Vibration and Dynamic behavior of Multi-Layer Sandwich Composite Piezoelectric Micro Beam Using Higher-Order Elasticity Theory
محورهای موضوعی : فصلنامه شبیه سازی و تحلیل تکنولوژی های نوین در مهندسی مکانیکMehrdad Soltani 1 , Javad Jafari 2 , Seyed Ali Galehdari 3 , Rasoul Tarkesh Esfahani 4 , Mohamad Shahgholi 5
1 - Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
2 - Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
3 - Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
4 - Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
5 - Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
کلید واژه: Multi-Layer Sandwich Composite, Micro beam, higher-order elasticity theory, vibration and dynamic analysis ,
چکیده مقاله :
Numerous scientists have examined the mechanical properties of materials at the micro- and nanoscale in recent years. Conversely, the remarkable advancements in micro and nanotechnology across several fields and industries, such as their extensive applications in micro- and nano-electro-mechanical systems (MEMS and NEMS), have piqued the curiosity of researchers. In this paper, vibration and dynamic behavior of multi-layer sandwich composite piezoelectric micro beam using higher-order elasticity theory by considering strain gradient and surface effects are investigated. The Hamilton’s principle is utilized to derive the sandwich micro beam model with Gurtin- Murdoch surface theory and generalized differential quadrature method is used to discretize and solve the differential equation Moreover, the effects of higher order materials and geometry of model on control respond and frequency behavior have been presented. In addition, the role of different theories based FFT results has been examined. The results show that the small material length scale considering in the higher order theories plays a key role in the dynamic respond of models. Also, the result of higher order theories should be considered in micro and nano scale and the classical theory could not predict the mechanical behavior very well. The study's conclusions imply that the effectiveness of controller scheme is within the piezoelectric voltage range in terms of vibration control and feedback damping factors.
Numerous scientists have examined the mechanical properties of materials at the micro- and nanoscale in recent years. Conversely, the remarkable advancements in micro and nanotechnology across several fields and industries, such as their extensive applications in micro- and nano-electro-mechanical systems (MEMS and NEMS), have piqued the curiosity of researchers. In this paper, vibration and dynamic behavior of multi-layer sandwich composite piezoelectric micro beam using higher-order elasticity theory by considering strain gradient and surface effects are investigated. The Hamilton’s principle is utilized to derive the sandwich micro beam model with Gurtin- Murdoch surface theory and generalized differential quadrature method is used to discretize and solve the differential equation Moreover, the effects of higher order materials and geometry of model on control respond and frequency behavior have been presented. In addition, the role of different theories based FFT results has been examined. The results show that the small material length scale considering in the higher order theories plays a key role in the dynamic respond of models. Also, the result of higher order theories should be considered in micro and nano scale and the classical theory could not predict the mechanical behavior very well. The study's conclusions imply that the effectiveness of controller scheme is within the piezoelectric voltage range in terms of vibration control and feedback damping factors.
[1] Oveissi, S., Toghraie, D. S., & Eftekhari, S. A. (2017). Analysis of transverse vibrational response and instabilities of axially moving CNT conveying fluid. International Journal of Fluid Mechanics Research, 44(2).
[2] Chen, J., Khabaz, M. K., Ghasemian, M. M., Altalbawy, F. M., Jalil, A. T., Eftekhari, S. A., ... & Albahash, Z. F. (2023). Transverse vibration analysis of double-walled carbon nanotubes in an elastic medium under temperature gradients and electrical fields based on nonlocal Reddy beam theory. Materials Science and Engineering: B, 291, 116220.
[3] Al-Shujairi, M., & Mollamahmutoğlu, Ç. (2018). Buckling and free vibration analysis of functionally graded sandwich micro-beams resting on elastic foundation by using nonlocal strain gradient theory in conjunction with higher order shear theories under thermal effect. Composites Part B: Engineering, 154, 292-312..
[4] Zhang, Y., Hammoodi, K. A., Sajadi, S. M., Li, Z., Jasim, D. J., Nasajpour-Esfahani, N., ... & Khabaz, M. K. (2024). Obtaining an accurate prediction model for viscosity of a new nano-lubricant containing multi-walled carbon nanotube-titanium dioxide nanoparticles with oil SAE50. Tribology International, 191, 109185.
[5] Lin, C., Zhou, J., Lu, Q., Khabaz, M. K., Andani, A. K., Al-Yasiri, M., & Pan, G. (2023). Thermal conductivity prediction of WO3-CuO-Ag (35: 40: 25)/water hybrid ternary nanofluid with Artificial Neural Network and back-propagation algorithm. Materials Today Communications, 36, 106807.
