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J. Appl. Mech. 2017;84(9):091001-091001-10. doi:10.1115/1.4037030.

A modified Fourier–Ritz approach is developed in this study to analyze the free in-plane vibration of orthotropic annular sector plates with general boundary conditions. In this approach, two auxiliary sine functions are added to the standard Fourier cosine series to obtain a robust function set. The introduction of a logarithmic radial variable simplifies the expressions of total energy and the Lagrangian function. The improved Fourier expansion based on the new variable eliminates all the potential discontinuities of the original displacement function and its derivatives in the entire domain and effectively improves the convergence of the results. The radial and circumferential displacements are formulated with the modified Fourier series expansion, and the arbitrary boundary conditions are simulated by the artificial boundary spring technique. The number of terms in the truncated Fourier series and the appropriate value of the boundary spring retraining stiffness are discussed. The developed Ritz procedure is used to obtain accurate solution with adequately smooth displacement field in the entire solution domain. Numerical examples involving plates with various boundary conditions demonstrate the robustness, precision, and versatility of this method. The method developed here is found to be computationally economic compared with the previous method that does not adopt the logarithmic radial variable.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(9):091002-091002-12. doi:10.1115/1.4037159.

We analyze small amplitude shear waves (SWs) propagating in dielectric elastomer (DE) laminates subjected to finite deformations and electrostatic excitations. First, we derive long wave estimates for phase and group velocities of the shear waves propagating in any direction in DE laminates subjected to any homogenous deformation in the presence of an electric filed. To this end, we utilize a micromechanics-based energy potential for layered media with incompressible phases described by neo-Hookean ideal DE model. The long wave estimates reveal the significant influence of electric field on the shear wave propagation. However, there exists a configuration, for which electric field does not influence shear waves directly, and can only alter the shear waves through deformation. We study this specific configuration in detail, and derive an exact solution for the steady-state small amplitude waves propagating in the direction perpendicular to the finitely deformed DE layers subjected to electrostatic excitation. In agreement with the long wave estimate, the exact dispersion relation and the corresponding shear wave band gaps (SBGs)—forbidden frequency regions—are not influenced by electric field. However, SBGs in DE laminates with highly nonlinear electroelastic phases still can be manipulated by electric field through electrostatically induced deformation. In particular, SBGs in DE laminates with electroelastic Gent phases widen and shift toward higher frequencies under application of an electric field perpendicular to the layers. However, in laminates with neo-Hookean ideal DE phases, SBGs are not influenced either by electric field or by deformation. This is due to the competing mechanisms of two governing factors: changes in geometry and material properties induced by deformation. In this particular case, these two competing factors entirely cancel each other.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(9):091003-091003-6. doi:10.1115/1.4037148.

Unidirectional acoustic transmission is acquired in a one-dimensional graded phononic crystal. The distinct feature of the present design is that waves can propagate unidirectionally at a certain frequency from the left to right, and waves at another frequency can propagate in the opposite direction from the right to left. This two-way asymmetric propagation behavior is realized at the narrow resonant frequencies in the acoustic band gap by a novel mechanism, which is totally linear and obeys the time-reversal symmetry. Simulation shows that for the graded heterogeneous structure, the resonant peaks of frequency in the acoustic band gap for opposite propagation directions become different. In the transmission spectrum, this mechanism corresponds to a pass-band splitting, and each separated peak represents a unidirectional propagation behavior. The separation of two peaks has been proved to have a close relation to the grading degree of the material property in the spatially periodic components. The unique propagation characteristic obtained at resonant frequencies in the band gaps may provide us a new way to realize a two-way unidirectional narrow-band acoustic filter.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(9):091004-091004-8. doi:10.1115/1.4037158.

We propose a method to find an approximate theoretical solution to the mean first exit time (MFET) of a one-dimensional bistable kinetic system subjected to additive Poisson white noise, by extending an earlier method used to solve stationary probability density function. Based on the Dynkin formula and the properties of Markov processes, the equation of the mean first exit time is obtained. It is an infinite-order partial differential equation that is rather difficult to solve theoretically. Hence, using the non-Gaussian property of Poisson white noise to truncate the infinite-order equation for the mean first exit time, the analytical solution to the mean first exit time is derived by combining perturbation techniques with Laplace integral method. Monte Carlo simulations for the bistable system are applied to verify the validity of our approximate theoretical solution, which shows a good agreement with the analytical results.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(9):091005-091005-9. doi:10.1115/1.4037147.

Compared to the conventional rigid robots, the soft robots driven by soft active materials possess unique advantages with their high adaptability in field exploration and seamless interaction with human. As one type of soft robot, soft aquatic robots play important roles in the application of ocean exploration and engineering. However, the soft robots still face grand challenges, such as high mobility, environmental tolerance, and accurate control. Here, we design a soft robot with a fully integrated onboard system including power and wireless communication. Without any motor, dielectric elastomer (DE) membrane with a balloonlike shape in the soft robot can deform with large actuation, changing the total volume and buoyant force of the robot. With the help of pressure sensor, the robot can move to and stabilize at a designated depth by a closed-loop control. The performance of the robot has been investigated both experimentally and theoretically. Numerical results from the analysis agree well with the results from the experiments. The mechanisms of actuation and control may guide the further design of soft robot and smart devices.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;84(9):091006-091006-11. doi:10.1115/1.4037160.

The energy absorption capacity of origami crash boxes (OCB) subjected to oblique loading is investigated in the present study. A conventional square tube (CST) with identical weight is employed as benchmark. The comparative study reveals that the origami crash box is more desirable than the conventional square tube in most of the range of load angle. A parameter study is performed to assess the effect of geometry parameters on the energy absorption characteristics. The geometry parameters are tube length L, tube width b, module length l, and width of folded lobe c. Considering that bamboo with large slenderness ratio could effectively resist wind load, a bulkhead-reinforced origami crash box is proposed as a high-performance energy absorption device. And an optimum structure designed based on the parameter study is investigated. The result suggests that the proposed tube performs much better than the original design.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Appl. Mech. 2017;84(9):094501-094501-3. doi:10.1115/1.4037149.

The ribbons selectively bonded to a prestrained elastomeric substrate may buckle into three-dimensional (3D) microstructures after the prestrain release, leading to three possible deformation modes, global, local, and no buckling, depending on the adhesion between the ribbons and substrate. This note establishes analytically the critical length-to-thickness ratio of ribbons, above which the global buckling mode (preferred for mechanically guided 3D deterministic assembly) occurs without material failure.

Commentary by Dr. Valentin Fuster

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