An innovative series solution for dynamic response of rectangular Mindlin plate on two-parameter elastic foundation, with general boundary conditions

2021 ◽  
Vol 88 ◽  
pp. 104274
Author(s):  
Reyhaneh Mohammadesmaeili ◽  
Seyedemad Motaghian ◽  
Massood Mofid
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Series Solution ◽  
General Boundary ◽  
Mindlin Plate ◽  
General Boundary Conditions ◽  
Two Parameter

scholarly journals Benchmark Solution for Free Vibration of Moderately Thick Functionally Graded Sandwich Sector Plates on Two-Parameter Elastic Foundation with General Boundary Conditions

2017 ◽  
Vol 2017 ◽  
pp. 1-35 ◽  
Author(s):  
Haichao Li ◽  
Fuzhen Pang ◽  
Xueren Wang ◽  
Shuo Li
Keyword(s):  
Fourier Series ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Functionally Graded ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Special Cases ◽  
Ritz Procedure ◽  
Two Parameter

The free vibration analysis of moderately thick functionally graded (FG) sector plates resting on two-parameter elastic foundation with general boundary conditions is presented via Fourier-Ritz method, which is composed of the modified Fourier series approach and the Ritz procedure. The material properties are assumed to vary continuously along the thickness according to the power-law distribution. The bilayered and single-layered functionally graded sector plates are obtained as the special cases of sandwich plates. The first-order shear deformation theory (FSDT) is adopted to construct the theoretical model. Under current framework, regardless of boundary conditions, each displacement and each rotation of plates is represented by the modified Fourier series consisting of a standard Fourier cosine series and several closed-form auxiliary functions introduced to ensure and accelerate the convergence of the series representation. Then, the accurate solutions are obtained by using the Ritz procedure based on the energy function of sector plates. The present method shows good convergence, reliability, and accuracy by comprehensive investigation with some selected classical boundary conditions. Numerous new vibration results for moderately thick FG sandwich sector plates are provided. The effects of the elastic restraint parameters and so forth on free vibration characteristic of sector plates are presented.

scholarly journals Response of Fractionally Damped Beams with General Boundary Conditions Subjected to Moving Loads

2012 ◽  
Vol 19 (3) ◽  
pp. 333-347 ◽  
Author(s):  
R. Abu-Mallouh ◽  
I. Abu-Alshaikh ◽  
H.S. Zibdeh ◽  
Khaled Ramadan
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Initial Conditions ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Damping Characteristics ◽  
The Laplace Transform ◽  
The Right

This paper presents the transverse vibration of Bernoulli-Euler homogeneous isotropic damped beams with general boundary conditions. The beams are assumed to be subjected to a load moving at a uniform velocity. The damping characteristics of the beams are described in terms of fractional derivatives of arbitrary orders. In the analysis where initial conditions are assumed to be homogeneous, the Laplace transform cooperates with the decomposition method to obtain the analytical solution of the investigated problems. Subsequently, curves are plotted to show the dynamic response of different beams under different sets of parameters including different orders of fractional derivatives. The curves reveal that the dynamic response increases as the order of fractional derivative increases. Furthermore, as the order of the fractional derivative increases the peak of the dynamic deflection shifts to the right, this yields that the smaller the order of the fractional derivative, the more oscillations the beam suffers. The results obtained in this paper closely match the results of papers in the literature review.

Dynamic Response of a Spinning Timoshenko Beam With General Boundary Conditions and Subjected to a Moving Load

1994 ◽  
Vol 61 (1) ◽  
pp. 152-160 ◽  
Author(s):  
J. W.-Z. Zu ◽  
R. P. S. Han
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Timoshenko Beam ◽  
Moving Load ◽  
Original System ◽  
Adjoint System ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Adjoint Systems ◽  
Analysis Technique

The dynamic response of a spinning Timoshenko beam with general boundary conditions and subjected to a moving load is solved analytically for the first time. Solution of the problem is achieved by formulating the spinning Timoshenko beams as a non-self-adjoint system. To compute the system dynamic response using the modal analysis technique, it is necessary to determine the eigenquantities of both the original and adjoint systems. In order to fix the adjoint eigenvectors relative to the eigenvectors of the original system, the biorthonormality conditions are invoked. Responses for the four classical boundary conditions which do not involve rigidbody motions are illustrated. To ensure the validity of the method, these results are compared with those from Euler-Bernoulli and Rayieigh beam theories. Numerical simulations are performed to study the influence of the four boundary conditions on selected system parameters.

scholarly journals Dynamic and Sound Radiation Characteristics of Rectangular Thin Plates with General Boundary Conditions

2019 ◽  
Vol 6 (1) ◽  
pp. 117-131
Author(s):  
Yuan Du ◽  
Haichao Li ◽  
Qingtao Gong ◽  
Fuzhen Pang ◽  
Liping Sun
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Ritz Method ◽  
Sound Radiation ◽  
Current Method ◽  
Thin Plates ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Radiation Characteristics ◽  
Aspect Ratios

AbstractBased on the classical Kirchhoff hypothesis, the dynamic response and sound radiation of rectangular thin plates with general boundary conditions are studied. The transverse displacements of plate are represented by a double Fourier cosine series and three supplementary functions. The potential discontinuity associated with the original governing equation can be transferred to auxiliary series functions. All kinds of boundary conditions can be easily achieved by varying stiffness value of springs on each edge. The natural frequencies and vibration response of the plates are obtained by means of the Rayleigh–Ritz method. Sound radiation characteristics of the plate are derived using Rayleigh integral formula. Current method works well when handling dynamic response and sound radiation of plates with general boundary conditions. The accuracy and reliability of current method are confirmed by comparing with related literature and FEM. The non-dimensional frequency parameters of the rectangular plates with different boundary conditions and aspect ratios are presented in the paper, which may be useful for future researchers.Meanwhile, some interesting points are foundwhen analyzing acoustic radiation characteristics of plates.

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