# Application of Generalized S-Transform in the Measurement of Dynamic Elastic Modulus
## 1 Introduction  
For civil engineering, in-place costs associated with concrete are about 30 percent. Since 2013, global cement production has exceeded 4 billion tons, prompting the industry to increase its focus on concrete quality detection. The dynamic elastic modulus is a crucial mechanical parameter for rigid materials such as concrete. It represents the elasticity of materials under dynamic loads, which is of great significance for predicting and evaluating the structural deformation and stress distribution of buildings and bridges. By measuring the dynamic elastic modulus, engineers can predict the small deformation response of building materials to external pressure within a specific frequency range, providing insight into the durability of these materials. Consequently, the measurement of dynamic modulus of elasticity holds significant importance in the quality assessment and monitoring of construction projects [1]. However, there is still much research work to be conducted to achieve high-precision measurements of the dynamic elastic modulus based on embedded devices. In the measurement of the dynamic elastic modulus, dynamic loading can be conducted to concrete samples by vibration table, acoustic emission, etc. [2; 3; 4]. To measure sample deformation, non-contact laser vibrometers, contact Linear Variable Differential Transformer (LVDT), nanoindentation, and piezoelectric ceramics are commonly employed [5; 6; 7]. Nowadays, commercial instruments for measuring the dynamic elastic modulus are: the resonance method, dynamic uniaxial shear, dynamic triaxial test, etc. [8; 9]. The dynamic triaxial apparatus is primarily employed in laboratory settings to assess the dynamic and static elastic modulus, as well as the damping ratio, in order to achieve morerealistic strength and deformation results for concrete samples. The dynamic uniaxial shear is mainly used for measuring the dynamic elastic modulus of non-rigid materials such as clay and particles. The resonance method is widely utilized in industrial sites for determining the dynamic elastic modulus of concrete. The dynamic elastic modulus of concrete is a single value function of resonance frequency, so by measuring the resonance frequency of the concrete specimen, the dynamic elastic modulus of the specimen can be calculated in accordance with strength theory [10]. Therefore, the strength measurement of concrete can be streamlined by initially determining its resonance frequency, and then the dynamic elastic modulus can be calculated by using the geometric parameters of concrete samples [11; 12]. Currently, numerous studies are being conducted on determining the elastic modulus of rigid materials, and these works have made substantial advancements in the fields of structural dynamics within construction and earthquake engineering [13]. Due to the challenges of accurately measuring the static elastic modulus outside of a laboratory setting, [PERSON] investigated the correlation between static and dynamic elastic modulus for various Poisson's ratios [8]. [PERSON] summarized various empirical calculation methods for the conversion of static elastic modulus and dynamic elastic modulus and proposed an accurate calculation method of static modulus using dynamic modulus [14]. [PERSON] measured the dynamic elastic modulus of tropical wood samples processed by chemical processes and summarized the effects of different processing methods on wood properties [15; 16]. [PERSON] conducted a study of dynamic and static elastic modulus of North Sea chalk on both dry and water-saturated chalk, and proposed that the LVDT is not able to accurately measure the small deformations of the samples during loading at relatively low stresses [17]. Inspired by the resonant frequency test to measure the dynamic elastic modulus of normal concrete, [PERSON] investigated the resonant frequency test to continuously monitor the modulus buildup of foam concrete [18].