Guest Editorial

J. Appl. Mech. 2018;86(2):020301-020301-4. doi:10.1115/1.4042130.

Presented at the ASME Applied Mechanics Division Banquet, Pittsburgh, PA, Nov. 13, 2018.

Commentary by Dr. Valentin Fuster

Research Papers

J. Appl. Mech. 2018;86(2):021001-021001-11. doi:10.1115/1.4041765.

The improvement of the accuracy and efficiency of microforming process of polymers is of great significance to meet the miniaturization of polymeric components. When the nonuniform deformation is reduced to the microscopic scale, however, the mechanics of polymers shows a strong reinforcement behavior. Traditional theoretical models of polymers which have not considered material feature lengths are difficult to describe the size effect in micron scale, and the process simulation models based on the traditional theory could not provide effective and precise guidance for polymer microfabrication techniques. The work reported here proposed strategies to simulate size effect behaviors of glassy polymers in microforming process. First, the strain gradient elastoviscoplastic model was derived to describe the size affected behaviors of glassy polymers. Based on the proposed constitutive model, an eight-node finite element with the consideration of nodes' rotation was developed. Then, the proposed finite element method was verified by comparisons between experiments and simulations for both uniaxial compression and microbending. Finally, based on the FE model, under the consideration of the effect of rotation gradient, the strain distribution, the deformation energy, and the processing load were discussed. These strategies are immediately applicable to other wide-ranging classes of microforming process of glassy polymers, thereby foreshadowing their use in process optimizations of microfabrication of polymer components.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(2):021002-021002-6. doi:10.1115/1.4041825.

This paper presents results related to the stability of gyroscopic systems in the presence of circulatory forces. It is shown that when the potential, gyroscopic, and circulatory matrices commute, the system is unstable. This central result is shown to be a generalization of that obtained by Lakhadanov, which was restricted to potential systems all of whose frequencies of vibration are identical. The generalization is useful in stability analysis of large scale multidegree-of-freedom real life systems, which rarely have all their frequencies identical, thereby expanding the compass of applicability of stability results for such systems. Comparisons with results in the literature on the stability of such systems are made, and the weakness of results that deal with only general statements about stability is exposed. It is shown that the commutation conditions given herein provide definitive stability results in situations where the well-known Bottema–Karapetyan–Lakhadanov result is inapplicable.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(2):021003-021003-15. doi:10.1115/1.4041910.

Exact steady-state solutions are obtained for the motion of an single-degree-of-freedom (SDOF) system that is provided with a highly nonlinear auxiliary mass damper (AMD), which resembles a conventional dynamic vibration neutralizer (DVN), whose relative motion with respect to the primary system is constrained to remain within a specified gap, thus operating as a “pounding DVN.” This configuration of a conventional DVN with motion-limiting stops could be quite useful when a primary structure with a linear DVN is subjected to transient loads (e.g., earthquakes) that may cause excessive relative motion between the auxiliary and primary systems. Under the assumption that the motion of the nonlinear system under harmonic excitation is undergoing steady-state motion with two impacts per period of the excitation, an exact, closed-form solution is obtained for the system motion. This solution is subsequently used to develop an approximate analytical solution for the stationary response of the pounding DVN when subjected to random excitation with white spectral density and Gaussian probability distribution. Comparison between the analytically estimated rms response of the primary system and its corresponding response obtained via numerical simulation shows that the analytical estimates are quite accurate when the coupling (tuning parameters) between the primary system and the damper are weak, but only moderately accurate when the linear components of the tuning parameters are optimized. It is also shown that under nonstationary, the pounding DVN provides slightly degraded performance compared to the linear one but simultaneously limits the damper-free motion to specified design constraints.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(2):021004-021004-10. doi:10.1115/1.4042011.

The alternating stop-band characteristics of periodic structures have been widely used for narrow band vibration control applications. The objective of this work is to extend this idea for broadband excitations. Toward this end, we seek to synthesize a longitudinal and a flexural periodic structure having the largest fraction of the frequencies falling in the attenuation bands of the structure. Such a periodic structure when subjected to broadband excitation has minimal transmission of the response away from the source of excitation. The unit cell of such a periodic structure is constituted of two distinct regions having different inertial and stiffness properties. We derive guidelines for suitable selection of inertial and stiffness properties of the two regions in the unit cell such that the maximal frequency region corresponds to attenuation bands of the periodic structure. It is found that maximal dissimilarity between the neighboring regions of the unit cell leads to maximal attenuating frequencies. In the extreme case, it is found that more than 98% of the frequencies are blocked. For seismic excitations, it is shown that large, finite periodic structures corresponding to the optimal unit cell derived using the infinite periodic structure theory has significant vibration isolation benefits in comparison to a homogeneous structure or an arbitrarily chosen periodic structure.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(2):021005-021005-18. doi:10.1115/1.4041766.

Finite element analysis (FEA) has become the method of choice for the stress analysis of many of the complex configurations encountered in practice. Such configurations can contain stress singularities. Then, it is critical for the necessarily finite estimates from finite elements to be rejected as valid results for the infinite stresses present. There is an extensive literature devoted to the asymptotic identification of stress singularities that can often, but not always, provide a means for such rejection. The present study seeks to offer a further means of rejection: mesh refinement with divergence checks. These divergence checks are a natural counterpart to the convergence checks of ASME. The two are used together on 265 finite element stresses at 32 different singularities: all of these finite element stresses are thus rejected.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(2):021006-021006-11. doi:10.1115/1.4042045.

