## 1 Introduction  
Material extrusion (ME), one of the most promising rapid prototyping technologies, has been increasingly used to manufacture functional parts for electronic, automotive, aerospace, and bioengineering applications [1, 2, 3]. Despite the fact that it has been studied for a few decades, the layer-by-layer manufacturing process leads to obvious defects in the parts, such as porosity and no interlayer pressure. This leads to lower mechanical properties of the built parts compared to those manufactured by traditional technology and limits their applications. Therefore, improving the mechanical properties of the built parts is one of the key development orientations of the ME technique. Fortunately, the research and development work to fine-tune it and improve the mechanical performance of the built parts has been ongoing all the time. [PERSON] et al. [4, 5, 6] mixed the polymer raw material with materials of high mechanical strength (glass fiber, ceramics, carbon fiber, etc.). The test results showed that the mechanical and thermodynamic properties of ME parts could be effectively improved. However, this method changes the original material, and it is complicated and costly. A large number of scholars [7; 8; 9; 10; 11; 12; 13] have found that optimizing ME processing parameters (i.e., extrusion width, layer height, build direction, processing speed, nozzle diameter, infill condition, number of contours, extruder temperature, raster angle and gap, etc.) could help enhance the built products' mechanical properties. However, the optimized processing parameters are not universal (only applicable for the specified equipment), and the improvement on the built parts' forming quality is limited as the allowance for these parameter values is small. [PERSON] [14] used the atmospheric pressure plasma to enhance the hydrophilicity between ME processing layers. It was shown that the inter-layer bonding strength of the built parts can be effectively improved (nearly up by 15%) and, thus, the parts' mechanical properties were enhanced. However, this method decreases the surface quality of the parts and consumes too much energy. A system able to automatically detect weak links in the CAD model was developed by [PERSON] [15]. The revised parts' strength could be obviously increased by local thickening, support increase, and weight reduction. However, this method dramatically alters the original design's structure and appearance. [PERSON] et al. [16; 17] carried out the post-processing treatment of ultrasonic vibration on ME specimens to improve their mechanical properties. The results showed that the tensile strength and Young's modulus of the processed parts were significantly increased and the surface quality was enhanced. In the field of rapid prototyping, [PERSON] [18] pioneered introducing vibration (onto the platform) into the manufacturing process. Vibrating laser powder deposition (LPD) equipment was set up mainly by combining a five-axis CNC machining center, a material powder delivery system, a high-power laser system, and an electromagnetic exciter. The exciter, connected to the platform, was to introduce and control the vibration (amplitude, frequency, and direction). The test results showed that applying vibration could effectively reduce the defect of pores in the LPD parts by 80% and thereby improve the parts' mechanical strength and ductility. [PERSON] [19; 20] introduced vibration into the ME process by using two vibrating motors fixed on the extrusion liquefier and performed a series of experimental test, as well as theoretical and computational analyses of the melt flow behavior of polylactic acid (PLA) in the extrusion liquefier. The results show that the applied vibration can significantly improve the forming quality of the built parts. However, there is no information available about the influencing rule of different types of vibration on the ME parts' tensile property. The corresponding mechanism needs to be investigated accordingly.