**6. Conclusion**

**6. Conclusion**

The effects of the SLGS length and the imposed external voltage to the PVDF nanoplate on the buckling load ratio are shown in Fig. 5. It is noted that the length of the SLGS is considered between 10< *L* <40 *nm*, since the maximum length of the graphene sheet taken is 45.2896 *nm* in the literature by Sakhaee Pour [30], Pradhan and Murmu [13], and Samaei et al. [17]. As length of the graphene sheet increases, the buckling load ratio increases. It is also observed that for a given length, the SLGS, applying negative external voltage to PVDF nanoplate, will buckle

Figure 6 depicts the effects of axial half wave number (*m*) and external voltage on the buckling load ratio of the SLGS. It is obvious that the buckling load ratio decreases sharply with increasing *m*. As can be seen, with the increase of external voltage, buckling load ratio is increased. Moreover, the effect of *V*0 is not considerable for *m*<2. It means that the external

Buckling smart control of SLGS using PVDF nanoplate versus shear modulus parameter (*Kg*) is plotted in Fig. 7. The obtained results show that at a given *Kg*, when the imposed external voltage changes from *-*1 V to 1 V, the buckling load ratio increases. It is also worth mentioning that the influences of *V*0 at higher *Kg* values are more apparent than at lower *Kg* 's. As the shear modulus parameter of the coupled system increases, generally, the buckling load ratio reduces and approaches a constant value. This is because increasing shear modulus parameter

Fig. 5 The effect of the external voltage on the buckling load ratio versus graphene length.

**Figure 5.** The effect of the external voltage on the buckling load ratio versus graphene length.

10 15 20 25 30 35 40

Length, (nm)

*L*

 = -1 volt = -0.5 volt = 0 volt = 0.5 volt = 1 volt

 = -1 volt = -0.5 volt = 0 volt = 0.5 volt = 1 volt

*V0 V0 V0 V0 V0*

*V0 V0 V0 V0 V0*

Fig. 6 The effect of the external voltage on the buckling load ratio versus axial half wave

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65

Buckling Load Ratio,

0.25

0.3

0.35

0.4

0.45

Buckling Load Ratio,

0.5

0.55

0.6

0 1 2 3 4 5 6 7 8 9 10

*m*

Axial half wave number,

number.

first as compared to the SLGS with positive one.

increases the structure stiffness.

voltage effect decreases with decrease of the axial half wave number.

Fig. 5 The effect of the external voltage on the buckling load ratio versus graphene length. Buckling response of graphene sheets has applications in designing many NEMS/MEMS devices such as strain sensor, mass and pressure sensors, and atomic dust detectors. Buckling

Fig. 6 The effect of the external voltage on the buckling load ratio versus axial half wave number.

Fig. 7 The effect of the external voltage on the buckling load ratio versus shear modulus parameter.

Buckling response of graphene sheets has applications in designing many NEMS/MEMS devices

such as strain sensor, mass and pressure sensors, and atomic dust detectors. Buckling smart control

of the SLGS using elastically bonded PVDF nanoplate which is subjected to external voltage is the

main contribution of the present paper. The elastic medium between SLGS and PVDF nanoplate is

simulated by a Pasternak foundation. The governing equations are obtained based on nonlocal

Mindlin plate theory so that the effects of small-scale, elastic medium coefficient, mode number,

parameter.

smart control of the SLGS using elastically bonded PVDF nanoplate which is subjected to external voltage is the main contribution of the present paper. The elastic medium between SLGS and PVDF nanoplate is simulated by a Pasternak foundation. The governing equations are obtained based on nonlocal Mindlin plate theory so that the effects of small-scale, elastic medium coefficient, mode number, and graphene length are discussed. The results indicate that the imposed external voltage is an effective controlling parameter for buckling of the SLGS. It is found that the effect of external voltage becomes more prominent at higher nonlocal parameter and shear modulus. It is also observed that for a given length, the SLGS with negative external voltage will buckle first as compared to the SLGS with positive one. The results of this study are validated as far as possible by the buckling of SLGS in the absence of PVDF nanoplate, as presented by [16, 17, 28, and 29]. Finally, it is hoped that the results presented in this paper would be helpful for study and design of bonded systems based on smart control and electromechanical systems.