A new kind of nonlinear energy sink (NES) is proposed to control the vibration of a flexible structure with simply supported boundaries in the present work. The new kind of absorber is assembled at the end of structures and absorbs energy through the rotation angle at the end of the structure. It is easy to design and attached to the support of flexible structures. The structure and the absorber are coupled just with a nonlinear restoring moment and the damper in the absorber acts on the structure indirectly. In this way, all the linear characters of the flexible structure will not be changed. The system is investigated by a special perturbation method and verified by simulation. Parameters of the absorber are fully discussed to optimize the efficiency of it. For the resonance, the maximum motion is restrained up to 90% by the optimized absorber. For the impulse, the vibration of the structure could attenuate rapidly. In addition to the high efficiency, energy transmits to the absorber uniaxially. For the high efficiency, convenience of installation and the immutability of linear characters, the new kind of rotating absorber provides a very good strategy for the vibration control.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(2):021007-021007-9. doi:10.1115/1.4041965.

This work proposes a novel strategy to render mixed boundary conditions on circular linear elastic homogeneous domain to displacement-based condition all along the surface. With Michell solution as the starting point, the boundary conditions and extent of the domain are used to associate the appropriate type and number of terms in the Airy stress function. Using the orthogonality of sine and cosine functions, the modified boundary conditions lead to a system of linear equations for the unknown coefficients in the Airy stress function. Solution of the system of linear equations provides the Airy stress function and subsequently stresses and displacement. The effectiveness of the present approach in terms of ease of implementation, accuracy, and versatility to model variants of circular domain is demonstrated through excellent comparison of the solution of following problems: (i) annulus with mixed boundary conditions on outer radius and prescribed traction on the inner radius, (ii) cavity surface with mixed boundary conditions in an infinite plane subjected to far-field uniaxial loading, and (iii) circular disc constrained on part of the surface and subjected to uniform pressure on rest of the surface.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(2):021008-021008-13. doi:10.1115/1.4042046.

This paper details a numerical study of the dynamic stability of a cylindrical shell structure under combined hydrostatic and dynamic pressure loading within a tubular environment as compared to the traditional loading of hydrostatic pressure alone. Simulations are executed using a coupled Eulerian–Lagrangian scheme, within the dynamic system mechanics advanced simulation (DYSMAS) code, to explicitly model the (1) structural response of a single unstiffened cylindrical shell to dynamic pressure loading and (2) the fluid flow field within the surrounding environment due to the shock and the shell structural response. Simulations involve a non-pressure-compensated aluminum 6061-T6 cylindrical structure with a length-to-diameter ratio, L/D, equal to 9.6. This structure is 31.8 mm (1.25-in) in outer diameter and is concentrically and longitudinally centered within the outer tube, which has an inner diameter of 177.8 mm (7.00-in) and total internal length of 2.13 m (84-in). Simulations are run at four hydrostatic tank pressures, which are categorized by percentage of measured critical collapse pressure, Pc, of the shell structure: 66% Pc, 80% Pc, 85% Pc, and 90%Pc. For each case, the shell structure is subjected to shock loading created by the detonation of a commercial blasting cap at a given standoff to the structure within the confining tube. Simulated pressure histories are compared to experimental pressure data at gage locations. The simulations and corresponding experiments produce the same overall result for three of four cases (i.e., survive: 66%Pc or implode: 85%Pc and 90%Pc). For the 80%Pc case, the overall result differs between simulation and experiment in that the specimen in the experiment survives but the simulated cylinder implodes. However, the discrepancy between the overall experimental result and corresponding simulation is not deemed a failure for the 80%Pc case; instead, this signifies a transitional case for the dynamic stability of the shell structure (i.e., collapse is sensitive to small deviations from assumed conditions in this regime).

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2018;86(2):021009-021009-9. doi:10.1115/1.4042132.

A six-node incompatible graded finite element is developed and studied. Such element is recommended for use since it is more accurate than four-node compatible element and more efficient than eight-node compatible element in two-dimensional plane elasticity. This paper presents comparison between six-node incompatible (QM6) and four-node compatible (Q4) graded elements. Numerical solution is obtained from abaqus using UMAT capability of the software and exact solution is provided as reference for comparison. A graded plate with exponential and linear gradation subjected to traction and bending load is considered. Additionally, three-node triangular (T3) and six-node triangular (T6) graded elements are compared to QM6 element. Incompatible graded element is shown to give better performance in terms of accuracy and computation time over other element formulations for functionally graded materials (FGMs).

Commentary by Dr. Valentin Fuster

Technical Brief

J. Appl. Mech. 2018;86(2):024501-024501-6. doi:10.1115/1.4041824.

This paper presents an investigation on the free vibration of an oscillator containing a viscoelastic damping modeled by fractional derivative (FD). Based on the fact that the vibration has slowly changing decay rate and frequency, we present an approach to analytically obtain the initial decay rate and frequency. In addition, ordinary differential equations governing the decay rate and frequency are deduced, according to which accurate approximation is obtained for the free vibration. Numerical examples are presented to validate the accuracy and effectiveness of the presented approach. Based on the obtained results, we analyze the decay rate and the frequency of the free vibration. Emphasis is put on their time-dependence, indicating that the decay rate decreases but the frequency increases with time increasing.

Commentary by Dr. Valentin Fuster

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