The overall assessment of closed-form solution methods for free vibrations of rectangular thin plates

Xing, Yufeng; Sun, Qiaozhen; Liu, Bo; Wang, Zekun

doi:10.1016/j.ijmecsci.2018.03.013

Cited by 19 publications

(3 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The dynamic behavior of plates was investigated in the past decades by many researchers [1][2][3][4], due to their wide-range applications in various fields, such as: aerospace, marine engineering and naval architecture. Thus, Wang and Wereley [5] have proposed analytical solutions for the modal frequencies and displacement mode shapes in a rectangular plate with different boundary conditions, by involving the Kantorovich-Krylov method.…”

Section: Introductionmentioning

confidence: 99%

A python application to calculate the mode shapes of rectangular plates

Nedelcu¹,

Barbinta²,

Gillich³

et al. 2020

Vib. proced.

View full text Add to dashboard Cite

We propose a continuous model for rectangular plates that involves a mesh of slender interconnected beams. These beams are disposed orthogonally. The advantage of this model is that simple equations are involved and the behavior of the plate is accurately described. After a brief description of the model, we present an application written in the Python programing language that allows calculating the mode shapes for rectangular plates with various boundary conditions. The mode shapes achieved with the application for a specific plate are found to be similar with those obtained from simulation involving the SolidWorks software. In consequence, we conclude that the proposed model is reliable and the application developed on this base can be used to study the behavior of rectangular plates with different boundary conditions.

show abstract

Section: Introductionmentioning

confidence: 99%

A python application to calculate the mode shapes of rectangular plates

Nedelcu¹,

Barbinta²,

Gillich³

et al. 2020

Vib. proced.

View full text Add to dashboard Cite

show abstract

“…Impact on 3D panel flutter properties of different boundary conditions (SSSS, SCSC and SFSF) were investigated using the assumed mode method and finite element method in 2014 [8]. Yufeng Xing gave the overall assessment of closed-form solution methods for free vibrations of rectangular thin plate [9] With the increase of the flight speed of modern aircrafts, the Mach number can reach more than five Mach. Therefore, it is urgent to systematically give the flutter calculation results under all constraint boundaries of the two-dimensional plate model.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution for Thermal Flutter of Laminates in Supersonic Speeds

Dai¹,

Sun²

2020

JAMP

Self Cite

View full text Add to dashboard Cite

As a basic component of engineering fields such as aeronautics, astronautics and shipbuilding, panel structure has been widely used in engineering and scientific research. It is of great theoretical and practical significance to study the vibration of panels. The panel flutter problem has caused widely concerned by researchers at home and abroad during to the emergence of high-speed aircrafts. With regard to the eigenvalue problem of rectangular panels, it is generally believed that it is difficult to obtain a closed form eigen solution in the case of an adjacent boundaries clamped-supported or a free boundary that cannot be decoupled. Aiming at the problem, this paper studies the two-dimensional symmetric orthogonal laminated plate structure in the hypersonic flow in the thermal environment, and combines the first-order piston aerodynamic theory to study a high-precision separation variable method. Through this method, analytical solution to the closed form of the thermal flutter problem of rectangular panels can be obtained under any homogeneous boundary conditions.

show abstract

“…The response (acceleration or speed) of structures subjected to human- or machine-induced vibration is compared to the tolerance limit of human comfort [2,3,4,5]. Several recent publications deal with the analysis and design of rectangular plates for both static and dynamic loads [6,7,8,9].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Response of Long Rectangular Floors Subjected to Periodic Force Excitation

Pap

Kollár

2019

Materials

View full text Add to dashboard Cite

Since damping in lightweight floors is usually low, dynamic amplification can be rather high. Long rectangular plates subjected to concentrated loads are often investigated by a replacement beam with a so called “effective width”. Although this approach is a reliable tool for static loads, the steady-state dynamic response of beams and long plates subjected to periodic loads are significantly different. The maximum displacements and accelerations of beams (and of not-long rectangular plates) are obtained by using a dynamic amplification factor, which in the case of resonance is equal to 1 / 2 ξ , where ξ is the damping ratio. For long plates (and for not-long orthotropic rib-stiffened plates), as discussed in the paper, the response and the amplification factor are substantially different from those of beams. Hence, design based on effective width may lead to 2–4 times higher acceleration than the real values. In an economic design, to avoid unnecessary damping enhancement, this effect must be taken into account.

show abstract

The overall assessment of closed-form solution methods for free vibrations of rectangular thin plates

Cited by 19 publications

References 38 publications

A python application to calculate the mode shapes of rectangular plates

A python application to calculate the mode shapes of rectangular plates

Analytical Solution for Thermal Flutter of Laminates in Supersonic Speeds

Dynamic Response of Long Rectangular Floors Subjected to Periodic Force Excitation

Contact Info

Product

Resources

About