Impact Hammer Research Articles

Experimental and numerical analyses on the modal behaviour of an aluminium alloy sheet

Abstract The study of modal behaviour for vehicle body panels represents a field of interest for automotive engineering, having a major influence on automotive comfort, with respect to vehicle noise, vibration and harshness, but also concerning the durability of vehicle body. The investigation of natural frequencies and vibration mode shapes is crucial in the design phase, because essential information can be obtained concerning the behaviour of the components in dynamic conditions. The current paper focuses on the investigation of vibration modes and frequency response function on an aluminium alloy sheet. The aim of the paper is to perform the study of modal behaviour both experimentally and theoretically, through measurements using the impact hammer method and respectively through finite element analysis. The CAD model of the aluminium alloy sheet has been developed in Catia V5 environment in view of elaborating the finite element model, which has been used for investigation of modal behaviour, taking into account the case of free vibrations. Through the modal finite element analysis performed in Ansys Workbench, the natural frequencies of the aluminium alloy sheet, as well as the corresponding mode shapes have been obtained. Experiments have been performed on an aluminium alloy sheet, mounted on an elastic support with low natural frequency. The impact hammer method has been used for obtaining the natural frequencies, through frequency analysis of accelerations measured with two piezoelectric accelerometers mounted on the aluminium alloy sheet. The frequency response function has been computed from the response acceleration measured on the aluminium alloy sheet and the impact force measured using the force transducer of the impact hammer. Virtual instruments have been developed in LabVIEW environment for data acquisition, time domain and frequency analysis, as well as for determining the frequency response function using the measured signals. The natural frequencies obtained from the finite element analyses have been compared to the results of measurements and very good similarities have been ascertained. The experimental investigation of modal behaviour contributed to the validation of the finite element model, but further research is required to investigate the possibilities of improving the modal behaviour of the aluminium alloy sheet.

Band gap generation in cantilever beams through periodic material removal

Traditional methods for generating band gaps in beams usually involve adding periodic elements like tuned mass dampers or masses, or applying complex geometrical changes. This research suggests a subtraction-based method achieved by removing material in the thickness direction through straightforward machining operations, thus forming periodic cells. The numerical studies start with band gap analysis, using periodic theory to assess different periodic cell configurations. This is followed by numerical and experimental studies on cantilever beams, each containing a set number of these periodic cells. Non-contact vibration measurements are conducted on one plain and six machined aluminum beams using a multipoint laser vibrometer and an automated impact hammer. The experimental findings corroborate the band gaps predicted by the numerical model, confirming the effectiveness of this approach. The study notes that the optimal periodicity of the cells and the contrast in thickness vary with the beam’s dimensions, and that the thickness contrast markedly affects the quantity, width, and intensity of the resulting band gaps. These results indicate that (1) periodic material removal in beam-like structures allows improved vibration reduction while mass is reduced, and (2) manufacturing can play a key role in vibration control in simple structures.

Design and Development of a Pipeline Maintenance System for Pipe Surge and Water Hammer Equipment Based on Siemens S7-1200 PLC

Fluids play a crucial role in the lives of living beings, as they are substances that can flow. In a piping system, a common issue is water pressure fluctuation caused by sudden closures of water flow (Idul, 2021). Pipe surge and water hammer equipment are utilized to demonstrate the transient pressure effect resulting from abrupt changes in flow velocity within pipes (David, 1981). Water hammer can lead to pressure surges throughout the piping system, potentially causing failures that result in leaks in pipes, valves, pipe joints, and even pumps if the pressure exceeds the pipe's capacity (Prasetya, 2016). The likelihood of pipe ruptures or leaks at joints increases significantly. Additionally, equipment movement, slope, and precision of pipe installation can also contribute to leaks during water hammer events. This research aims to develop a pipe leakage monitoring system to address the impact of water hammer. The system will be installed in areas deemed susceptible to this phenomenon, along with a periodic maintenance indicator system to minimize the impact of pipe leaks. The research will also investigate the potential risks associated with varying fluid flow rates in the piping system. The monitoring, indicator, and sensor systems will be integrated into a PLC and HMI system for data processing.

