Closed Form Solutions for Vibration and Sound Radiation of Orthotropic Plates under Thermal Environment

• Published in: International journal of structural stability and dynamics Vol. 18; no. 7; p. 1850098
• Main Authors: Zhou, Kai, Su, Jinpeng, Hua, Hongxing
• Format: Journal Article
• Language: English
• Published: Singapore World Scientific Publishing Company 01.07.2018; World Scientific Publishing Co. Pte., Ltd
• Subjects: Acoustics; Boundary conditions; Closed form solutions; Equations of motion; Exact solutions; Loads (forces); Numerical methods; Orthotropic plates; Sound waves; Thermal analysis; Thermal environments; Vibration control; thermal environment; sound radiation; closed form solution; vibration; Orthotropic plate
• ISSN: 0219-4554; 1793-6764
• DOI: 10.1142/S0219455418500980

This paper presents a closed form solution for the vibration and acoustic problem of orthotropic plates under a thermal environment. Hamilton’s principle is utilized to derive the governing equation of motion for the orthotropic plate with thermal loads, which is then solved by the method of separation of variables. The frequency equations and mode functions obtained for the orthotropic heated plates with at least two adjacent edges clamped are much simpler than those by the conventional methods. Several numerical examples are carried out for the modal, dynamic and acoustic analysis of orthotropic heated plates with different combinations of thermal loads and boundary conditions. The results of the parametric study for the orthotropic plate with different thermal loads are discussed in detail. The validity of the present formulation is confirmed by comparing the results obtained with the numerical ones. Due to its accuracy, efficiency and versatility, the present method offers an efficient tool for the structural and acoustic analysis of the orthotropic plate under the thermal environment.