On a Singular Robin Problem with Convection Terms

In this paper, the existence of smooth positive solutions to a Robin boundary-value problem with non-homogeneous differential operator and reaction given by a nonlinear convection term plus a singular one is established. Proofs chiefly exploit sub-super-solution and truncation techniques, set-valued analysis, recursive methods, nonlinear regularity theory, as well as fixed point arguments. A uniqueness result is also presented.

Connection looseness detection of steel grid structures using piezoceramic transducers

Connection looseness phenomena of steel grid structures might induce issues of lowering integrity, large deformation, even total collapse of the structures. The goal of this article is to propose an evaluation method for bolt-sphere joint looseness of steel grid structures using piezoceramic guided wave–based method through experiments and numerical simulations. A single bolt-sphere joint looseness experimental model is established and tested, considering grid member connection angles of 0°, 45°, 90°, and 180°, respectively. Then, multiple bolt-sphere joint looseness detection tests by selecting six kinds of cases for a steel grid structure model are performed. Piezoceramic patch arrays bonded on the surface of grid members are used as transducers to generate and receive detection guided waves, and external torques are applied to indirectly simulate the bolt-sphere joint looseness effect. The experimental results show that the bolt-sphere joint looseness impact on the ultrasonic wave energy attenuation has a nonlinear regularity. Based on the regularity, an evaluation method and key techniques for the bolt-sphere joint looseness detection based on guided wave energy are proposed and experimentally validated. To further clarify the bolt-sphere joint looseness detection mechanism, the ABAQUS software is used for a finite element analysis of the single bolt-sphere joint looseness evaluation. The numerical and experimental results match well, verifying the feasibility of the proposed method.

Dynamic Analysis and Multiparameters Optimization of Hydrostatic Supported Worktable System

The natural frequency at lower orders for hydrostatic supported worktable system may easily give rise to vibration as in resonance with excitation frequency. This paper is concerned with the geometrical optimum design and dynamic modal analysis for system with hydrostatic oil fluid and worktable simultaneously. The variations of eigenfrequency, respect to oil film thickness, outer radius of worktable, recess shape and number, were discussed. The results show that, under linear increment/decrement of geometry dimension, frequency increase/decrease but in nonlinear regularity. Therefore there exists an optimum dimension resulting the optimum frequency that deviate from the rotary frequency at work and its multiple ones. Then two-phase optimization strategy was effectively programmed to get involved with finite element analysis software. It is theoretically critical to get the optimum parameter of hydrostatic supported worktable on how and practically important to guide the design in engineering.