The investigation of the nonlocal longitudinal stress waves with modified couple stress theory

Love–Bishop rod solution based on strain gradient elasticity theory

“…Thus, for l 0 = l 1 = 0, Eq. ( 34) gives the modified couple stress theory solution [21]. Hence, the present strain gradient elasticity theory may be regarded as the wider form of the modified couple stress theory.…”

“…In principle, the present wave motion analysis is based on the Love rod model [17] and in the same time the Bishop correction is adopted [18][19][20][21][22] in the framework of the Love rod model. Thus, the effects of shear strain components are also taken into account while calculating the total strain energy (for both the local and nonlocal components).…”

“…In Fig. 1, the present general solution based on the strain gradient elasticity theory proposed by Lam et al, and the degenerate solution [21] based on the modified couple stress theory are compared, where c * sge and c * mc denote the dimensionless phase velocities for the strain gradient elasticity and the modified couple stress theories, respectively, k a is the dimensionless wave number and l/a is the dimensionless material length scale parameter. Fig.…”

“…To our knowledge, there is no theoretical investigation with the strain gradient elasticity theory of Lam et al on the longitudinal stress waves based Love-Bishop rod model. In this work, the propagation of longitudinal stress waves considering the lateral deformation [17] and the shear strain effects [18][19][20][21][22] is investigated using the strain gradient elasticity theory for microbars. The aim of the analysis is to develop a more comprehensive solution based on the strain gradient elasticity theory with three scale parameter for size effects in the micro/nanostructures elements.…”

Axial wave propagation and vibration of nonlocal nanorods with radial deformation and inertia

“…Although many researches have been done for 1D nanostructures with the size effect using the nonlocal theory, works with consideration of lateral/radial deformation and its inertia in analyzing longitudinal free vibration and wave characteristics of nanorods are very limited. In this field, Guven [18,19] considered the effects of lateral deformation and analyzed longitudinal wave propagation characteristics of nanorods when subjected to initial stress and using modified couple stress theory, respectively. Furthermore, Love-Bishop rod solution based on strain gradient elasticity theory has been given by Guven [20].…”