Inspection of a Rectangular Plate Dynamics Under a Moving Mass With Varying Velocity Utilizing BCOPs

Abstract

This research is dedicated to the inspection of a thin rectangular plate dynamic behavior traversed by an accelerated moving mass. BCOPs (boundary characteristic orthogonal polynomials) are utilized to treat the constitutive equation of plate vibration for different boundary conditions. Comprehensive parametric surveys are carried out to shed light on the effects of the plate fixities and aspect ratios as well as the moving mass weight, velocity and acceleration on the plate DAF (dynamic amplification factor). The convenience of adopting the presented solution dealing with various plate fixity cases makes it a superior approach comparing with eigenfunction expansion method.

Experimental studies on the dynamic response of thin rectangular plates subjected to moving mass

“…From the above equations, it is clear that to calculate the elements of the matrices in equation (10), the normalized mode shapes of the plate are required. In this study, the mode shapes ϕi(x,y) of the plate with clamped boundary conditions are generated by the boundary characteristic orthogonal polynomials and the Gram–Schmidt algorithm (Niaz and Nikkhoo, 2015). Consider the following linearly independent set of functionswhere p 1 , p 2 , p 3 , and p 4 are determined based on the boundary conditions of the plate, and for the clamped boundary conditions on all edges of the plate, p 1 = p 2 = p 3 = p 4 = 2.…”

Vibration control of bridges under simultaneous effects of earthquake and moving loads using steel pipe dampers

“…Ebrahimzadeh Niaz and Nikkhoo 2015;Nikkhoo 2014;) is adopted for calculation of the displacement field. In the following section, the efficiency of the method is demonstrated through a benchmark numerical example.…”

“…A number of methods are available to solve equation (14) in the time domain. In this paper, the matrix-exponential method, proposed by Brogan (1985) and utilized by a number of other researchers (e.g., Ebrahimzadeh Hassanabadi et al., 2014; Nikkhoo, 2014; Nikkhoo et al., 2016; Niaz and Nikkhoo, 2015) is adopted for calculation of the displacement field. In the following section, the efficiency of the method is demonstrated through a benchmark numerical example.…”

The Rayleigh–Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review

“…Pradhan and Chakraverty (2015c) used the Rayleigh–Ritz with simple algebraic polynomials method to study transverse vibration of isotropic thick rectangular plates based on new inverse trigonometric shear deformation theories. Niaz and Nikkhoo (2015) determined the dynamic response of a thin rectangular plate excited by a traveling mass and having arbitrary boundary conditions. Karthikeyan and Rama (2015) carried out modal analysis of thin orthotropic piezoelectric (PVDF/PZT4) rectangular plates using the Rayleigh–Ritz method.…”