Enhanced impact resistance of RC beams using various types of high-performance fiber-reinforced cementitious composites

This study investigates the impact resistance of reinforced concrete (RC) beams using various types of high-performance fiber-reinforced cementitious composites (HPFRCCs). A total of ten large-sized RC beams were fabricated and tested under static and impact loading conditions. Four different types of HPFRCCs with 2% by volume of steel, polyvinyl alcohol (PVA), and polyethylene (PE) fibers were considered. Ultra-high-performance fiber-reinforced concrete (UHPFRC) based on steel fibers demonstrated superior compressive and tensile strengths, while high-performance strain-hardening cementitious composite (HP-SHCC) based on PE fibers exhibited the highest strain and energy absorption capacities. The steel-bar reinforced (R-) UHPFRC and HP-SHCC beams showed superior flexural load capacity compared to reinforced normal strength concrete (R-NSC) beams. The highest ductility of 8.02 was found in the R-HP-SHCC beam, almost 5 times higher than that of the R-NSC beam. By drop hammer impact with a kinetic energy of 30 kJ, the R-UHPFRC beam completely failed due to its higher reaction load and lower structural ductility, while other RC beams made of NSC and HPFRCCs withstood the identical impact load. The R-HP-SHCC beam exhibited the best impact resistance, with a 29.1% lower maximum deflection compared to the R-NSC beam, and the largest residual load capacity after the impact damages. The R-HP-SHCC beam, despite being damaged, showed no reduction in flexural stiffness, yet it demonstrated an impressive 5.4% increase in load capacity compared to the undamaged beam.

Dynamic behaviors of bridge with corroded RC piers under barge collisions

Reinforced concrete (RC) bridge piers located in navigable waterways are susceptible to chloride-induced corrosion, which may cause severe damage or even entire collapse of bridge under potential barge collisions. The present study aims to examine the failure patterns and dynamic responses of typical simply supported girder bridge with corroded RC piers under barge collisions. Firstly, nine RC column specimens with three designed corrosion degrees and two corrosion strategies were prepared using the impressed anodic current technique. Secondly, the drop hammer impact and axial compression tests were successively performed to examine the residual axial load bearing capacities of both unimpacted and impacted specimens. Furthermore, by comprehensively considering the effects of corrosion-induced deteriorations on the effective cross-sectional area and yield strength of reinforcements, concrete strength, as well as the rebar-concrete bond-slip relationship, the refined finite element (FE) models of specimens were established and validated. Finally, the dynamic behaviors of a prototype simply supported girder bridge with corroded RC piers under barge collisions at different service lives, i.e., 0–60 years, were numerically assessed. It indicates that: (i) under drop hammer impact, six specimens all exhibit global flexure failure, and relatively severe concrete cracking and spalling occur in the specimens with 15 % designed corrosion degree; (ii) the axial load bearing capacities of specimens with 5 % and 15 % designed corrosion degrees are reduced by 15.46 % and 34.86 % compared to the unimpacted non-corroded specimen, and 11.29 % and 43.30 % compared to the impacted non-corroded specimen; (iii) the transverse impact resulted in 25.93 %, 22.27 % and 35.53 % reductions in axial load bearing capacities for 0 %, 5 % and 15 % designed corrosion degree, respectively; (iv) for the prototype barge-bridge collision scenario, the failure patterns vary from minor bending cracks to remarkable flexural failure as the service live increases from 0 to 60 years. The corrosion-induced degradations of bridge performance should be concerned for the vessel collision-resistant design of bridge.

3D mode shapes characterization under hammer impact using 3D-DIC and phase-based motion magnification

Modal analysis constitutes a fundamental aspect of structural investigation within diverse engineering domains, encompassing sectors such as automotive, wind energy, and aerospace. The prominence of high-frequency excitation loads, exemplified by the combustion phenomena in liquid rocket engines, necessitates an in-depth examination of the high-frequency vibrational response within structural components. However, the complexity of evaluating high-frequency vibrations arises from the negligible displacement associated with these responses. When using an optical full-field measurement system based on a high-speed camera for vibration measurement, it is usually severely affected by noise. Direct analysis of raw data using an optical measurement system (3D-DIC) is not feasible. In this paper, we combine phase-based motion magnification and digital image correlation methods to obtain the high-frequency vibration modes of the structure. 3D-DIC(3D Digital Image Correlation)analysis is performed on the magnified images to quantify the out-of-plane vibration modes of the structure. Using the cantilever beam as an example, the first five out-of-plane vibration mode shapes were separated from the response video under a single hammer excitation. Especially the 5th order natural frequency is as high as 3503 Hz, and the corresponding structural response was below the noise floor of the camera system. The vibration mode results obtained by this method are highly consistent with the vibration modes obtained by the 3D-SLDV(3D Scanning Laser Doppler Vibrometer) method. Finally, this method was applied to identify the out-of-plane vibration modes of real engine pipe. The combination of motion magnification techniques and DIC can enhance the capability of traditional 3D-DIC, which is beneficial for high-frequency structural identification. Future research could concentrate on optimizing motion amplification factors for different structures and loads, and creating automated algorithms for analyzing and visualizing amplified motion data in real time.