[6] Salarnia, M., Toghraie, D., Fazilati, M. A., Mehmandoust, B., & Pirmoradian, M. (2023). The effects of different nanoparticles on physical and thermal properties of water in a copper oscillating heat pipe via molecular dynamics simulation. Journal of the Taiwan Institute of Chemical Engineers, 143, 104721.
[7] Torkan, E., Pirmoradian, M., & Hashemian, M. (2017). Occurrence of parametric resonance in vibrations of rectangular plates resting on elastic foundation under passage of continuous series of moving masses. Modares Mechanical Engineering, 17(9), 225-236.
[8] Balootaki, A. A., Karimipour, A., & Toghraie, D. (2018). Nano scale lattice Boltzmann method to simulate the mixed convection heat transfer of air in a lid-driven cavity with an endothermic obstacle inside. Physica A: Statistical Mechanics and Its Applications, 508, 681-701.
[9] Abdulhameed, M., Muhammad, M. M., Gital, A. Y., Yakubu, D. G., & Khan, I. (2019). Effect of fractional derivatives on transient MHD flow and radiative heat transfer in a micro-parallel channel at high zeta potentials. Physica A: Statistical Mechanics and its Applications, 519, 42-71.
[10] Kong, S., Zhou, S., Nie, Z., & Wang, K. (2008). The size-dependent natural frequency of Bernoulli–Euler micro-beams. International Journal of Engineering Science, 46(5), 427-437.
[11] Kong, S., Zhou, S., Nie, Z., & Wang, K. (2009). Static and dynamic analysis of micro beams based on strain gradient elasticity theory. International Journal of Engineering Science, 47(4), 487-498.
[12] Belardinelli, P., Hauzer, L. M. F. R., Šiškins, M., Ghatkesar, M. K., & Alijani, F. (2018). Modal analysis for density and anisotropic elasticity identification of adsorbates on microcantilevers. Applied Physics Letters, 113(14).
[13] Eringen, A. C., & Edelen, D. (1972). On nonlocal elasticity. International journal of engineering science, 10(3), 233-248.
[14] Saffari, S., Hashemian, M., & Toghraie, D. (2017). Dynamic stability of functionally graded nanobeam based on nonlocal Timoshenko theory considering surface effects. Physica B: Condensed Matter, 520, 97-105.
[15] Alashti, A. R., & Abolghasemi, A. H. (2014). A size-dependent Bernoulli-Euler beam formulation based on a new model of couple stress theory. International Journal of Engineering TRANSACTIONS C, 27(6), 951-960.
[16] Nikpourian, A., Ghazavi, M. R., & Azizi, S. (2019). Size-dependent secondary resonance of a piezoelectrically laminated bistable MEMS arch resonator. Composites Part B: Engineering, 173, 106850.
[17] Jomehzadeh, E., Noori, H. R., & Saidi, A. R. (2011). The size-dependent vibration analysis of micro-plates based on a modified couple stress theory. Physica E: Low-dimensional Systems and Nanostructures, 43(4), 877-883.
[18] Sedighi, H. M., Keivani, M., & Abadyan, M. (2015). Modified continuum model for stability analysis of asymmetric FGM double-sided NEMS: corrections due to finite conductivity, surface energy and nonlocal effect. Composites Part B: Engineering, 83, 117-133.
[19] Ding, N., Xu, X., Zheng, Z., & Li, E. (2017). Size-dependent nonlinear dynamics of a microbeam based on the modified couple stress theory. Acta Mechanica, 228, 3561-3579.
[20] Farokhi, H., Ghayesh, M. H., & Amabili, M. (2013). Nonlinear dynamics of a geometrically imperfect microbeam based on the modified couple stress theory. International Journal of Engineering Science, 68, 11-23.
[21]Sahmani, S., & Bahrami, M. (2015). Size-dependent dynamic stability analysis of microbeams actuated by piezoelectric voltage based on strain gradient elasticity theory. Journal of Mechanical Science and Technology, 29, 325-333.
[22] Lazopoulos, K. A., & Lazopoulos, A. K. (2010). Bending and buckling of thin strain gradient elastic beams. European Journal of Mechanics-A/Solids, 29(5), 837-843.
[23] Trindade, M. A., & Benjeddou, A. (2008). Refined sandwich model for the vibration of beams with embedded shear piezoelectric actuators and sensors. Computers & Structures, 86(9), 859-869.
[24] Ghazavi, M. R., Rezazadeh, G., & Azizi, S. (2010). Pure parametric excitation of a micro cantilever beam actuated by piezoelectric layers. Applied Mathematical Modelling, 34(12), 4196-4207.
