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A dynamic model of laminated material extrusion additive manufacturing plate with the property of orthogonal anisotropy

Shijie Jiang (Northeastern University, Shenyang, China)
Mingyu Sun (Northeastern University, Shenyang, China)
Yang Zhan (Guidaojiaotong Polytechnic Institute, Shenyang, China)
Hui Li (Northeastern University, Shenyang, China)
Wei Sun (Northeastern University, Shenyang, China)

Rapid Prototyping Journal

ISSN: 1355-2546

Article publication date: 21 May 2021

Issue publication date: 4 June 2021




The purpose of this study is to set up a dynamic model of material extrusion (ME) additive manufacturing plates for the prediction of their dynamic behavior (i.e. dynamic inherent characteristic, resonant response and damping) and also carry out its experimental validation and sensitivity analysis.


Based on the classical laminated plate theory, a dynamic model is established using the orthogonal polynomials method, taking into account the effect of lamination and orthogonal anisotropy. The dynamic inherent characteristics of the ME plate are worked out by Ritz method. The frequency-domain dynamic equations are then derived to solve the plates’ resonant responses, with which the damping ratio is figured out according to the half-power bandwidth method. Subsequently, a series of experimental tests are performed on the ME samples to obtain the measured data.


It is shown that the predictions and measurements in terms of dynamic behavior are in good agreement, validating the accuracy of the developed model. In addition, sensitivity analysis shows that increasing the elastic modulus or Poisson’s ratio will increase the corresponding natural frequency of the ME plate but decrease the resonant response. When the density is increased, both the natural frequency and resonant response will be decreased.

Research limitations/implications

Future research can be focused on using the proposed model to investigate the effect of processing parameters on the ME parts’ dynamic behavior.

Practical implications

This study shows theoretical basis and technical insight into improving the forming quality and reliability of the ME parts.


A novel reliable dynamic model is set up to provide theoretical basis and principle to reveal the physical phenomena and mechanism of ME parts.



This research was supported by the National Natural Science Foundation of China (No. 51705068) and the Fundamental Research Funds for the Central Universities (No. N180703009 and N170302001).


Jiang, S., Sun, M., Zhan, Y., Li, H. and Sun, W. (2021), "A dynamic model of laminated material extrusion additive manufacturing plate with the property of orthogonal anisotropy", Rapid Prototyping Journal, Vol. 27 No. 4, pp. 785-796.



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