Chapter 23
The Application of Time–Domain DQM
to the Dynamically Forced Vibration
of Simply Supported Plates
Fan Lin, Jianshe Peng, Shifeng Xue, and Liu Yang
Abstract The time–domain DQM is for discretizing space domain of continuous
functions as well as time domain of that. In this paper, a study of the forced vibration
of simply supported plates subjected to a transverse uniform load is presented on
the basis of the time–domain DQM. Applying DQM both in space domain and time
domain, the partial differential governing equations and initial–boundary conditions
are discretized into linear algebraic equations which are solved easily to obtain the
transverse deflection of simply supported plates subjected to a transverse load. The
numerical results of two examples show that these numerical results of time–domain
DQM are in good agreement with analytical solution and that the accuracy and
efficiency of time–domain DQM are excellent under certain number of nodes. It is
simple and easy for the mathematical principle of space–time DQM to implement in
program, so it has a bright application prospect in the dynamic analysis field and is
worthy of a further study.
Keywords Time–domain DQM · Forced vibration · Plate · Adj.R2
23.1 Introduction
The differential quadrature method (DQM) which was first developed by Bellman
and Cacti in 1971 [1] has been extensively used for discretizing differential equations
into algebraic ones. Compared to conventional numerical methods, DQM is relatively
simple and has less computational effort in terms of achieving excellent accuracy of
numerical solutions.
The time–domain DQM is for discretizing space domain of continuous functions as well as time domain of that and is utilized successfully for gaining the
F. Lin · S. Xue (B)
College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao
266580, China
e-mail: sfeng@upc.edu.cn
J. Peng · L. Yang
School of Mechanical Engineering, Cheng Du University, Cheng Du 610106, China
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
J. Xu and K. M. Pandey (eds.), Mechanical Engineering and Materials,
Mechanisms and Machine Science 100,
https://doi.org/10.1007/978-3-030-68303-0_23
283
The Application of Time–Domain DQM
to the Dynamically Forced Vibration
of Simply Supported Plates
Fan Lin, Jianshe Peng, Shifeng Xue, and Liu Yang
Abstract The time–domain DQM is for discretizing space domain of continuous
functions as well as time domain of that. In this paper, a study of the forced vibration
of simply supported plates subjected to a transverse uniform load is presented on
the basis of the time–domain DQM. Applying DQM both in space domain and time
domain, the partial differential governing equations and initial–boundary conditions
are discretized into linear algebraic equations which are solved easily to obtain the
transverse deflection of simply supported plates subjected to a transverse load. The
numerical results of two examples show that these numerical results of time–domain
DQM are in good agreement with analytical solution and that the accuracy and
efficiency of time–domain DQM are excellent under certain number of nodes. It is
simple and easy for the mathematical principle of space–time DQM to implement in
program, so it has a bright application prospect in the dynamic analysis field and is
worthy of a further study.
Keywords Time–domain DQM · Forced vibration · Plate · Adj.R2
23.1 Introduction
The differential quadrature method (DQM) which was first developed by Bellman
and Cacti in 1971 [1] has been extensively used for discretizing differential equations
into algebraic ones. Compared to conventional numerical methods, DQM is relatively
simple and has less computational effort in terms of achieving excellent accuracy of
numerical solutions.
The time–domain DQM is for discretizing space domain of continuous functions as well as time domain of that and is utilized successfully for gaining the
F. Lin · S. Xue (B)
College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao
266580, China
e-mail: sfeng@upc.edu.cn
J. Peng · L. Yang
School of Mechanical Engineering, Cheng Du University, Cheng Du 610106, China
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
J. Xu and K. M. Pandey (eds.), Mechanical Engineering and Materials,
Mechanisms and Machine Science 100,
https://doi.org/10.1007/978-3-030-68303-0_23
283