - piezoelectric materials
KW - strains and stresses
UR - https://hdl.handle.net/1959.7/uws:56642
U2 - 10.1007/s10483-020-2620-8
DO - 10.1007/s10483-020-2620-8
M3 - Article
SN - 0253-4827
VL - 41
SP - 859
EP - 880
JO - Applied Mathematics and Mechanics
JF - Applied Mathematics and Mechanics
IS - 6
ER -