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Nonlinear forced vibration analysis of micro-rotating shaft-disk systems through a formulation based on the nonlocal strain gradient theory

Panahi Ramin, Asghari Mohsen, Borjalilou Vahid

Archives of Civil and Mechanical Engineering

2023

Vol. 23, no. 2

art. no. e85, 2023

The paper presents an upgraded size-dependent formulation for micro-rotating shaft-disks system to study their nonlinear forced vibration behavior. The novel formulation is based on the nonlocal strain gradient theory (NSGT). To achieve this goal, first of all, by incorporating the geometrical nonlinearity within the Rayleigh beam theory, the governing equations of the lateral motion of the system are derived by the Hamilton principle and then converted into a complex form. By defning some dimensionless parameters, the normalized form of the complex governing equation is also extracted. In the next step, the Galerkin method is implemented to establish an infinite set of ordinary differential equations (ODEs). Then, with the help of the method of multiple scales, the nonlinear ODE is solved to attain the vibrational amplitude of the system as well as its forward and backward natural frequencies. Lastly, an all-out parametric study is conducted to appraise the impact of some important factors like the nonlocal theory parameter, the strain gradient length scale parameter, the rotational speed, the amount of mass eccentricity and the internal damping coeffcient on the motion amplitude and natural frequencies. The numerical outcomes illuminate well that depending on the relative value of two non-classical parameters of NSGT, this theory have the potential to reflect the hardening or softening attribute of small-scaled mechanical elements.

Size effect of synthetic fibre reinforced concrete - investigation using a semi-discrete analytical beam model

Tóth Mária Erdélyiné, Pluzsik Anikó

Architecture Civil Engineering Environment

2023

Vol. 16, no. 3

117--129

The size effect is a well-known characteristic of concrete structures. However, in the case of fibre-reinforced concrete (FRC), this issue is not thoroughly explored. Most design recommendations of FRC neglect the size effect or handle the behaviour of FRC structures in case of different structural sizes similar to plain concrete structures (assuming FRC is a homogeneous material). The aim of this paper is to show that the size effect of FRC can be divided, the share of the concrete matrix and the fibres in the size-dependent properties is separable. For the size effect research fifteen synthetic macro fibre reinforced concrete and six plain concrete beam specimens were prepared and tested in three different sizes and then evaluated with the semi-discrete analytical (SDA) model. The analysis of the experimental specimens has shown that the size effect significantly influences the concrete material in the case of FRC with softening material behaviour, but the residual loadbearing capacity which mainly arise from the local bridging effect of fibres is essentially independent of the structural size. It is also shown in this paper that the two defining parameters of the SDA model is independent of the structural size, so the model provides an excellent tool in case of the design of real-sized FRC structures.