Magnetorheological (MR) materials exhibit rapid variations in their rheological properties when subjected to varying magnetic field and thus offer superior potential for applications in smart structures requiring high bandwidth. MR sandwich structures can apply distributed control force to yield variations in stiffness and damping properties of the structure in response to the intensity of the applied magnetic field and could thus provide vibration suppression over a broad range of external excitation frequencies. This study investigates the properties of a multi-layered beam with MR fluid as a sandwich layer between the two layers of the continuous elastic structure. The governing equations of a multi-layer MR beam are formulated in the finite element form and using the Ritz method. A free oscillation experiment is performed to estimate the relationship between the magnetic field and the complex shear modulus of the MR materials in the pre-yield regime. The validity of the finite element and Ritz formulations developed is examined by comparing the results from the two models with those from the experimental investigation. Various parametric studies have been performed in terms of variations of the natural frequencies and loss factor as functions of the applied magnetic field and thickness of the MR fluid layer for various boundary conditions. The forced vibration responses of the MR sandwich beam are also evaluated under harmonic force excitation. The results illustrate that the natural frequencies could be increased by increasing the magnetic field while the magnitudes of the peak deflections could be considerably decreased, which demonstrates the vibration suppression capability of the MR sandwich beam.

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The concept of 4D printing involves the formation of complex three-dimensional structures having the ability to adopt different shapes and forms when subjected to different environmental stimuli. Some researchers simply view this technique as an extension of 3D printing or additive manufacturing with the added constraint of time. However, the unique shape change mechanism exhibited in this process is due to a combination of shape programming and the usage of smart active materials mostly polymers. This review article highlights the various smart materials, activation mechanisms and the shape-changing techniques employed in the 4D printing process. The potential of these shape-changing structures and their current applications in various biomedical and engineering fields is also explored. The article aims to emphasize the potential and viability of 4D printing and is directed towards providing an in-depth insight into the 4D printing process.

This study investigates the dynamic properties of a laminated composite magnetorheological (MR) fluid sandwich plate. The governing differential equations of motion of a sandwich plate embedding a MR fluid layer as the core layer and laminated composite plates as the face layers are presented in a finite element formulation. The validity of the developed finite element formulation is demonstrated by comparing the results in terms of the natural frequencies derived from the present finite element formulation with those in the available literature. Various parametric studies are also performed to investigate the effect of a magnetic field on the variation of the natural frequencies and loss factors of the MR fluid composite sandwich plate under various boundary conditions. Furthermore, the effect of the thickness of the MR fluid layer and the ply orientation of the composite face layers on the variation of the natural frequencies and loss factors are studied. The free vibration mode shapes under various boundary conditions of a MR fluid laminated composite sandwich plate are also presented. The forced vibration response of a MR fluid composite plate is investigated to study the dynamic response of the sandwich plate under harmonic force excitations in various magnetic fields. The study suggests that the natural frequency increases with increasing magnetic field, irrespective of the boundary conditions. The reduction in peak deflection at each mode under a harmonic excitation force with variation of the applied magnetic field shows the effectiveness of the MR fluid layer in reducing the vibration amplitude of the composite sandwich plate.

This study presents synthesis of full-state and limited state flexible mode shape (FMS)based controllers for suppression of free-and forced vibration of a cantilever beam fully and partially treated with the magneto-rheological (MR) fluid. The governing equations of motion of the three layer MR sandwich beam are expressed in the state variable form comprising a function of the control magnetic field. An optimal control strategy based on the linear quadratic regulator (LQR) and a full-state dynamic observer is formulated to suppress the vibration of the beam under a limited magnetic field intensity. The lower flexural mode shapes of the passive beam are used to obtain the estimates of the deflection states so as to formulate a limited state LQR control synthesis. The free-and forced vibration control performances of both the full-state observer-based and limited state FMS-based LQR control strategies are evaluated for the fully as well as partially treated MR-fluid sandwich beams. The results show that the full-state observer-based LQR control can substantially reduce the tip deflection responses and the settling time of the free vibration oscillations. The limited-state LQR control based on the mode shapes effectively adapts to the deflections of the closed-loop beams and thus yields vibration attenuation performance comparable to that of the full-state LQR controller. The partially-treated beam with MR-fluid concentration near the free end also yields vibration responses comparable to the fully treated beam, while the natural frequencies of the partially treated beams are considerably higher.

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The modal damping characteristics of beams partially treated with magnetorheological (MR) fluid elements are studied using the modal strain energy approach and the finite element method. Different configurations of a sandwich beam partially treated with MR fluid are considered, including a beam with a cluster of MR fluid segments and a beam with arbitrarily located MR fluid segments. The significance of the location of the MR fluid segments on the modal damping factor is investigated under different end conditions. An optimization problem is formulated by combining finite element analysis with optimization algorithms based on sequential quadratic programming (SQP) and the genetic algorithm (GA) to identify optimal locations for MR fluid treatment to achieve maximum modal damping corresponding to the first five modes of flexural vibration, individually and simultaneously. The solutions of the optimization problem revealed that the GA converges to the global solutions rapidly compared to the SQP method, which in some modal configurations usually entraps in the local optimum. The results suggest that the optimal location of the MR fluid treatment is strongly related to the end conditions and also the mode of vibration. Furthermore, partial treatments with MR fluid can significantly alter the deflection modes of the beam. It has also been demonstrated that optimal locations of the MR fluid segments based on linear combination of the modal damping factors of the first five modes are identical to those obtained based on the first mode, irrespective of the end conditions. However, the optimal locations of the MR fluid segments, identified based on the logarithmic summation of the modal damping factors of the first five modes, would yield a more uniform shear energy distribution compared to that attained by considering individual modes or a linear summation of the individual modes.

In this study, the vibration responses of a partially treated laminated composite magnetorheological (MR) fluid sandwich plate have been investigated. The governing differential equations of motion for a partially treated laminated sandwich plate embedding MR fluid and rubber as the core layer and the laminated composite plate as the face layers are presented in finite element formulation. The validity of the developed finite element formulation is demonstrated by comparing the results in terms of natural frequencies derived from the present finite element formulation with the experimental measurements. Various configurations of a partially treated laminated composite MR fluid sandwich plate are considered to study the effect of location and size of the MR fluid segment under various boundary conditions. The effect of magnetic field on the variation of natural frequencies and loss factor of the partially treated laminated composite MR fluid sandwich plate are also analyzed for various configurations at different boundary conditions. The free vibration mode shapes of various configurations of a partially treated laminated composite MR fluid sandwich plate are also presented. The forced vibration responses of the various configuration of a partially treated laminated composite MR fluid sandwich plate are also analyzed under harmonic force excitations. This analysis suggests that the natural frequency, loss factor and transverse displacements of the partially treated laminated composite MR fluid sandwich plate are strongly influenced by the location and size of the MR fluid segment apart from the intensities of the applied magnetic field. The application of the partial treatment alters the deflection pattern of the sandwich plate, particularly the location of peak deflection, which shows that it can be applied to critical components of a large structure to realize a more efficient and compact vibration control mechanism with variable damping.