In the present article, we focus on the forced vibration and control analysis of functionally graded (FG) graphene-polymer composites bonded with piezoelectric layers considering strong electric fields. Different non-uniform gradient distributions of graphene platelets (GPLs) are assumed through the thickness direction. The Modified Halpin-Tsai micromechanics model is used to obtain the effective material properties of GPL/polymer composites. Electromechanical coupling of piezoelectric layers is described by two rotationally invariant non-linear constitutive relations. A four-node shell element considering transverse shear effect based on the Reissner-Mindlins hypothesis has been developed for forced vibration and control analysis of smart FG-GPL/composites using the principle of virtual work considering nonlinear material law for the piezoelectric layers. The developed element is verified and compared with the numerical results those available in the literature. Different configurations of FG-GPL composite shells have been analysed and discussed to compare in terms of settling time, first resonance frequency and absolute amplitude corresponding to first resonant frequency by carrying out time and frequency response analysis, and the effects of weight fraction of GPLs on vibration response of such shell structures are also discussed. The influence of electromechanical nonlinear constitutive relations is also presented and discussed by performing active control analysis on different FG-GPL composite shell structures. Moreover, the results show that the GPL distribution and weight-fraction of GPLs have a significant effect on the vibration and damping characteristics of the FG-GPL composite shell structures.

This paper studies the vibration mitigation of a sandwich beam with tip mass using piezoelectric active control. The core of the sandwich beam is made of foam and the face sheets are made of steel with a bonded piezoelectric actuator and sensor. The three-layer sandwich beam is clamped at one end and carries a payload at the other end. The tip mass is such that its center of mass is offset from the point of attachment. The extended higher-order sandwich panel (HSAPT) theory is employed in conjunction with the Hamilton’s principle to derive the governing equations of motion and boundary conditions. The obtained partial differential equations are solved using the generalized differential quadrature (GDQ) method. Free and forced vibration analyses are carried out and the results are compared with those obtained from the use of the commercial finite element software ANSYS. Derivative feedback control algorithm is employed to control the vibration of the system. Parametric studies are conducted to examine the arrangement impact of the piezoelectric sensors and actuators on the system vibrational behavior.

In this study, the primary response of an Euler-Bernoulli beam resting on nonlinear elastic foundation is investigated. The beam is subjected to thermal and magnetic axial loads. The nonlocal Eringen’s elasticity theory is used to derive the mathematical model to account for the scale effect of the beam. A simply supported beam is considered in the analysis, and the multi-mode approach is used to obtain the reduced nonlinear temporal equations of motion that contain quadratic and cubic nonlinear terms. The method of multiple-scales is applied to obtain approximate analytical solutions for the nonlinear natural frequencies in addition to the primary resonance response curves. Moreover, the effective nonlinearity is obtained as a function of the natural frequencies and the coefficients of the elastic foundation. The results reveal that the scale parameter has a significant effect on the frequencies and amplitudes of the beam. The obtained results are presented over a selected range of physical parameters such as the scale effect parameter, foundation parameters, thermal and magnetic loads, and the excitation level. Time responses, phase planes and Poincaré maps are generated for the beam under consideration.

This paper presents vibration analysis and structural optimization of a self-assembled structure for swimming. The mode shapes of the structure resemble the body waveform of a swimming Mackerel fish. The lateral deformation waveform of the body of Mackerel is extracted from literature. At higher swimming speeds fish generate the waveform at a higher frequency. Their body waveform stays the same at almost all normal swimming speeds. At the final destination, the box self-assembles using shape memory alloys. The shape memory alloys used for configuration change of the box robot cannot be used for swimming since they fail to operate at high frequencies. MFCs are actuated at the fundamental natural frequency of the structure. This excites the primary mode of resonance. The primary mode of resonance involves rotations of the joints of the robot in the desired fashion. The MFCs are therefore used to indirectly generate the body waveform. We optimize the thickness of the panels and the stiffness of the joints to most efficiently generate the swimming waveforms. Unlike eel we change the speed of the robot by changing the amplitude of the body motions. This is because the frequency of the motion is fixed to the first natural frequency of the robot. The swimming box can swim over the surface and can also swim underwater. With slight modification the boxes can crawl or slither over the land.

Due to the small linear region in electrorheological (ER) fluid, vibration analysis of the sandwich structure containing ER fluid should be investigated in nonlinear region where the material properties depend on frequency, amplitude and electric field. In present work, the nonlinear equations of motion have been obtained using finite element technique. The nonlinear amplitude dependent stiffness matrices in equations of motion have been previously expressed by B and N notations. In B-notation an asymmetric amplitude dependent stiffness matrix is achieved. On the other hand in N-notation a symmetric form of the nonlinear stiffness matrices is achieved. The main problem in nonlinear vibration analysis of structure using direct integration technique is the time-consuming integrations, which should be performed for several times throughout this method. Due to numerous degrees of freedom in sandwich shell/plate structures, the computational costs in finite element modeling of sandwich shell/plate structures becomes more expensive. In this study, by considering kinetic and potential energies attributed to the elastic and ER fluid layers and using Lagrange equations, nonlinear finite element formulation has been derived for the ER based sandwich shell structures. Also a new technique is developed to represent the equations of motion in a new notation referred to as H-notation which fundamentally reduces the computational costs in nonlinear vibration damping analysis of sandwich shell structure. Finally, parametric study is conducted to show the effect of small/ large displacement, electric field intensities and core thickness ratio on damping behavior of the ER based sandwich shell structures for different boundary conditions.

In the recent years, using piezoelectric material as sensors and actuators has drawn significant attention in vibration analysis and control of structures. In the present paper, bonded piezoelectric sensors and actuators have been used to control the aeroelastic oscillations of a cantilever wing under the effects of three-dimensional unsteady subsonic aerodynamic loading. An aerodynamic model using a numerical panel method is developed and validated to calculate the three-dimensional unsteady aerodynamic loading and finite element formulation is applied to model the wing structure as a cantilever plate undergoing small transverse oscillations. The structural and aerodynamic models are combined to simulate the aeroelastic oscillations and interchange the data simultaneously. An active feedback control method to suppress the oscillations is presented and investigated. Finally, an analysis is performed to examine the effects of actuator placement on the wing surface in suppression of oscillations.