Jinpeng Su

Longitudinal and Transverse Coupling Dynamic Properties of a Timoshenko Beam with Mass Eccentricity

Non-uniform mass distribution on a beam will lead to the coupling between lateral and axial vibrations of the beam. To simulate the mass eccentricity, a double-layered Timoshenko beam model is developed. Based on Hamilton’s principle, the coupled governing equations are derived and mass and stiffness coupling coefficients are also derived. Moreover, the spectral element method (SEM), with high frequency accuracy by employing the dynamic shape functions, is utilized to study the dynamic properties of the beam. In addition, a corresponding finite element model is established to verify the SEM model. The coupling vibration characteristics are investigated and the coupling mechanism is revealed. Furthermore, the effects of mass non--uniformity on the free vibration and forced vibration of the beam with classical and flexible boundary conditions are analyzed. Finally, an optimal control method for reducing the contributions of bending modes under the axial excitation is presented with the results displayed.

Closed Form Solutions for Vibration and Sound Radiation of Orthotropic Plates under Thermal Environment

This paper presents a closed form solution for the vibration and acoustic problem of orthotropic plates under a thermal environment. Hamilton’s principle is utilized to derive the governing equation of motion for the orthotropic plate with thermal loads, which is then solved by the method of separation of variables. The frequency equations and mode functions obtained for the orthotropic heated plates with at least two adjacent edges clamped are much simpler than those by the conventional methods. Several numerical examples are carried out for the modal, dynamic and acoustic analysis of orthotropic heated plates with different combinations of thermal loads and boundary conditions. The results of the parametric study for the orthotropic plate with different thermal loads are discussed in detail. The validity of the present formulation is confirmed by comparing the results obtained with the numerical ones. Due to its accuracy, efficiency and versatility, the present method offers an efficient tool for the st...

Axial–bending coupling vibration of mass eccentric double-beam system with discrete elastic connections

The existence of mass eccentricity will lead to the energy transfer between axial and flexural vibrations of a beam. To study the coupling properties of a double-Timoshenko beam system, a non-uniform coupled double-beam system is modeled in which the upper beam is typical and the lower beam is mass eccentric simulated by a non-uniform two-layer Timoshenko beam. By incorporating Hamilton’s principle and spectral element method, the axial–bending coupled governing equations of the system are derived and the approach can also be easily used to analyze the influences of the parameters and other coupled beam systems. Both the free and forced vibration results of a double-beam system by this method are consistent with the corresponding finite element model’s and thus this method is validated. The coupled properties and their mechanism are revealed. The influences of axial and transverse flexible connection on the coupling properties including free and forced vibration are investigated. A systematic matching principle of reducing the vibration of the coupled system is proposed.

Modal coupling in the vibro-acoustic responses of submerged spherical-cylindrical-spherical shells stiffened by ribs and plates

This article presents a modal decomposition method for the analysis of radiated sound power of coupled shell structures submerged in infinite heavy fluid. This method provides greater physical insight into the self- and mutual-modal radiations of the in-vacuo modes. The corresponding cross-modal radiation efficiency is defined and formulated to analyze the mechanism of the energy transfer among the structural modes. A fully coupled finite element/boundary element model is developed for a simplified submarine hull, which is composed of a coupled sphericalcylindrical-spherical shell and a series of ring stiffeners and bulkheads. The interactions of different circumferential modes of the hull are examined. Modal coupling among the n = 1 grouped modes (including rigid body modes) is carried out to reveal the cross-modal coupling characteristics of the modes in the axial direction. In addition to the cross-modal radiation efficiencies, modal sound directivity is employed to show the physical mechanism of the modal coupling. The effects of apparent relative mass on the modal coupling are also investigated.

Vibration and sound radiation analysis of rectangular plates resting on Winkler foundation in thermal environment with closed form solutions

This article studies the structural and acoustic responses of a rectangular plate resting on the Winkler foundation under thermal environment. The solutions for the vibration analysis are based on a closed form method, and the Rayleigh integral method is adopted to predict sound radiation from the vibrating heated plate. Not only can the cases with any combination of simply supported and clamped boundary conditions be readily dealt with, but boundary conditions with free edges and the other pair of parallel edges simply supported can also be well considered. Under the current framework, the corresponding frequency equations and mode functions which are simpler than those by the traditional methods are formulated. An excellent accuracy of the proposed method can be observed by comparing the obtained results with the numerical results. Moreover, a considerable number of numerical examples are carried out to reveal the influence of key parameters on the dynamic and acoustic responses of the rectangular plate. Different combinations of the plate geometries, temperature changes, stiffness values of Winkler foundation, and boundary conditions are considered. The proposed method can be employed to investigate the vibration and sound radiation problems of plate subjected to thermo-mechanical loads for all kinds of combinations of simply supported and clamped boundary conditions and a few cases involving free edges.