Resonance characteristics of asymmetric and axisymmetric modes in orthotropic plates under moving load excitation

Abstract

This work investigates the flexural vibrations of a thin, orthotropic circular plate on elastic foundation. Kinematic relations are developed with von Karman strain-displacement relations. The dynamical equations are derived using Hamilton’s principle, yielding three coupled partial differential equations in the transverse, radial, and tangential directions. The material symmetry about the two orthogonal directions leads to a fourth-order ordinary differential equation with variable coefficients in the spatial domain. A Frobenius series based semi-analytical procedure is introduced here possibly for the first time for orthotropic circular plates on elastic foundation under moving loads to obtain accurate mode shapes for both simply supported and clamped boundary conditions. Further, the deflection at any point on the plate is determined using axisymmetric and asymmetric eigenfunctions within the mode summation framework. The effect of orthotropy ratio, moving load frequency, and foundation stiffness are analyzed. It is found that symmetric modes, characterized by zero nodal diameter, do not capture the moving load frequency in the frequency spectrum and therefore exhibit only the natural frequencies of the system. In contrast, asymmetric modes with non-zero nodal diameters capture both the natural frequencies and the moving load frequency. It is further observed that the plate vibrates about a shifted non-zero equilibrium position, primarily due to axisymmetric mode contributions. The influence of foundation stiffness is investigated, revealing a significant effect on the fundamental frequencies in symmetric responses, while its influence on higher modes and asymmetric responses remains relatively limited. In addition, the effect of damping on both axisymmetric and asymmetric vibrations of the plate under moving loads is examined. The results show that resonance occurs only in asymmetric modes, and damping effectively controls their amplitude and enhances the stability of the response.