Ultrasonic Guided Waves In Multilayer Magneto-Electro-Elastic Plate Structures

The superior properties of magneto-electro-elastic composite materials can realize the conversion between electrical energy,magnetic energy and mechanical energy.It is widely used in aerospace,nuclear energy,biomedicine and other engineering fields,and it also brings new opportunities to the development of electromagnetic ultrasonic transducers.As an efficient and low-cost non-destructive testing technology,ultrasonic testing technology has a good application prospect in the field of non-destructive testing of magneto-electro-elastic materials.Studying the wave characteristics in magneto-electro-elastic composites can provide a theoretical basis for ultrasonic testing and the design and optimization of transducers.It is difficult to solve the guided wave of multi-layer magneto-elastic composite material,because of problems such as the field of electrical displacement and stress at the interface.The previous Legendre polynomial method will generate discontinuous normal stress,electrical displacement,and magnetic induction intensity curve distributions when solving the propagation characteristics of guided waves of multilayer magneto-electro-elastic structures.And that up to now,few literatures give the stress,electrical displacement,and magnetic induction intensity distributions of multilayer magneto-elastic waveguide structures.In this paper,the Legendre orthogonal polynomial series method is improved to calculate the guided wave dispersion curves,stress and electrical displacement distributions of multilayer magneto-electro-elastic structures.Compared with the published results and the original Legendre polynomial method,the correctness and advancedness of the improved method are verified.The previous polynomial method expands the displacement,electric potential,and magnetic potential into a Legendre polynomial series over the entire multilayer section,while the improved method expands each layer's displacement,electric potential,and magnetic potential into one independent Legendre polynomial series.The wave differential equation is transformed into a eigenvalue calculation problem.The obtained eigenvalue can calculate the dispersion curve,and the eigenvector can describe the stress field,electric displacement field,and magnetic induction intensity distribution.Based on this method,the Lamb wave and SH guided wave characteristics in a multilayer magneto-electro-elastic plate are studied,the distribution of the physical field quantity is calculated,and the law of wave propagation characteristics at different wave numbers is revealed.It found that as the wave number increases,the distribution of the stress field and magnetic induction intensity of the Lamb wave gradually diffuses from the middle to the two sides.The SH wave stress and electrical displacement are little affected by wave number changes,and they are mainly distributed at the interlayer interface,and the amplitude decreases gradually away from the interface.Subsequently,the method is introduced into a cylindrical coordinate system,and the characteristics of the circumferential Lamb-like and SH-waves in a multilayered magneto-electro-elastic cylinder are studied.The effects of the diameter-thickness ratio and wave number on the characteristics of the guided waves are revealed.It found that,with the increase of the diameter-thickness ratio,the phase velocity and cutoff frequency of each order mode decrease;the stress of lamb wave-like at wavelet number is mainly distributed near the outer surface;the peak values of the SH-wave electrical displacement and magnetic induction intensity are located in the middle of the corresponding material layer.As the modal order increases,the amplitude of the field quantity shows an increasing trend;as the wave number increases,the peak value of electrical displacement gradually moves from the inner layer to the outer layer,and the peak value of stress gradually concentrates at the interface.Finally,the method was introduced into a spherical coordinate system to study the guided wave characteristics of multilayer magneto-electro-elastic spherical plates.The results show that the characteristics of the guided wave in a spherical plate are very close to the circumferential wave of a cylinder,and the gap between the two is mainly at the low frequency.Compared with the cylindrical structure,the spherical plate is curved in the transverse direction of wave propagation.The wavelength and the effect of this curvature are directly proportional.