Vibration analysis of a micro-cylindrical sandwich panel with reinforced shape-memory alloys face sheets and porous core

Abstract

The mechanical properties of SMAs can be modified using temperature or stress changes. This specific characteristic allows building smart materials that can repair or improve themselves. Shape-memory alloys provide adjustable natural frequencies, using the mentioned character, which is highly practical in producing any component sensitive to vibrations. In this study, the vibration behaviors of a thick-walled micro-cylindrical sandwich panel with two types of reinforcements carbon nanotubes (CNTs), and graphene platelets (GPLs) for the SMA-based layers (shape-memory alloy face sheets) is investigated. Using two well-known core materials (porous, and foam cores) has covered various structures and components. The higher-order shear deformation theory is considered, and based on Hamilton's principle, the governing equations of motion are driven. Navier's method is used to obtain the natural frequencies. The effects of different parameters such as aspect ratios, the volume fraction of CNTs or GPLs, various porous patterns, and temperature changes on the natural frequency are studied. The natural frequencies usually decrease when the temperature rises, while the use of SMA materials as the matrix has led to a rise in the magnitudes of the natural frequencies. It is believed that shape-memory alloys can bring fundamental changes to the industry; therefore, this study is the base point for further numerical and more specific works in the future.

Appendix A

The rule of mixture for carbon nanotubes is determined in Eq (A.1):

$$ \frac{{\eta_{3} }}{{G_{12} }} = \frac{{V_{CNT} }}{{G_{12\_CNT} }} + \frac{{V_{m} }}{{G_{m} }} $$

(A.1-1)

$$ \frac{{\eta_{2} }}{{E_{22} }} = \frac{{V_{{{\text{CNT}}}} }}{{E_{22\_CNT} }} + \frac{{V_{m} }}{{G_{m} }} $$

(A.1-2)

$$ E_{11} = \eta_{1} V_{{{\text{CNT}}}} E_{{11\_{\text{CNT}}}} + V_{m} E_{m} $$

(A.1-3)

$$ V_{{{\text{CNT}}}} + V_{m} = 1 $$

(A.1-4)

$$ \nu_{12} = V_{{{\text{CNT}}}} \nu_{{12\_{\text{CNT}}}} + V_{m} \nu_{m} $$

(A.1-5)

$$ \rho = V_{{{\text{CNT}}}} \rho_{{{\text{CNT}}}} + V_{m} \rho_{m} $$

(A.1-6)

It should be noted that η_i, E, G, V, and ρ are efficiency coefficients of carbon nanotubes, Young’s modulus, shear modulus, volume fraction, and density.

The efficiency coefficients for CNTs are considered in Table

Table 8 The efficiency coefficient for CNTs

8.