Analytical Modeling for Free and Forced Nonlinear Vibration of Porous Functionally Graded Magneto-Electro-Elastic Smart Plate

Analytical Modeling for Free and Forced Nonlinear Vibration of Porous Functionally Graded Magneto-Electro-Elastic Smart Plate


Analytical Modeling for Free and Forced Nonlinear Vibration of Porous Functionally Graded Magneto-Electro-Elastic Smart Plate

نوع: Type: thesis

مقطع: Segment: masters

عنوان: Title: Analytical Modeling for Free and Forced Nonlinear Vibration of Porous Functionally Graded Magneto-Electro-Elastic Smart Plate

ارائه دهنده: Provider: Mohammad Hossein Mohammadi

اساتید راهنما: Supervisors: Dr. Aliraza Shooshtari

اساتید مشاور: Advisory Professors:

اساتید ممتحن یا داور: Examining professors or referees: Dr. Mahdi Karimi- Dr. Mahdi Shaban

زمان و تاریخ ارائه: Time and date of presentation: 2023/11/05

مکان ارائه: Place of presentation: Seminar2- Mechanical engineering Department

چکیده: Abstract: The current research discusses the analytical modeling of free and forced nonlinear vibrations of smart functionally graded magneto-electro-elastic porous plates. For this purpose, a rectangular plate of functionally graded magneto-electro-elastic porous materials and four types of uniform porosity, V, O, and X-shaped, distributed along its thickness, have been considered. The upper surface of the plate comprises a 100% magnetostrictive metal phase, and the lower surface comprises a 100% piezoelectric ceramic phase. The mechanical boundary conditions of the plate are simple, and the electrical and magnetic boundary conditions are also considered closed circuits. The plate's effective physical and mechanical properties are modeled using the law of mixtures and the power distribution function. The plate motion equations were extracted using the first-order shear theory and Gauss' law as seven coupled nonlinear partial differential equations and simplified using the Galerkin method. Then, the mentioned equations have been reduced to the equation of transverse movement of the plate. According to the equation, the plate's natural frequency has been calculated. Nonlinear free vibrations have been investigated by applying the Lindest-Poincaré method. An analytical relationship has been presented to calculate the ratio of the nonlinear natural frequency to the linear natural frequency of the plate. The forced vibrations of the plate have also been investigated using the method of multiple scales. Relationships have been obtained to explain the frequency response in primary and subharmonic resonance. The external excitation force has been applied in forced vibrations as a wide harmonic load in the time domain with constant amplitude. In the end, by presenting a numerical example and changing different parameters such as the gradient of material properties, types of porosity distribution, and different values of porosity index, the ratio of thickness to the length of a plate, the ratio of length to width of a plate, and the difference of magnetic and electric potentials in the gradient of different properties, the effect of each on The linear and nonlinear frequencies of the plate, as well as their effect on the frequency response diagram, have been investigated and analyzed

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