Static and dynamic analysis of polyethylene terephthalate foam core and different natural fiber-reinforced laminated composite-based sandwich plates through experimental and numerical simulation

This study explores the flexural behavior and free vibration analysis of sandwich plates including natural fiber-reinforced polymer composite faces and Polyethylene Terephthalate (PET) foam cores under a range of edge situations. ABAQUS is used to do numerical simulations with three-dimensional solid elements (C3D8R). To ascertain the natural frequencies of the plates, experimental procedures such as impact hammer testing and Fast Fourier Transform (FFT) analysis are carried out. The inference of different geometrical parameters on the natural frequencies is investigated through numerical simulation in ABAQUS. The study gives brief outlines regarding the sandwich plates for different engineering applications.

Synthetical improvement of dynamic mechanical property and toughness for precast concrete element based on optimization design of composition and curing regime

The brittleness and toughening measures of steam-cured concrete are currently less researched aspects. This study focuses on exploring the improvement in the toughness of steam-cured concrete and evaluating its influence on dynamic mechanical properties through a series of macroscopic performance tests. These tests include four-point bending tests, three-point bending fracture tests, uniaxial compression tests, and drop hammer impact tests, all conducted from the perspective of optimizing composition materials and steam curing regimes. The experimental results indicate that, under a relatively short heating time and a prolonged constant temperature curing period, the pure cement steam-cured concrete (S1 group), compared to the S2 group which used 20 % FA and 10 % GGBS to replace cement while also increasing the aggregate content with a modified steam curing regime, exhibited higher strength and elastic modulus but also showed greater brittleness. For example, the damping ratio increased to 0.6–0.7, the flexural-to-compressive strength ratio exceeded 6, and the number of specimens damaged by drop hammer impact significantly decreased, and the notch specimen exhibits lower peak load and displacement during fracture, with generally lower fracture parameter values. The fracture energy of the S2 group is 100–130 N·m-1 higher than that of the S1 group, reaching approximately 670 N·m-1, and the ductility index increased by 0.3–0.4. This research can provide technical support for the high-quality preparation of precast components using steam-cured concrete and offer a theoretical basis for reducing the brittleness of steam-cured concrete.

Study on Low-Velocity Impact and Residual Compressive Mechanical Properties of Carbon Fiber-Epoxy Resin Composites.

Room temperature drop hammer impact and compression after impact (CAI) experiments were conducted on carbon fiber-epoxy resin (CF/EP) composites to investigate the variation in impact load and absorbed energy, as well as to determine the residual compressive strength of CF/EP composites following impact damage. Industrial CT scanning was employed to observe the damage morphology after both impact and compression, aiding in the study of impact-damage and compression-failure mechanisms. The results indicate that, under the impact load, the surface of a CF/EP composite exhibits evident cratering as the impact energy increases, while cracks form along the length direction on the back surface. The residual compressive strength exhibits an inverse relationship with the impact energy. Impact damage occurring at an energy lower than 45 J results in end crushing during the compression of CF/EP composites, whereas energy exceeding 45 J leads to the formation of long cracks spanning the entire width of the specimen, primarily distributed symmetrically along the center of the specimen.

Cushioning performance of origami negative poisson's ratio honeycomb steel structure

The honeycomb structure with a negative Poisson's ratio, inspired by the Miura origami unit, exhibits three-dimensional negative Poisson's ratio characteristics and effective energy dissipation performance. This unique property provides significant potential in the field of protection applications. This study aims to comprehensively understand the impact of auxetic and origami structures on the cushioning performance of honeycomb structures. For this purpose, 316 L stainless steel specimens were fabricated using 3D printing technology and subjected to drop hammer impact tests, and the results were verified by finite element simulation. This paper focuses on assessing the deformation mode and energy dissipation performance of origami auxetic honeycomb structures with varying width-to-thickness ratios and folding angles under different impact energy levels. The results indicate that the negative Poisson's ratio origami specimens exhibit higher plateau stress and specific energy absorption compared to their positive and zero Poisson's ratio origami counterparts with the same geometry. In addition, a smaller width-to-thickness ratio and higher input impact energy enhance the cushioning performance of honeycomb structures.