[25] AkhavanAlavi, S. M., Mohammadimehr, M., & Edjtahed, S. (2019). Active control of micro Reddy beam integrated with functionally graded nanocomposite sensor and actuator based on linear quadratic regulator method. European Journal of Mechanics-A/Solids, 74, 449-461.
[26] Belardinelli, P., Sajadi, B., Lenci, S., & Alijani, F. (2019). Global dynamics and integrity of a micro-plate pressure sensor. Communications in Nonlinear Science and Numerical Simulation, 69, 432-444.
[27]Mohammadimehr, M., Mohammadi Hooyeh, H., Afshari, H., & Salarkia, M. R. (2017). Free vibration analysis of double-bonded isotropic piezoelectric Timoshenko microbeam based on strain gradient and surface stress elasticity theories under initial stress using differential quadrature method. Mechanics of Advanced Materials and Structures, 24(4), 287-303.
[28] Mirkalantari, S. A., Hashemian, M., Eftekhari, S. A., & Toghraie, D. (2017). Pull-in instability analysis of rectangular nanoplate based on strain gradient theory considering surface stress effects. Physica B: Condensed Matter, 519, 1-14.
[29] Eftekhari, S. A., Hashemian, M., & Toghraie, D. (2020). Optimal vibration control of multi-layer micro-beams actuated by piezoelectric layer based on modified couple stress and surface stress elasticity theories. Physica A: Statistical Mechanics and its Applications, 546, 123998.
[30]Eftekhari, S. A., & Toghraie, D. (2022). Vibration and dynamic analysis of a cantilever sandwich microbeam integrated with piezoelectric layers based on strain gradient theory and surface effects. Applied Mathematics and Computation, 419, 126867.
[31]Pirmoradian, M., & Karimpour, H. (2017). Nonlinear effects on parametric resonance of a beam subjected to periodic mass transition. Modares Mechanical Engineering, 17(1), 284-292.
[32] Arani, A. G., Abdollahian, M., & Kolahchi, R. (2015). Nonlinear vibration of a nanobeam elastically bonded with a piezoelectric nanobeam via strain gradient theory. International Journal of Mechanical Sciences, 100, 32-40.
[33]Eftekhari, S. A., & Toghraie, D. (2022). Vibration and dynamic analysis of a cantilever sandwich microbeam integrated with piezoelectric layers based on strain gradient theory and surface effects. Applied Mathematics and Computation, 419, 126867.
[34]Mohammadimehr, M., Mohammadi Hooyeh, H., Afshari, H., & Salarkia, M. R. (2017). Free vibration analysis of double-bonded isotropic piezoelectric Timoshenko microbeam based on strain gradient and surface stress elasticity theories under initial stress using differential quadrature method. Mechanics of Advanced Materials and Structures, 24(4), 287-303.
[35] Keivani, M., Koochi, A., Kanani, A., Mardaneh, M. R., Sedighi, H. M., & Abadyan, M. (2017). Using strain gradient elasticity in conjunction with Gurtin–Murdoch theory for modeling the coupled effects of surface and size phenomena on the instability of narrow nano-switch. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 231(17), 3277-3288.
[36] Pirmoradian, M., Naeeni, H. A., Firouzbakht, M., Toghraie, D., & Darabi, R. (2020). Finite element analysis and experimental evaluation on stress distribution and sensitivity of dental implants to assess optimum length and thread pitch. Computer methods and Programs in Biomedicine, 187, 105258.
[37] Hejazi, S. A. M., Feyzpour, A., Eslami, A., Fouladgar, M., Eftekhari, S. A., & Toghraie, D. (2023). Numerical investigation of rigidity and flexibility parameters effect on superstructure foundation behavior using three-dimensional finite element method. Case Studies in Construction Materials, 18, e01867.
[38] Chen, J., Khabaz, M. K., Ghasemian, M. M., Altalbawy, F. M., Jalil, A. T., Eftekhari, S. A., ... & Albahash, Z. F. (2023). Transverse vibration analysis of double-walled carbon nanotubes in an elastic medium under temperature gradients and electrical fields based on nonlocal Reddy beam theory. Materials Science and Engineering: B, 291, 116220.
[39] Abdi, F., Ghasemi, A., Ariaei, A., Eftekhari, S. A., Nasr, M., Khabaz, M. K., & Salahshour, S. (2025). Free vibration and buckling analysis of axially functionally graded tapered Timoshenko beams using B-spline-based isogeometric analysis. Heliyon, 11(1).
