Stochastic analysis of lattice, nonlocal continuous beams in vibration

In this paper, we study the stochastic behavior of some lattice beams, called Hencky bar-chain model and their non-local continuous beam approximations. Hencky bar-chain model is a beam lattice composed of rigid segments, connected by some homogeneous rotational elastic links. In the present stochastic analysis, the stiffness of these elastic links is treated as a continuous random variable, with given probability density function. The fundamental eigenfrequency of the linear difference eigenvalue problem is also a random variable in this context. The reliability is defined as the probability that this fundamental frequency is less than an excitation frequency. This reliability function is exactly calculated for the lattice beam in conjunction with various boundary conditions. An exponential distribution is considered for the random stiffness of the elastic links. The stochastic lattice model is then compared to a stochastic nonlocal beam model, based on the continualization of the difference equation of the lattice model. The efficiency of the nonlocal beam model to approximate the lattice beam model is shown in presence of rotational elastic link randomness. We also compare such stochastic function with the one of a continuous local Euler-Bernoulli beam, with a special emphasis on scale effect in presence of randomness. Scale effect is captured both in deterministic and non-deterministic frameworks.

Internal Force Analysis and Field Test of Lattice Beam Based on Winkler Theory for Elastic Foundation Beam

As a new flexible supporting structure, prestressed anchor cable lattice beams have been widely used in high-slope support engineering and have achieved good results. However, theoretical research on the internal force analysis of lattice beams is far behind engineering practice. Based on the theory of the Winkler elastic foundation model, a mechanical model of a prestressed anchor cable lattice beam at the tension stage was established. Considering the nonhomogeneous lattice beam materials, a calculation method was given and applied to engineering examples. A calculation method of the measured moment was introduced in the field test conducted in the Zhouqu County “8·8” debris flow disaster reconstruction project. Comparisons between the test results and the theoretical results were performed. The results showed that the theoretical results of the distribution trend of the lattice beam moment were consistent with the test results, which verified the rationality of the proposed calculation method. The inertia moment of the beam section solved by the transformed section method was more realistic. The results of the transformed section method could improve the bending resistance of the lattice beam and reduce the reinforcement ratio. The greater the anchoring force was, the more obvious the lifting effect was. The anchoring force was an important influencing factor of the internal force of the lattice beam. The greater the anchoring force was, the greater the lattice beam moment was, and they showed the same proportional change phenomenon. Compared with the theoretical moment, the measured moment obtained by the test was smaller, which indicated that the lattice beam of the tested slope was safe at the present stage.

SSPIM: a beam shaping toolbox for structured selective plane illumination microscopy

An important aim of the development of selective plane illumination microscopy (SPIM) is to present a completely open and flexible microscope set-up for nonspecialist users. Here, we report Structured SPIM (SSPIM), which provides an open-source, user-friendly and compact toolbox for beam shaping that can generate digital patterns for a wide range of illumination beams. SSPIM represents a toolbox to produce static, spherical Gaussian, Bessel and Airy beams by simple control of a Spatial Light Modulator (SLM). In addition, it is able to produce patterns for incoherent and coherent (lattice beam) array beam formation and tiling for all types of beams supported. We demonstrate the workflow and experimental and simulation results using the SSPIM toolbox. In final, the capability of the SSPIM is investigated with 3D imaging of Drosophila embryo using three different illumination beams such as scanned/dithered Gaussian, Bessel and Lattice beam which engineered with SSPIM. SSPIM toolbox is easy to use and applicable for a wide range of applications to generate and optimize the desired beam pattern and thus can help developing adaptation of the Open SPIM system towards a wider range of biological samples.