Numerical study on the anti-collision performance of recycled foam concrete beam guardrail under vehicle collision

Recycled foam concrete (RFC) possessed excellent energy absorption capabilities and could be used in the anti-collision field. To address the insufficient anti-collision performance of existing guardrails, this paper presented a novel RFC beam guardrail by combining RFC with box-shaped steel shells. The quasi-static compressive tests and drop hammer impact tests were applied to analyze the static and dynamic mechanical characteristics of RFC with different densities and sand-cement ratios. Then, the vehicle collision performance of the RFC beam guardrail (RBG) and standard beam guardrail (SBG) was tested by LS-DYNA. The results showed that, compared with SBG, RBG had better guiding and energy absorption effects, reduced the peak vehicular acceleration by 44.15 % and the maximum guardrail displacement by 73.22 % during vehicle collisions, and mitigated the damage to the vehicle. Therefore, it is a viable way to utilize RFC to fabricate RBG, which could not only repurpose the construction and demolition wastes (CDW) but also acquire guardrails with enhanced anti-collision performance.

Impact Experiment and Buckling Criterion Analysis of Thin-Walled Cylindrical Shells

The impact test of tubular components is usually carried out by way of drop hammer impact. In fact, in many ships’ equipment, the form of load is often carried out by way of drop impact test. In this paper, the drop impact test is used to study the buckling of tubular structure under impact load, so as to make it closer to the impact form of components in actual ship structure. Firstly, the stress, strain, acceleration at each moment and the buckling deformation mode of the tubular member after the impact are obtained through the drop impact experiment, and then the impact process is analyzed. Secondly, the finite element method is used for numerical simulation of the impact process, and the accuracy of the finite element analysis results is verified by comparing with it. Thirdly, the finite element method proved to be effective and was used to simulate single and multiple drop impacts under more working conditions, and a large amount of data was obtained. Finally, according to the existing impact criteria based on the results of drop weight impact, it is applied to the drop impact process, and the accuracy of each impact criterion is analyzed and compared. This method makes up for the deficiency of the traditional experimental method of using falling weight to simulate impact, and provides a reference for the critical buckling condition of similar thin-walled cylindrical shells under impact.

Effect of clamshell powder on the mechanical and damping properties of epoxy-bamboo composites

Compared to single natural fibre composites, hybridising natural fibres with filler particles presents a promising avenue for enhancing composites physical, mechanical, and damping properties. This study delves into incorporating clamshell powder, a filler derived from clams’ hard protective outer shells, into polymer composites. The focus is on investigating the potential of clamshell powder as a filler material to augment the mechanical and damping properties of epoxy-bamboo mat composites. The weight ratio of clamshell fillers varied from 0% to 9%, and the compression moulding method was used to fabricate the composites. As per ASTM standards, mechanical properties were evaluated by conducting tensile and flexural tests. Free vibration tests by impact hammer technique were employed to evaluate the natural frequency, damping ratio, and mode shapes of developed composites to measure damping properties. Results revealed that adding clamshell filler significantly improved composites tensile strength, flexural strength, and damping properties. The addition of clamshell elevated the tensile strength by 18.5%, and flexural strength by 24.2% for composite with 6 wt% filler, which can be attributed to the efficiency of load transfer and the interfacial bonding between fillers and epoxy matrix. SEM analysis supported the experimental results obtained. The highest damping value is received for 9 wt% filler, showing 30% enhancement compared to composites without clamshell filler. Modal analyses using ANSYS software further validated the positive impact of clamshell filler. This study underscores the potential of clamshell filler in enhancing the mechanical and damping properties of epoxy-bamboo composites, broadening their applicability in various fields.

Particle Size Distribution and Energy Dissipation in Drop Hammer Impact Damage of Gas-Containing Coal.

Coal and gas outburst is the mechanical damage behavior of gas-containing coal in a complex environment. In this paper, the established experimental system is used to carry out hammer damage experiments on coal adsorption of different gases under different gas pressures and analyze the mass distribution and surface area distribution characteristics of coal samples in each particle size interval after the hammer damage of coal samples. The energy of the crushing process was analyzed by using the specific work of crushing, mass of newly generated particle size added per unit of energy, newly added surface area per unit of energy, and newly added specific surface area per unit of energy. The results show that the crushing effect of gas-containing coal samples during hammer damage is related to the type and pressure of the adsorbed gas. The stronger the gas adsorption performance and the higher the gas pressure, the weaker the effect of gas-containing coal hammer damage. Meanwhile, the energy required for the mass and surface area of coal samples with newly generated particle size decreased, indicating that the stronger the gas adsorption and the higher the gas pressure, the more serious the energy dissipation in the hammering damage process of gas-containing coal samples. The research results are conducive to an in-depth understanding of the coal and gas outburst processes, which can provide a theoretical basis for the damage characteristics and energy dissipation of coal and gas outbursts.

