Abstract.A direct approach is used to derive the exact solution for the free vibration of thin rectangular plates with discrete sprung masses attached. The plate is simply supported along two opposite edges and elastically supported along the two other edges. The elastic support can represent a range of boundary conditions from free to clamped supports. Considering only the compatibility of the internal forces between the plate and the sprung masses, the equations of the coupled vibration of the plate-spring-mass system are derived. The exact expressions for mode and frequency equations of the coupled vibration of the plate and sprung masses are determined. The solutions converge steadily and monotonically to exact values. The correctness and accuracy of the solutions are demonstrated through comparison with published results. A parametric study is undertaken focusing on the plate with one or two sprung masses. The results can be used as a benchmark for further investigation.The solution provided in the paper is general and includes several special cases, such as the plate with classical boundary conditions, the plate attached with discrete rigid masses, the plate supported by discrete springs and the plate restricted by rigid vertical point-supports.

Compared with traditional wooden building materials, polyvinyl chloride (PVC)-based wood–plastic composites have advantages of good weather resistance, easy processing capability, energy conservation, and environmental protection and have been popular and widely used in the field of civil construction and garden engineering in recent years. Due to the difference in the thermal expansion coefficient between its component materials, the stress will accumulate in the wood–plastic composites (WPCs) when the temperature changes, which will affect the mechanical properties of the material and structure. In order to explore the changes in mechanical properties of WPCs under different temperatures and achieve a safe and controllable design, the differential scanning calorimetry (DSC) method was used in this study to measure the glass transition temperature of the WPC between 78.45°C and 88.30°C, and the glass transition temperature (Tg) was about 83.54°C. The tensile, compressive, and bending mechanical property tests of PVC-based wood–plastic composite materials under different temperatures were carried out in the ambient temperature chamber to obtain the failure characteristics, the load–displacement curve, and the influence of temperature on their mechanical properties.