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Since the efficiency of non-classical continuum theories is strongly dependent on the recognition of the suitable values of small length scale parameters and there is still uncertainty about them, a novel approach, equivalent lattice stiffness method is developed here. This approach without the characteristic length scale parameter which arises in non-classical continuum theories, such as nonlocal theory and strain gradient theory, is capable to capture size effect more easily and accurately. This method is proposed based on the concept of lattice dynamics but a Taylor series expansion is involved to approximate the displacements of the continuous domain; accordingly, this approach is in... 

Since the efficiency of non-classical continuum theories is strongly dependent on the recognition of the suitable values of small length scale parameters and there is still uncertainty about them, a novel approach, equivalent lattice stiffness method is developed here. This approach without the characteristic length scale parameter which arises in non-classical continuum theories, such as nonlocal theory and strain gradient theory, is capable to capture size effect more easily and accurately. This method is proposed based on the concept of lattice dynamics but a Taylor series expansion is involved to approximate the displacements of the continuous domain; accordingly, this approach is in... 

This work studies the nonlinear oscillations of an elastic rotating shaft with acceleration to pass through the critical speeds. A mathematical model incorporating the Von-Karman higher-order deformations in bending is developed and analyzed to investigate the nonlinear dynamics of rotors. A flexible shaft on flexible bearings with springs and dampers is considered as rotor system for the present work. The shaft is modeled as a beam with a circular cross-section and the Euler Bernoulli beam theory is applied. The kinetic and strain energies of the rotor system are derived and Lagrange method is then applied to obtain the coupled nonlinear differential equations of motion for 6° of freedom.... 

This work studies the nonlinear oscillations of an elastic rotating shaft with acceleration to pass through the critical speeds. A mathematical model incorporating the Von-Karman higher-order deformations in bending is developed and analyzed to investigate the nonlinear dynamics of rotors. A flexible shaft on flexible bearings with springs and dampers is considered as rotor system for the present work. The shaft is modeled as a beam with a circular cross-section and the Euler Bernoulli beam theory is applied. The kinetic and strain energies of the rotor system are derived and Lagrange method is then applied to obtain the coupled nonlinear differential equations of motion for 6° of freedom.... 

In the present study, the in-plane elastic stiffness coefficients of graphene within the framework of first strain gradient theory are calculated on the basis of an accurate molecular mechanics model. To this end, a Wigner–Seitz primitive cell is adopted. Additionally, the first strain gradient theory for graphene with trigonal crystal system is formulated and the relation between elastic stiffness coefficients and molecular mechanics parameters are calculated. Thus, the ongoing research challenge on providing the accurate mechanical properties of graphene is addressed herein. Using results obtained, the in-plane free vibration of graphene is studied and a detailed numerical investigation is... 

In the present study, the in-plane elastic stiffness coefficients of graphene within the framework of first strain gradient theory are calculated on the basis of an accurate molecular mechanics model. To this end, a Wigner–Seitz primitive cell is adopted. Additionally, the first strain gradient theory for graphene with trigonal crystal system is formulated and the relation between elastic stiffness coefficients and molecular mechanics parameters are calculated. Thus, the ongoing research challenge on providing the accurate mechanical properties of graphene is addressed herein. Using results obtained, the in-plane free vibration of graphene is studied and a detailed numerical investigation is...