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Couple stress-based nonlinear primary resonant dynamics of FGM composite truncated conical microshells integrated with magnetostrictive layers

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Abstract

The size-dependent geometrically nonlinear harmonically soft excited oscillation of composite truncated conical microshells (CTCMs) made of functionally graded materials (FGMs) integrated with magnetostrictive layers is analyzed. It is supposed that the FGM CTCMs are subjected to mechanical soft excitations together with external magnetic fields. An analytical framework is created by a microstructure-dependent shell model having the 3rd-order distribution of shear deformation based on the modified couple stress (MCS) continuum elasticity. With the aid of the discretized form of differential operators developed via the generalized differential quadrature technique, a numerical solution methodology is introduced for obtaining the couple stress-based amplitude and frequency responses related to the primary resonant dynamics of the FGM CTCMs. Jump phenomena due to the loss of the first stability branch and falling down to the lower stable branch can be seen in the nonlinear primary resonance of the FGM CTCMs. It is demonstrated that the hardening type of nonlinearity results in bending the frequency response to the right side, and the MCS type of size effect weakens this pattern. Moreover, for higher material gradient indexes, the hardening type of nonlinearity is enhanced, and the MCS-based frequency response bends more considerably to the right side.

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Authors and Affiliations

  1. School of Civil Engineering, Guangzhou University, Guangzhou, 510006, China

    Yong Yang

  2. Mechanical Rotating Equipment Department, Niroo Research Institute (NRI), Tehran, 14665-517, Iran

    S. Sahmani

  3. Department of Mechanical Engineering, Eastern Mediterranean University, Famagusta, 99628, North Cyprus via Mersin 10, Turkey

    B. Safaei

Authors
  1. Yong Yang
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  2. S. Sahmani
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  3. B. Safaei
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Corresponding author

Correspondence to S. Sahmani.

Additional information

Citation: YANG, Y., SAHMANI, S., and SAFAEI, B. Couple stress-based nonlinear primary resonant dynamics of FGM composite truncated conical microshells integrated with magnetostrictive layers. Applied Mathematics and Mechanics (English Edition) (2021) https://doi.org/10.1007/s10483-021-2704-6

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Yang, Y., Sahmani, S. & Safaei, B. Couple stress-based nonlinear primary resonant dynamics of FGM composite truncated conical microshells integrated with magnetostrictive layers. Appl. Math. Mech.-Engl. Ed. 42, 209–222 (2021). https://doi.org/10.1007/s10483-021-2704-6

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  • DOI: https://doi.org/10.1007/s10483-021-2704-6

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