Vibration dynamic response analysis of an rectangular thin plate coupled with concentrated masses is presented by numerical analysis method in this paper. Effects of magnitude and positions of lumped masses on the plate on its natural frequencies of vibration are studied. Many complicated engineering structures can be simplified as this kind of mechanics model, such as ship decks, wings coupled with oil tank and floors equipped with rotating machinery of civil buildings subjected to any kinds of forces. Natural frequency and natural mode of the plate coupled with concentrated masses are given through the method of constrained modal analysis method, considering the power balance method and orthogonality of natural modes of rectangular thin plate with no lumped masses, decoupled differential equations of motion with modal coordinates are given by Lagrange method. The symbolic numerical solution of the differential equation is carried out. The vibration displacement response of rectangular thin plate with lumped masses is simulated numerically. Methods and simulation results given in this paper can be used in the study of vibration displacement response control of rectangular thin plates with lumped masses under various boundary conditions.
Associate Professor, Rose-Hulman Institute of Technology
Professional interests include undergraduate engineering education, finite element modeling, ground-borne vibrations, vibrations of musical instruments, and dynamics of toys.