Pickleball sounds: impact induced vibration and radiated sound

The rapid growth in popularity of pickleball and the ever-increasing number of pickleball courts has resulted in growing concerns about the effect of pickleball sounds on nearby neighbors. The vibration of the ball and paddle that is generated at impact, and which is the source of the radiated sound, was measured for different paddles as a function of frequency using an impact hammer instrumented with a force gage. Average vibration velocities over the paddle surface were generated that scale the radiated sound. Animations of paddle vibration were also generated. A paddles vibration level depends on its internal mechanical damping which was also measured. A performance metric is proposed where the paddles' sound levels are compared at the same "power" in terms of the change in momentum (velocity) of the pickleball on impact. Outdoor directivity measurements of the sound for a paddle were "dipole-like" in character with lower levels, by 10 dB or more, in the plane of the paddle compared to levels perpendicular to its face. The orientation of the courts may be important if the sound levels during play are quieter in the general direction along the nets.

Residual load-carrying performance of ECC-RC composite beam after drop hammer impact

Four types of specimens with various thicknesses of ECC layer in the tensile side of RC beam are fabricated. The influence of ECC layer on the dynamic response and residual capacity of RC beams is investigated through drop hammer impact test and post-impact static loading test. The results reveal that increasing the thickness of the ECC layer in the tensile side leads to less major cracks and more tiny cracks on the beam side under impact, and the damage of concrete in the impact zone alleviates. The incorporation of the ECC layer plays an insignificant role in displacement restitution and residual load-carrying capacity. However, ECC-RC composite beams effectively mitigate displacement ductility degradation. Compared to RC beam, ECC-RC composite beams also exhibit superior energy dissipation capacity at the post-impact loading stage. The parametric analysis indicates that a thicker ECC layer in composite beams with a low tensile reinforcement ratio effectively reduces maximum impact displacement but has a negligible influence on residual load-carrying capacity. In contrast, increasing the ECC layer in beams with a high tensile reinforcement ratio offers a limited reduction in maximum impact displacement but its residual load-carrying capacity significantly improves after impact.

Bioinspired stiff–soft gradient network structure for high-performance impact-resistant elastomers

Traditional impact-resistance materials relying on the combination of supporting materials and energy-dissipation elastomers can effectively reduce shock load, yet the sharp interface between two types of materials causes discontinuous stress transfer and cracking. Here, inspired by the squid beak, we report a type of high impact-resistance gradient elastomers with large-scale modulus gradient with about three orders of magnitude (modulus range of 7 × 103 ∼ 7 × 106 Pa) and high energy dissipation (loss factor > 0.6) over a wide temperature range by diffusively introducing stiff polymers in a highly damping elastomer with controlled mechanical properties. Under the action of an external force, our gradient elastomers exhibit soft-while-stiff attributes, combining cushioning and support. In drop hammer impact tests, our gradient materials can reduce impact strength by 80 %, significantly better than commercial protective gear. It is worth mentioning that the modulus of the bottom layer matches that of the tissues for better protection.

Experimental research on the mechanical properties of alkali-resistant glass fiber concrete acting as tunnel seismic isolation layer under periodic cyclic dynamic loading

