Vibration of an orthotropic nanoplate resting on a viscoelastic foundation: nonlocal and fractional derivative viscoelasticity approach
Abstract
Here, we investigate the free vibration behavior of a nanoplate resting on a foundation
with viscoelastic properties using nonlocal elasticity and fractional viscoelasticity
approach. Nanoplate is modeled using nonlocal and fractional viscoelastic constitutive
equation and orthotropic Kirchhoff-Love plate theory. Viscoelastic foundation is
represented by the viscoelastic model with fractional derivative operator. Governing
equation is derived using D’Alambert’s principle and solution is assumed in terms of
Fourier series using separation of variables method and satisfying the simply supported
boundary conditions for nanoplate. Fractional differential equation is solved using the
Laplace and Mellin-Fourier transforms and residue theory. Complex poles of unknown
function are determined by finding the roots of the characteristic equation using technique
that is available in the literature. In order to show the effect of fractional derivative
parameters, damping coefficients and... nonlocal parameter on complex roots i.e. damped
frequency and damping ratio as well as on nanoplate’s displacement, few numerical
examples are given.
Keywords:
nonlocal elasticity / nanoplate / fractional viscoelasticity / damped vibrationSource:
Proceedings of International Conference on Fractional Differentiation and its Application ICFDA16, 18-20 July 2016, Novi Sad, Serbia, 2016, 491-500Publisher:
- Belgrade: Serbian Society of Mechanics
- Faculty of Technical Sciences Novi Sad
Funding / projects:
- Serbia-China bilateral project under the number 3-12
- Development of methods and techniques for early diagnostic of cervical, colon, oral cavity cancer and melanoma based on a digital image and excitation-emission spectrum in visible and infrared domain (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-41006)
- Dynamics of hybrid systems with complex structures. Mechanics of materials. (RS-MESTD-Basic Research (BR or ON)-174001)
- Dynamic stability and instability of mechanical systems subjected to stochastic excitations (RS-MESTD-Basic Research (BR or ON)-174011)
Collections
Institution/Community
Mašinski fakultetTY - CONF AU - Cajić, Milan AU - Lazarević, Mihailo AU - Sun, HongGuang AU - Karličić, Danilo AU - Chen, Wen PY - 2016 UR - https://machinery.mas.bg.ac.rs/handle/123456789/4186 AB - Here, we investigate the free vibration behavior of a nanoplate resting on a foundation with viscoelastic properties using nonlocal elasticity and fractional viscoelasticity approach. Nanoplate is modeled using nonlocal and fractional viscoelastic constitutive equation and orthotropic Kirchhoff-Love plate theory. Viscoelastic foundation is represented by the viscoelastic model with fractional derivative operator. Governing equation is derived using D’Alambert’s principle and solution is assumed in terms of Fourier series using separation of variables method and satisfying the simply supported boundary conditions for nanoplate. Fractional differential equation is solved using the Laplace and Mellin-Fourier transforms and residue theory. Complex poles of unknown function are determined by finding the roots of the characteristic equation using technique that is available in the literature. In order to show the effect of fractional derivative parameters, damping coefficients and nonlocal parameter on complex roots i.e. damped frequency and damping ratio as well as on nanoplate’s displacement, few numerical examples are given. PB - Belgrade: Serbian Society of Mechanics PB - Faculty of Technical Sciences Novi Sad C3 - Proceedings of International Conference on Fractional Differentiation and its Application ICFDA16, 18-20 July 2016, Novi Sad, Serbia T1 - Vibration of an orthotropic nanoplate resting on a viscoelastic foundation: nonlocal and fractional derivative viscoelasticity approach EP - 500 SP - 491 UR - https://hdl.handle.net/21.15107/rcub_machinery_4186 ER -
@conference{ author = "Cajić, Milan and Lazarević, Mihailo and Sun, HongGuang and Karličić, Danilo and Chen, Wen", year = "2016", abstract = "Here, we investigate the free vibration behavior of a nanoplate resting on a foundation with viscoelastic properties using nonlocal elasticity and fractional viscoelasticity approach. Nanoplate is modeled using nonlocal and fractional viscoelastic constitutive equation and orthotropic Kirchhoff-Love plate theory. Viscoelastic foundation is represented by the viscoelastic model with fractional derivative operator. Governing equation is derived using D’Alambert’s principle and solution is assumed in terms of Fourier series using separation of variables method and satisfying the simply supported boundary conditions for nanoplate. Fractional differential equation is solved using the Laplace and Mellin-Fourier transforms and residue theory. Complex poles of unknown function are determined by finding the roots of the characteristic equation using technique that is available in the literature. In order to show the effect of fractional derivative parameters, damping coefficients and nonlocal parameter on complex roots i.e. damped frequency and damping ratio as well as on nanoplate’s displacement, few numerical examples are given.", publisher = "Belgrade: Serbian Society of Mechanics, Faculty of Technical Sciences Novi Sad", journal = "Proceedings of International Conference on Fractional Differentiation and its Application ICFDA16, 18-20 July 2016, Novi Sad, Serbia", title = "Vibration of an orthotropic nanoplate resting on a viscoelastic foundation: nonlocal and fractional derivative viscoelasticity approach", pages = "500-491", url = "https://hdl.handle.net/21.15107/rcub_machinery_4186" }
Cajić, M., Lazarević, M., Sun, H., Karličić, D.,& Chen, W.. (2016). Vibration of an orthotropic nanoplate resting on a viscoelastic foundation: nonlocal and fractional derivative viscoelasticity approach. in Proceedings of International Conference on Fractional Differentiation and its Application ICFDA16, 18-20 July 2016, Novi Sad, Serbia Belgrade: Serbian Society of Mechanics., 491-500. https://hdl.handle.net/21.15107/rcub_machinery_4186
Cajić M, Lazarević M, Sun H, Karličić D, Chen W. Vibration of an orthotropic nanoplate resting on a viscoelastic foundation: nonlocal and fractional derivative viscoelasticity approach. in Proceedings of International Conference on Fractional Differentiation and its Application ICFDA16, 18-20 July 2016, Novi Sad, Serbia. 2016;:491-500. https://hdl.handle.net/21.15107/rcub_machinery_4186 .
Cajić, Milan, Lazarević, Mihailo, Sun, HongGuang, Karličić, Danilo, Chen, Wen, "Vibration of an orthotropic nanoplate resting on a viscoelastic foundation: nonlocal and fractional derivative viscoelasticity approach" in Proceedings of International Conference on Fractional Differentiation and its Application ICFDA16, 18-20 July 2016, Novi Sad, Serbia (2016):491-500, https://hdl.handle.net/21.15107/rcub_machinery_4186 .