scholarly journals Transverse free vibration of Euler-Bernoulli beam with pre-axial pressure resting on a variable Pasternak elastic foundation under arbitrary boundary conditions

2020 ◽  
Vol 17 (7) ◽  
Author(s):  
Yingqian Xu ◽  
Ning Wang
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Bernoulli Beam ◽  
Axial Pressure ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Pasternak Elastic Foundation ◽  
Euler Bernoulli Beam

Free Vibrations of Beams with Arbitrary Boundary Conditions Based on Wave Propagation Method

2011 ◽  
Vol 66-68 ◽  
pp. 753-757
Author(s):  
Wan You Li ◽  
Hai Jun Zhou ◽  
Jun Dai ◽  
Bing Lin Lv ◽  
Dong Hua Wang ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Beam Theory ◽  
Free Vibrations ◽  
Bernoulli Beam ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Wave Propagation Method ◽  
Wave Numbers ◽  
Euler Bernoulli Beam

Under the Euler-Bernoulli beam theory, the wave propagation method is used for the vibration analysis of beams with arbitrary boundary conditions. The boundary conditions end the beam could be arbitrary that all the conventional homogeneous beam boundary conditions can be included by setting the stiffnesses of the springs be infinity or zero. In this paper, the flexural displacement of the beam is expressed in the wave propagation form including wave numbers. The wavenumber could be obtained in a known form for conventional boundary conditions. So the results are obtained through the boundary conditions and the known wavenumbers and compared with the numerical results. In order to validate the correctness, results with different stiffness are compared with those obtained by previous published papers.

scholarly journals Free Vibration Analysis of Circular Cylindrical Shells with Arbitrary Boundary Conditions by the Method of Reverberation-Ray Matrix

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Dong Tang ◽  
Guoxun Wu ◽  
Xiongliang Yao ◽  
Chuanlong Wang
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Traveling Wave ◽  
Vibration Analysis ◽  
Cylindrical Shells ◽  
Free Vibration Analysis ◽  
Wave Form ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Circular Cylindrical Shells

An analytical procedure for free vibration analysis of circular cylindrical shells with arbitrary boundary conditions is developed with the employment of the method of reverberation-ray matrix. Based on the Flügge thin shell theory, the equations of motion are solved and exact solutions of the traveling wave form along the axial direction and the standing wave form along the circumferential direction are obtained. With such a unidirectional traveling wave form solution, the method of reverberation-ray matrix is introduced to derive a unified and compact form of equation for natural frequencies of circular cylindrical shells with arbitrary boundary conditions. The exact frequency parameters obtained in this paper are validated by comparing with those given by other researchers. The effects of the elastic restraints on the frequency parameters are examined in detail and some novel and useful conclusions are achieved.

An Experimental Approach to the Design of PVDF Modal Sensors

2001 ◽  
Author(s):  
Daniel Cuhat ◽  
Patricia Davies
Keyword(s):  
Boundary Conditions ◽  
Experimental Approach ◽  
Experimental Methodology ◽  
Laser Doppler Velocimeter ◽  
Piezoelectric Film ◽  
Bernoulli Beam ◽  
Beam Structure ◽  
Arbitrary Boundary ◽  
Classical Boundary ◽  
Euler Bernoulli Beam

Abstract The principle of modal sensing is based on the use of a shaped PVDF piezoelectric film measuring strains on the surface of a bending beam and acting as a modal filter. So far, the use of this type of sensors has remained confined to studies involving uniform structures with classical boundary conditions. The goal of this paper is to present an experimental methodology for the design of a shaped modal sensor applicable to an non-uniform Euler-Bernoulli beam with arbitrary boundary conditions. This approach is illustrated with test data collected on a cantilever beam structure with a laser Doppler velocimeter.

Sound Radiation Analysis of Functionally Graded Porous Plates with Arbitrary Boundary Conditions and Resting on Elastic Foundation

2020 ◽  
Vol 20 (05) ◽  
pp. 2050068 ◽  
Author(s):  
Zhengmin Hu ◽  
Kai Zhou ◽  
Yong Chen
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Sound Radiation ◽  
Functionally Graded ◽  
Harmonic Load ◽  
Arbitrary Boundary ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Arbitrary Boundary Conditions ◽  
Porosity Coefficient

In this paper, the sound radiation behaviors of the functionally graded porous (FGP) plate with arbitrary boundary conditions and resting on elastic foundation are studied by means of the modified Fourier series method. It is assumed that a total of three types of porosity distributions are considered in the present study. The material parameters are determined according to the porosity coefficient used to denote the size of pores in the plate. The governing equations of the FGP plate are derived by utilizing the Hamilton’s principle on the basis of the first-order deformation theory (FSDT). Each displacement component of the FGP plate is expanded as the Fourier cosine series combined with auxiliary polynomial functions introduced to enhance the convergence rate of the series expansions. The acoustic response of the FGP plate due to a concentrated harmonic load is calculated by evaluating the Rayleigh integral. Good agreements are attained by comparing the present results with those in available literatures, which show the accuracy and versatility of the developed method in this paper. Finally, the influences of the porosity distribution type, porosity coefficient, boundary condition and elastic foundation on the sound radiation of the FGP plate are analyzed in detail.

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