The installation of seismic isolation layer is an effective measure to ensure the safe operation of underground projects such as tunnels during extreme seismic activities. Material parameters, mechanical properties, and design patterns of the seismic isolation layer are key research topics in exploring effective reduction of seismic response. This study mainly focused on the dynamic performance of the seismic isolation layer in tunnels. A series of drop hammer impact tests and laboratory shaking table tests were performed to reveal the seismic features of the seismic isolation layer under periodic external loading. The test results indicated that all cracks in the specimen initiated from the center and dispersed outwards under the cycle impact of the drop hammer. The incorporation of alkali-resistant glass fibers in concrete (AR-GFRC) effectively provided "reinforcement " and "crack resistance" under cyclic loading of the drop hammer, and the minimum number and width of cracks were observed at a 0.75 % HD fiber content and a 0.5 % HP fiber content. In the x- and y-axis directions, the seismic isolation layer effectively mitigated peak acceleration, strain response, and displacement at the tunnel vault and invert, but significant nonlinearity was identified. When the thickness of seismic isolation layer was 10 mm, the peak seismic response of the lining were minimum at a 0.75 % HD fiber content and a 0.5 % HP fiber content. However, the thickness of the lining was not directly related to the destruction of the lining. The tunnel mainly experienced shear deformation in the x-axis direction, with significant deformations from the left arch waist to the right arch foot (45°-225°), resulting in transverse cracking. The tunnel primarily underwent tensile and compressive deformation in the y-axis direction, with significant deformations occurring in the inverted vault (0°-180°), resulting in tension and circumferential cracks. This research can provide valuable data support and reference for the design and construction of underground projects such as tunnels.

Median nerve electrical stimulation improves traumatic brain injury by reducing TACR1 to inhibit nuclear factor-κB and CCL7 activation in microglia.

The existing report elucidates that median nerve electrical stimulation (MNS) plays a role in treating traumatic brain injury (TBI). Herein, we explored the mechanism of MNS in TBI. A TBI-induced coma model (skull was hit by a cylindrical impact hammer) was established in adult Sprague-Dawley rats. Microglia were isolated from newborn Sprague-Dawley rats and was injured by lipopolysaccharide (LPS; 10 ng/mL). Consciousness was assessed by sensory and motor functions. Brain tissue morphology was detected using hematoxylin-eosin staining assay. Ionized calcium binding adapter molecule 1, NeuN and tachykinin receptor 1 (TACR1) level were detected by immunohistochemical assay. Levels of pro-inflammatory and anti-inflammatory factors were measured by enzyme linked immune sorbent assay (ELISA). Levels of TACR1, C-C motif chemokine 7 (CCL7), phosphorylation (p)-P65 and P65 were assessed by quantitative real time polymerase chain reaction (qRT-PCR) and western blot. M1 markers (inducible nitric oxide synthase and CD86) and M2 markers (arginase-1 (Arg1) and chitinase 3-like 3 (YM1)) of microglia as well as the transfection efficiency of short hairpin TACR1 (shTACR1) were assessed by qRT-PCR. Immunofluorescence and flow cytometry assay were used to detect microglia morphology and neuron apoptosis. MNS reduced neuron injury and microglia activation in the TBI-induced rat coma model. MNS reversed the effects of TBI on levels of inflammation-related factors, M1/M2 microglia markers, TACR1, p-P65/P65 and CCL7 in rats. shTACR1 reversed the effects of LPS on inflammation-related factors, M1/M2 microglia markers, microglia activation, neuron apoptosis, p-P65/P65 value and CCL7 level. Our results revealed that MNS improved TBI by reducing TACR1 to inhibit nuclear factor-κB (NF-κB) and CCL7 activation in microglia.

Influence of a waveform on the bit–rock impact response considering reflected waves in a drill rod

Percussive drilling is considered an efficient approach for penetrating hard formations. Understanding the responses and mechanical properties of rocks while being impacted and crushed by rock drills is essential for further improving their penetration efficiencies. This paper examines the consecutive impacts between the drill bit and rock, which are induced by the waves reflected in the drill rod after an initial hammer impact. Firstly, the loading and unloading principle for consecutive impacts is proposed. Based on this principle and one-dimensional (1-D) longitudinal wave propagation, a 1-D bit-rock interaction dynamics model is subsequently established. This model considers switches between the states of impact and separation, to instantly predict rock responses. Selecting marble as a representative material, the findings from the 1-D theoretical model and three-dimensional (3-D) Finite Element Method (FEM) simulations indicate that the number of repeated crushing impacts, which substantially contribute to the final penetration displacement, increases as the wavelength or the baseline level of fc (dimensionless crushing threshold force) in a rock decreases. fc is related to the loading rate, and its baseline level diminishes with decreasing impact energy (waveform amplitude). Due to the increases in fc and loading stiffness for short waves, the overall increasing trend of the final penetration displacement with decreasing wavelength weakens. A suitably-short wave with a high dimensionless exponential growth rate r or a long wave with approximately a unit of r can lead to a relatively-high final penetration displacement. In addition, we find that the dynamic loading and unloading stiffness and crushing threshold force have specific relationships with the penetration displacement and rock loading rate.